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[ "In the \"opposition\", a fencer takes an opponent's blade in any line and then extends in that line, diverting the opponent's blade, until the action is complete.", "The opposition can be done from any line, and it is a strong attack when done with a straight thrust.", "The amount of power needed to complete an opposition is just enough to carry the opponent's blade barely out of line, but not so much as to force it into a different line.", "The opposition is typically classified as an action in the French style of fencing, and it is similar to what the Italian school calls a \"glide\".", "However, some doctrines teach that the opposition and the glide are separate actions, but the glide can be done using an opposition.", "William Gaugler defines the opposition as an action completed during a thrust in which the hand is shifted against the opponent's blade in an attempt to close the line, while the glide slides along the opponent's blade onto target.", "Louis Rondelle instructs that a glide should be kept in opposition and that it is \"in reality a feint of direct thrust.\"", "Julio Martinez Castello refers to the glide as a \"sliding thrust\" that will dominate the opponent's blade by forcing it to the side.", "The \"bind\" takes the opponent's blade from any line diagonally to the opposing line.", "The action can be done from high to low line or vice versa.", "For example, from sixth, the opponent's blade is taken to seventh, or from eighth, the blade is taken to fourth.", "The bind is also known as a \"Transport\" or a \"Transport and Glide\".", "As with all other prise de fer actions, there are numerous fencing doctrines.", "Luigi Barbasetti teaches that the bind is only done from prime, seconde, tierce, quarte, and quinte.", "C-L. de Beaumont teaches that the bind is done by \"making a half-circular movement with the blades continually in contact, carrying the opponent's blade diagonally from a high to a low line on the opposite side of the target or vice versa.", "The attack is then made by extending the arm and lunging, while holding the opponent's blade.\"", "Julio Martinez Castello recommends that the bind be followed by a glide, but any attack is possible.", "To complete the bind from low line, first the forearm and blade are raised with the blade slightly off line.", "Once the blade is sufficiently raised to high line, the arm and blade are carried across to the new line until in position.", "Also see \"liement\" and \"flanconade\" below.", "The \"croisé\" carries the opponent's blade vertically from one line to the opposite line on the same side.", "For example, from sixth, the blade is carried to eighth.", "This action is sometimes referred to as a \"Cross\", and it is well described as a semibind.", "However, some fencing schools believe that the croisé is only done from high line to low line.", "Other fencing doctrines believe that the croisé from low line to high line is at least theoretical if not truth.", "There are also those that believe the croisé to be a bind, as Julio Martinez Castello wrote in his book \"The Theory and Practice of Fencing.\"", "Also see \"liement\", \"flanconade\", and \"copertino\" below.", "An \"envelopment\" is conducted by starting in a line and then completing a full circular motion in order to return to that same line.", "This action is also known as a \"Circular Transfer\" or an \"Enveloppement\".", "One school of thought is that the action is, in theory, done from any line, but it works best when done from sixth because of the difficulty of holding onto the opponent's blade otherwise.", "Jean-Jacques Gillet writes that the envolpment can be done from all lines but works particularly well in the actions that move the blade to the outside of the body.", "Roger Crosnier writes that the size of the circle in the envelopment needs to be limited, and in order to do so, the actions must be made with the wrist, because otherwise the action would be to too slow and cumbersome and thereby easily detected and deceived.", "Julio Martinez Castello teaches that the envelopment is essentially a combination of two binds since it completes two semicircles.", "In addition, he writes that the action can be followed by any attack, but preferably a glide, because that combination would continue to sustain a constant control of the opponent's blade.", "A \"liement\" is an action that takes the blade from high line to low line or vice versa.", "Depending on the motion of the action taken, the liement can be interpreted as either a bind or a croisé.", "A croisé from six as well as a bind from six takes the blade from high to low line.", "The \"flanconade\" is referenced as being a bind or a croisé.", "Imre Vass defines it as a \"bind thrust\" in which a fencer carries the opponent's blade from high line to low line on the same side but it will be the diagonal line for the opponent.", "Depending on the motion of the action, this can be interpreted as either a bind or a croisé.", "William Gaugler writes that there are three flanconades: the flanconade in fourth (or external flanconade), the internal flanconade, and the flanconade in second.", "The flanconade in fourth is the same as a croisé from fourth whereas the internal flanconade is a transport (bind) to first from third ending with a glide to the inside low line and the flanconade in second is a transport (bind) to second from fourth ending in a glide to the outside low line.", "Louis Rondelle explains the flanconade as starting in a high four, and then carries it downward until it terminates as a thrust under the opponent's arm.", "This description, against a right-handed opponent, can be interpreted as a croisé.", "The \"copertino\" is another term associated with the croisé as well as the flanconade.", "Imre Vass differentiates the copertino and the croisé by listing them both as a \"bind thrust\" actions on the same side but the copertino ends on the opposite side of the opponent's blade while the croisé simply ends in the opposite line.", "The copertino is also interpreted as a croisé." ]

[ 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 ]

[ "Prise de fer is a movement used in fencing in which a fencer takes the opponent's blade into a line and holds it there in preparation to attack.", "There are four prise de fer actions: opposition, croisé, bind, and envelopment.", "However, each fencing master and fencing doctrine has a separate view of prise de fer.", "Any prise de fer action requires that the blades be engaged, and it works best against an opponent who uses and maintains a straight arm." ]

[ "In the \"opposition\", a fencer takes an opponent's blade in any line and then extends in that line, diverting the opponent's blade, until the action is complete.", "The opposition can be done from any line, and it is a strong attack when done with a straight thrust.", "The amount of power needed to complete an opposition is just enough to carry the opponent's blade barely out of line, but not so much as to force it into a different line.", "The opposition is typically classified as an action in the French style of fencing, and it is similar to what the Italian school calls a \"glide\".", "However, some doctrines teach that the opposition and the glide are separate actions, but the glide can be done using an opposition.", "William Gaugler defines the opposition as an action completed during a thrust in which the hand is shifted against the opponent's blade in an attempt to close the line, while the glide slides along the opponent's blade onto target.", "Louis Rondelle instructs that a glide should be kept in opposition and that it is \"in reality a feint of direct thrust.\"", "Julio Martinez Castello refers to the glide as a \"sliding thrust\" that will dominate the opponent's blade by forcing it to the side.", "The \"bind\" takes the opponent's blade from any line diagonally to the opposing line.", "The action can be done from high to low line or vice versa.", "For example, from sixth, the opponent's blade is taken to seventh, or from eighth, the blade is taken to fourth.", "The bind is also known as a \"Transport\" or a \"Transport and Glide\".", "As with all other prise de fer actions, there are numerous fencing doctrines.", "Luigi Barbasetti teaches that the bind is only done from prime, seconde, tierce, quarte, and quinte.", "C-L. de Beaumont teaches that the bind is done by \"making a half-circular movement with the blades continually in contact, carrying the opponent's blade diagonally from a high to a low line on the opposite side of the target or vice versa.", "The attack is then made by extending the arm and lunging, while holding the opponent's blade.\"", "Julio Martinez Castello recommends that the bind be followed by a glide, but any attack is possible.", "To complete the bind from low line, first the forearm and blade are raised with the blade slightly off line.", "Once the blade is sufficiently raised to high line, the arm and blade are carried across to the new line until in position.", "Also see \"liement\" and \"flanconade\" below.", "The \"croisé\" carries the opponent's blade vertically from one line to the opposite line on the same side.", "For example, from sixth, the blade is carried to eighth.", "This action is sometimes referred to as a \"Cross\", and it is well described as a semibind.", "However, some fencing schools believe that the croisé is only done from high line to low line.", "Other fencing doctrines believe that the croisé from low line to high line is at least theoretical if not truth.", "There are also those that believe the croisé to be a bind, as Julio Martinez Castello wrote in his book \"The Theory and Practice of Fencing.\"", "Also see \"liement\", \"flanconade\", and \"copertino\" below.", "An \"envelopment\" is conducted by starting in a line and then completing a full circular motion in order to return to that same line.", "This action is also known as a \"Circular Transfer\" or an \"Enveloppement\".", "One school of thought is that the action is, in theory, done from any line, but it works best when done from sixth because of the difficulty of holding onto the opponent's blade otherwise.", "Jean-Jacques Gillet writes that the envolpment can be done from all lines but works particularly well in the actions that move the blade to the outside of the body.", "Roger Crosnier writes that the size of the circle in the envelopment needs to be limited, and in order to do so, the actions must be made with the wrist, because otherwise the action would be to too slow and cumbersome and thereby easily detected and deceived.", "Julio Martinez Castello teaches that the envelopment is essentially a combination of two binds since it completes two semicircles.", "In addition, he writes that the action can be followed by any attack, but preferably a glide, because that combination would continue to sustain a constant control of the opponent's blade.", "A \"liement\" is an action that takes the blade from high line to low line or vice versa.", "Depending on the motion of the action taken, the liement can be interpreted as either a bind or a croisé.", "A croisé from six as well as a bind from six takes the blade from high to low line.", "The \"flanconade\" is referenced as being a bind or a croisé.", "Imre Vass defines it as a \"bind thrust\" in which a fencer carries the opponent's blade from high line to low line on the same side but it will be the diagonal line for the opponent.", "Depending on the motion of the action, this can be interpreted as either a bind or a croisé.", "William Gaugler writes that there are three flanconades: the flanconade in fourth (or external flanconade), the internal flanconade, and the flanconade in second.", "The flanconade in fourth is the same as a croisé from fourth whereas the internal flanconade is a transport (bind) to first from third ending with a glide to the inside low line and the flanconade in second is a transport (bind) to second from fourth ending in a glide to the outside low line.", "Louis Rondelle explains the flanconade as starting in a high four, and then carries it downward until it terminates as a thrust under the opponent's arm.", "This description, against a right-handed opponent, can be interpreted as a croisé.", "The \"copertino\" is another term associated with the croisé as well as the flanconade.", "Imre Vass differentiates the copertino and the croisé by listing them both as a \"bind thrust\" actions on the same side but the copertino ends on the opposite side of the opponent's blade while the croisé simply ends in the opposite line.", "The copertino is also interpreted as a croisé." ]

[ 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46 ]

[ "There are four prise de fer actions: opposition, croisé, bind, and envelopment." ]

[ "In the \"opposition\", a fencer takes an opponent's blade in any line and then extends in that line, diverting the opponent's blade, until the action is complete.", "The opposition can be done from any line, and it is a strong attack when done with a straight thrust.", "The amount of power needed to complete an opposition is just enough to carry the opponent's blade barely out of line, but not so much as to force it into a different line.", "The opposition is typically classified as an action in the French style of fencing, and it is similar to what the Italian school calls a \"glide\".", "However, some doctrines teach that the opposition and the glide are separate actions, but the glide can be done using an opposition.", "William Gaugler defines the opposition as an action completed during a thrust in which the hand is shifted against the opponent's blade in an attempt to close the line, while the glide slides along the opponent's blade onto target.", "Louis Rondelle instructs that a glide should be kept in opposition and that it is \"in reality a feint of direct thrust.\"", "Julio Martinez Castello refers to the glide as a \"sliding thrust\" that will dominate the opponent's blade by forcing it to the side.", "The \"bind\" takes the opponent's blade from any line diagonally to the opposing line.", "The action can be done from high to low line or vice versa.", "For example, from sixth, the opponent's blade is taken to seventh, or from eighth, the blade is taken to fourth.", "The bind is also known as a \"Transport\" or a \"Transport and Glide\".", "As with all other prise de fer actions, there are numerous fencing doctrines.", "Luigi Barbasetti teaches that the bind is only done from prime, seconde, tierce, quarte, and quinte.", "C-L. de Beaumont teaches that the bind is done by \"making a half-circular movement with the blades continually in contact, carrying the opponent's blade diagonally from a high to a low line on the opposite side of the target or vice versa.", "The attack is then made by extending the arm and lunging, while holding the opponent's blade.\"", "Julio Martinez Castello recommends that the bind be followed by a glide, but any attack is possible.", "To complete the bind from low line, first the forearm and blade are raised with the blade slightly off line.", "Once the blade is sufficiently raised to high line, the arm and blade are carried across to the new line until in position.", "Also see \"liement\" and \"flanconade\" below.", "The \"croisé\" carries the opponent's blade vertically from one line to the opposite line on the same side.", "For example, from sixth, the blade is carried to eighth.", "This action is sometimes referred to as a \"Cross\", and it is well described as a semibind.", "However, some fencing schools believe that the croisé is only done from high line to low line.", "Other fencing doctrines believe that the croisé from low line to high line is at least theoretical if not truth.", "There are also those that believe the croisé to be a bind, as Julio Martinez Castello wrote in his book \"The Theory and Practice of Fencing.\"", "Also see \"liement\", \"flanconade\", and \"copertino\" below.", "An \"envelopment\" is conducted by starting in a line and then completing a full circular motion in order to return to that same line.", "This action is also known as a \"Circular Transfer\" or an \"Enveloppement\".", "One school of thought is that the action is, in theory, done from any line, but it works best when done from sixth because of the difficulty of holding onto the opponent's blade otherwise.", "Jean-Jacques Gillet writes that the envolpment can be done from all lines but works particularly well in the actions that move the blade to the outside of the body.", "Roger Crosnier writes that the size of the circle in the envelopment needs to be limited, and in order to do so, the actions must be made with the wrist, because otherwise the action would be to too slow and cumbersome and thereby easily detected and deceived.", "Julio Martinez Castello teaches that the envelopment is essentially a combination of two binds since it completes two semicircles.", "In addition, he writes that the action can be followed by any attack, but preferably a glide, because that combination would continue to sustain a constant control of the opponent's blade.", "A \"liement\" is an action that takes the blade from high line to low line or vice versa.", "Depending on the motion of the action taken, the liement can be interpreted as either a bind or a croisé.", "A croisé from six as well as a bind from six takes the blade from high to low line.", "The \"flanconade\" is referenced as being a bind or a croisé.", "Imre Vass defines it as a \"bind thrust\" in which a fencer carries the opponent's blade from high line to low line on the same side but it will be the diagonal line for the opponent.", "Depending on the motion of the action, this can be interpreted as either a bind or a croisé.", "William Gaugler writes that there are three flanconades: the flanconade in fourth (or external flanconade), the internal flanconade, and the flanconade in second.", "The flanconade in fourth is the same as a croisé from fourth whereas the internal flanconade is a transport (bind) to first from third ending with a glide to the inside low line and the flanconade in second is a transport (bind) to second from fourth ending in a glide to the outside low line.", "Louis Rondelle explains the flanconade as starting in a high four, and then carries it downward until it terminates as a thrust under the opponent's arm.", "This description, against a right-handed opponent, can be interpreted as a croisé.", "The \"copertino\" is another term associated with the croisé as well as the flanconade.", "Imre Vass differentiates the copertino and the croisé by listing them both as a \"bind thrust\" actions on the same side but the copertino ends on the opposite side of the opponent's blade while the croisé simply ends in the opposite line.", "The copertino is also interpreted as a croisé." ]

[ 44, 45, 46 ]

[ "There are four prise de fer actions: opposition, croisé, bind, and envelopment." ]

[ "The standard had been under revision since 2000, with a target completion date of December 2006.", "The revision of an IEEE standard broadly follows three phases:\n# Working group – a committee that creates a draft standard\n# Ballot – interested parties subscribe to the \"balloting group\" and vote on the draft (75% of the group must participate, and 75% must approve for the draft to go forward); comments from the votes are resolved by a \"Ballot Resolution Committee\" (BRC) and changes made have to be recirculated with a new ballot if they are substantive\n# When all comments are resolved and there are no further changes, the draft is submitted to the IEEE for review, approval, and publication (this can also result in changes and ballots, although this is rare).", "On 11 June 2008, it was approved unanimously by the IEEE Revision Committee (RevCom), and it was formally approved by the IEEE-SA Standards Board on 12 June 2008.", "It was published on 29 August 2008.", "Participation in drafting the standard was open to people with a solid knowledge of floating-point arithmetic.", "More than 90 people attended at least one of the monthly meetings, which were held in Silicon Valley, and many more participated through the mailing list.", "Progress at times was slow, leading the chairman to declare at the 15 September 2005 meeting that \"no progress is being made, I am suspending these meetings until further notice on those grounds\".", "In December 2005, the committee reorganized under new rules with a target completion date of December 2006.", "New policies and procedures were adopted in February 2006.", "In September 2006, a working draft was approved to be sent to the parent sponsoring committee (the IEEE Microprocessor Standards Committee, or MSC) for editing and to be sent to sponsor ballot.", "The last version of the draft, version 1.2.5, submitted to the MSC was from 4 October 2006.", "The MSC accepted the draft on 9 October 2006.", "The draft has been changed significantly in detail during the balloting process.", "The first sponsor ballot took place from 29 November 2006 through 28 December 2006.", "Of the 84 members of the voting body, 85.7% responded—78.6% voted approval.", "There were negative votes (and over 400 comments) so there was a recirculation ballot in March 2007; this received an 84% approval.", "There were sufficient comments (over 130) from that ballot that a third draft was prepared for second, 15-day, recirculation ballot which started in mid-April 2007.", "For a technical reason, the ballot process was restarted with the 4th ballot in October 2007; there were also substantial changes in the draft resulting from 650 voters' comments and from requests from the sponsor (the IEEE MSC); this ballot just failed to reach the required 75% approval.", "The 5th ballot had a 98.0% response rate with 91.0% approval, with comments leading to relatively small changes.", "The 6th, 7th, and 8th ballots sustained approval ratings of over 90% with progressively fewer comments on each draft; the 8th (which had no in-scope comments: 9 were repeats of previous comments and one referred to material not in the draft) was submitted to the IEEE Standards Revision Committee ('RevCom') for approval as an IEEE standard.", "The IEEE Standards Revision Committee (RevCom) considered and unanimously approved the IEEE 754r draft at its June 2008 meeting, and it was approved by the IEEE-SA Standards Board on 12 June 2008.", "Final editing is complete and the document has now been forwarded to the IEEE Standards Publications Department for publication.", "The new IEEE 754 (formally IEEE Std 754-2008, the IEEE Standard for Floating-Point Arithmetic) was published by the IEEE Computer Society on 29 August 2008, and is available from the IEEE Xplore website\nThis standard replaces IEEE 754-1985.", "IEEE 854, the Radix-Independent floating-point standard was withdrawn in December 2008.", "The most obvious enhancements to the standard are the addition of a 16-bit and a 128-bit binary type and three decimal types, some new operations, and many recommended functions.", "However, there have been significant clarifications in terminology throughout.", "This summary highlights the main differences in each major clause of the standard.", "The scope (determined by the sponsor of the standard) has been widened to include decimal formats and arithmetic, and adds extendable formats.", "Many of the definitions have been rewritten for clarification and consistency.", "A few terms have been renamed for clarity (for example, \"denormalized\" has been renamed to \"subnormal\").", "The description of formats has been made more regular, with a distinction between \"arithmetic formats\" (in which arithmetic may be carried out) and \"interchange formats\" (which have a standard encoding).", "Conformance to the standard is now defined in these terms.", "The specification levels of a floating-point format have been enumerated, to clarify the distinction between:\n# the theoretical real numbers (an extended number line)\n# the entities which can be represented in the format (a finite set of numbers, together with −0, infinities, and NaN)\n# the particular representations of the entities: sign-exponent-significand, etc.\n# the bit-pattern (encoding) used.", "The sets of representable entities are then explained in detail, showing that they can be treated with the significand being considered either as a fraction or an integer.", "The particular sets known as \"basic formats\" are defined, and the encodings used for interchange of binary and decimal formats are explained.", "The binary interchange formats have the \"half precision\" (16-bit storage format) and \"quad precision\" (128-bit format) added, together with generalized formulae for some wider formats; the basic formats have 32-bit, 64-bit, and 128-bit encodings.", "Three new decimal formats are described, matching the lengths of the 32–128-bit binary formats.", "These give decimal interchange formats with 7, 16, and 34-digit significands, which may be normalized or unnormalized.", "For maximum range and precision, the formats merge part of the exponent and significand into a \"combination field\", and compress the remainder of the significand using either a decimal integer encoding (which uses \"Densely Packed Decimal\", or DPD, a compressed form of BCD) encoding or conventional binary integer encoding.", "The basic formats are the two larger sizes, which have 64-bit and 128-bit encodings.", "Generalized formulae for some other interchange formats are also specified.", "Extended and extendable formats allow for arithmetic at other precisions and ranges.", "This clause has been changed to encourage the use of static attributes for controlling floating-point operations, and (in addition to required rounding attributes) allow for alternate exception handling, widening of intermediate results, value-changing optimizations, and reproducibility.", "The \"round-to-nearest, ties away from zero\" rounding attribute has been added (required for decimal operations only).", "This section has numerous clarifications (notably in the area of comparisons), and several previously recommended operations (such as copy, negate, abs, and class) are now required.", "New operations include fused multiply–add (FMA), explicit conversions, classification predicates (isNan(\"x\"), etc.), various min and max functions, a total ordering predicate, and two decimal-specific operations (samequantum and quantize).", "The min and max operations are defined but leave some leeway for the case where the inputs are equal in value but differ in representation.", "In particular:\nIn order to support operations such as windowing in which a NaN input should be quietly replaced with one of the end points, min and max are defined to select a number, \"x\", in preference to a quiet NaN:\n\nThese functions are called \"minNum\" and \"maxNum\" to indicate their preference for a number over a quiet NaN. However, in the presence of a signaling NaN input, a quiet NaN is returned as with the usual operations.", "After the publication of the standard, it was noticed that these rules make these operations non-associative; for this reason, they have been replaced by new operations in IEEE 754-2019.", "Decimal arithmetic, compatible with that used in Java, C#, PL/I, COBOL, Python, REXX, etc., is also defined in this section.", "In general, decimal arithmetic follows the same rules as binary arithmetic (results are correctly rounded, and so on), with additional rules that define the exponent of a result (more than one is possible in many cases).", "Unlike in 854, 754-2008 requires correctly rounded base conversion between decimal and binary floating point within a range which depends on the format.", "This clause has been revised and clarified, but with no major additions.", "In particular, it makes formal recommendations for the encoding of the signaling/quiet NaN state.", "This clause has been revised and considerably clarified, but with no major additions.", "This clause has been extended from the previous Clause 8 ('Traps') to allow optional exception handling in various forms, including traps and other models such as try/catch.", "Traps and other exception mechanisms remain optional, as they were in IEEE 754-1985.", "This clause is new; it recommends fifty operations, including log, power, and trigonometric functions, that language standards should define.", "These are all optional (none are required in order to conform to the standard).", "The operations include some on dynamic modes for attributes, and also a set of reduction operations (sum, scaled product, etc.).", "This clause is new; it recommends how language standards should specify the semantics of sequences of operations, and points out the subtleties of literal meanings and optimizations that change the value of a result.", "This clause is new; it recommends that language standards should provide a means to write reproducible programs (i.e., programs that will produce the same result in all implementations of a language), and describes what needs to be done to achieve reproducible results.", "This annex is new; it lists some useful references.", "This annex is new; it provides guidance to debugger developers for features that are desired for supporting the debugging of floating-point code.", "This is a new index, which lists all the operations described in the standard (required or optional).", "Due to changes in CPU design and development, the 2008 IEEE floating-point standard could be viewed as historical or outdated as the 1985 standard it replaced.", "There were many outside discussions and items not covered in the standardization process, the items below are the ones that became public knowledge:\n\n In 754 the definition of underflow was that the result is tiny and encounters a loss of accuracy.", "Two definitions were allowed for the determination of the 'tiny' condition: before or after rounding the infinitely precise result to working precision, with unbounded exponent.", "Two definitions of loss of accuracy were permitted: inexact result or loss due only to denormalization.", "No known hardware systems implemented the latter and it has been removed from the revised standard as an option.", "Annex U of 754r recommended that only tininess after rounding and inexact as loss of accuracy be a cause for underflow signal." ]

[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 ]

[ "IEEE 754-2008 (previously known as \"IEEE 754r\") was published in August 2008 and is a significant revision to, and replaces, the IEEE 754-1985 floating-point standard, while in 2019 it was updated with a minor revision IEEE 754-2019." ]

[ "The standard had been under revision since 2000, with a target completion date of December 2006.", "The revision of an IEEE standard broadly follows three phases:\n# Working group – a committee that creates a draft standard\n# Ballot – interested parties subscribe to the \"balloting group\" and vote on the draft (75% of the group must participate, and 75% must approve for the draft to go forward); comments from the votes are resolved by a \"Ballot Resolution Committee\" (BRC) and changes made have to be recirculated with a new ballot if they are substantive\n# When all comments are resolved and there are no further changes, the draft is submitted to the IEEE for review, approval, and publication (this can also result in changes and ballots, although this is rare).", "On 11 June 2008, it was approved unanimously by the IEEE Revision Committee (RevCom), and it was formally approved by the IEEE-SA Standards Board on 12 June 2008.", "It was published on 29 August 2008.", "Participation in drafting the standard was open to people with a solid knowledge of floating-point arithmetic.", "More than 90 people attended at least one of the monthly meetings, which were held in Silicon Valley, and many more participated through the mailing list.", "Progress at times was slow, leading the chairman to declare at the 15 September 2005 meeting that \"no progress is being made, I am suspending these meetings until further notice on those grounds\".", "In December 2005, the committee reorganized under new rules with a target completion date of December 2006.", "New policies and procedures were adopted in February 2006.", "In September 2006, a working draft was approved to be sent to the parent sponsoring committee (the IEEE Microprocessor Standards Committee, or MSC) for editing and to be sent to sponsor ballot.", "The last version of the draft, version 1.2.5, submitted to the MSC was from 4 October 2006.", "The MSC accepted the draft on 9 October 2006.", "The draft has been changed significantly in detail during the balloting process.", "The first sponsor ballot took place from 29 November 2006 through 28 December 2006.", "Of the 84 members of the voting body, 85.7% responded—78.6% voted approval.", "There were negative votes (and over 400 comments) so there was a recirculation ballot in March 2007; this received an 84% approval.", "There were sufficient comments (over 130) from that ballot that a third draft was prepared for second, 15-day, recirculation ballot which started in mid-April 2007.", "For a technical reason, the ballot process was restarted with the 4th ballot in October 2007; there were also substantial changes in the draft resulting from 650 voters' comments and from requests from the sponsor (the IEEE MSC); this ballot just failed to reach the required 75% approval.", "The 5th ballot had a 98.0% response rate with 91.0% approval, with comments leading to relatively small changes.", "The 6th, 7th, and 8th ballots sustained approval ratings of over 90% with progressively fewer comments on each draft; the 8th (which had no in-scope comments: 9 were repeats of previous comments and one referred to material not in the draft) was submitted to the IEEE Standards Revision Committee ('RevCom') for approval as an IEEE standard.", "The IEEE Standards Revision Committee (RevCom) considered and unanimously approved the IEEE 754r draft at its June 2008 meeting, and it was approved by the IEEE-SA Standards Board on 12 June 2008.", "Final editing is complete and the document has now been forwarded to the IEEE Standards Publications Department for publication.", "The new IEEE 754 (formally IEEE Std 754-2008, the IEEE Standard for Floating-Point Arithmetic) was published by the IEEE Computer Society on 29 August 2008, and is available from the IEEE Xplore website\nThis standard replaces IEEE 754-1985.", "IEEE 854, the Radix-Independent floating-point standard was withdrawn in December 2008.", "The most obvious enhancements to the standard are the addition of a 16-bit and a 128-bit binary type and three decimal types, some new operations, and many recommended functions.", "However, there have been significant clarifications in terminology throughout.", "This summary highlights the main differences in each major clause of the standard.", "The scope (determined by the sponsor of the standard) has been widened to include decimal formats and arithmetic, and adds extendable formats.", "Many of the definitions have been rewritten for clarification and consistency.", "A few terms have been renamed for clarity (for example, \"denormalized\" has been renamed to \"subnormal\").", "The description of formats has been made more regular, with a distinction between \"arithmetic formats\" (in which arithmetic may be carried out) and \"interchange formats\" (which have a standard encoding).", "Conformance to the standard is now defined in these terms.", "The specification levels of a floating-point format have been enumerated, to clarify the distinction between:\n# the theoretical real numbers (an extended number line)\n# the entities which can be represented in the format (a finite set of numbers, together with −0, infinities, and NaN)\n# the particular representations of the entities: sign-exponent-significand, etc.\n# the bit-pattern (encoding) used.", "The sets of representable entities are then explained in detail, showing that they can be treated with the significand being considered either as a fraction or an integer.", "The particular sets known as \"basic formats\" are defined, and the encodings used for interchange of binary and decimal formats are explained.", "The binary interchange formats have the \"half precision\" (16-bit storage format) and \"quad precision\" (128-bit format) added, together with generalized formulae for some wider formats; the basic formats have 32-bit, 64-bit, and 128-bit encodings.", "Three new decimal formats are described, matching the lengths of the 32–128-bit binary formats.", "These give decimal interchange formats with 7, 16, and 34-digit significands, which may be normalized or unnormalized.", "For maximum range and precision, the formats merge part of the exponent and significand into a \"combination field\", and compress the remainder of the significand using either a decimal integer encoding (which uses \"Densely Packed Decimal\", or DPD, a compressed form of BCD) encoding or conventional binary integer encoding.", "The basic formats are the two larger sizes, which have 64-bit and 128-bit encodings.", "Generalized formulae for some other interchange formats are also specified.", "Extended and extendable formats allow for arithmetic at other precisions and ranges.", "This clause has been changed to encourage the use of static attributes for controlling floating-point operations, and (in addition to required rounding attributes) allow for alternate exception handling, widening of intermediate results, value-changing optimizations, and reproducibility.", "The \"round-to-nearest, ties away from zero\" rounding attribute has been added (required for decimal operations only).", "This section has numerous clarifications (notably in the area of comparisons), and several previously recommended operations (such as copy, negate, abs, and class) are now required.", "New operations include fused multiply–add (FMA), explicit conversions, classification predicates (isNan(\"x\"), etc.), various min and max functions, a total ordering predicate, and two decimal-specific operations (samequantum and quantize).", "The min and max operations are defined but leave some leeway for the case where the inputs are equal in value but differ in representation.", "In particular:\nIn order to support operations such as windowing in which a NaN input should be quietly replaced with one of the end points, min and max are defined to select a number, \"x\", in preference to a quiet NaN:\n\nThese functions are called \"minNum\" and \"maxNum\" to indicate their preference for a number over a quiet NaN. However, in the presence of a signaling NaN input, a quiet NaN is returned as with the usual operations.", "After the publication of the standard, it was noticed that these rules make these operations non-associative; for this reason, they have been replaced by new operations in IEEE 754-2019.", "Decimal arithmetic, compatible with that used in Java, C#, PL/I, COBOL, Python, REXX, etc., is also defined in this section.", "In general, decimal arithmetic follows the same rules as binary arithmetic (results are correctly rounded, and so on), with additional rules that define the exponent of a result (more than one is possible in many cases).", "Unlike in 854, 754-2008 requires correctly rounded base conversion between decimal and binary floating point within a range which depends on the format.", "This clause has been revised and clarified, but with no major additions.", "In particular, it makes formal recommendations for the encoding of the signaling/quiet NaN state.", "This clause has been revised and considerably clarified, but with no major additions.", "This clause has been extended from the previous Clause 8 ('Traps') to allow optional exception handling in various forms, including traps and other models such as try/catch.", "Traps and other exception mechanisms remain optional, as they were in IEEE 754-1985.", "This clause is new; it recommends fifty operations, including log, power, and trigonometric functions, that language standards should define.", "These are all optional (none are required in order to conform to the standard).", "The operations include some on dynamic modes for attributes, and also a set of reduction operations (sum, scaled product, etc.).", "This clause is new; it recommends how language standards should specify the semantics of sequences of operations, and points out the subtleties of literal meanings and optimizations that change the value of a result.", "This clause is new; it recommends that language standards should provide a means to write reproducible programs (i.e., programs that will produce the same result in all implementations of a language), and describes what needs to be done to achieve reproducible results.", "This annex is new; it lists some useful references.", "This annex is new; it provides guidance to debugger developers for features that are desired for supporting the debugging of floating-point code.", "This is a new index, which lists all the operations described in the standard (required or optional).", "Due to changes in CPU design and development, the 2008 IEEE floating-point standard could be viewed as historical or outdated as the 1985 standard it replaced.", "There were many outside discussions and items not covered in the standardization process, the items below are the ones that became public knowledge:\n\n In 754 the definition of underflow was that the result is tiny and encounters a loss of accuracy.", "Two definitions were allowed for the determination of the 'tiny' condition: before or after rounding the infinitely precise result to working precision, with unbounded exponent.", "Two definitions of loss of accuracy were permitted: inexact result or loss due only to denormalization.", "No known hardware systems implemented the latter and it has been removed from the revised standard as an option.", "Annex U of 754r recommended that only tininess after rounding and inexact as loss of accuracy be a cause for underflow signal." ]

[ 22, 23 ]

[ "IEEE 754-2008 (previously known as \"IEEE 754r\") was published in August 2008 and is a significant revision to, and replaces, the IEEE 754-1985 floating-point standard, while in 2019 it was updated with a minor revision IEEE 754-2019." ]

[ "A Place for Mom was founded in July 1999 by Pamala Temple, John Temple, and Brian Trisler.", "In 2006, A Place for Mom received $9.5 million in venture capital from Battery Ventures.", "In July 2010 a private equity firm, Warburg Pincus, purchased a majority stake of the company.", "In November 2016, A Place for Mom purchased the competing service OurParents, adding 2,500 facilities to its network.", "On August 11, 2017, Warburg Pincus sold its majority stake in the company to growth equity firm General Atlantic and technology investment firm Silver Lake.", "The two firms acquired equal stakes and added two members each to the company's board of directors.", "Silver Lake added Managing Partner and Managing Director Greg Mondre and Director Adam Karol.", "General Atlantic added Robbert Vorhoff, managing director and Global Head of Healthcare, and Anton Levy, managing director and Global Head of Internet and Technology.", "Financial services firm William Blair & Company and law firm Willkie Farr & Gallagher advised A Place for Mom in the transaction.", "On January 31, 2022, A Place for Mom raised $175 million in its latest round led by Insight Partners.", "Existing backers General Atlantic and Silver Lake also participated in the round, which valued the company at more than $1 billion, and added Eoin Duane, managing director at Insight Partners to their board.", "A Place for Mom's service is offered at no charge to families.", "The company derives its revenue from referrals to facilities and providers within its partner network, including residential care homes, assisted living and memory care communities, independent senior apartments, and home care services.", "In December 2017, a class-action lawsuit was brought against A Place for Mom for violations of the Telephone Consumer Protection Act, alleging that the service did not adequately inform users of, or receive written consent for the use of robocalling as part of its services.", "The parties reached a $6 million settlement in September 2019, but it was rejected by a Washington district court for not being based on \"clearly defined objective criteria\"." ]

[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]

[ "A majority of the company is owned since August 2017 by equity capital firms General Atlantic and Silver Lake.", "Insight Partners now owns a minority stake as part of the company's $175M capital raise in January 2022." ]

[ "A Place for Mom was founded in July 1999 by Pamala Temple, John Temple, and Brian Trisler.", "In 2006, A Place for Mom received $9.5 million in venture capital from Battery Ventures.", "In July 2010 a private equity firm, Warburg Pincus, purchased a majority stake of the company.", "In November 2016, A Place for Mom purchased the competing service OurParents, adding 2,500 facilities to its network.", "On August 11, 2017, Warburg Pincus sold its majority stake in the company to growth equity firm General Atlantic and technology investment firm Silver Lake.", "The two firms acquired equal stakes and added two members each to the company's board of directors.", "Silver Lake added Managing Partner and Managing Director Greg Mondre and Director Adam Karol.", "General Atlantic added Robbert Vorhoff, managing director and Global Head of Healthcare, and Anton Levy, managing director and Global Head of Internet and Technology.", "Financial services firm William Blair & Company and law firm Willkie Farr & Gallagher advised A Place for Mom in the transaction.", "On January 31, 2022, A Place for Mom raised $175 million in its latest round led by Insight Partners.", "Existing backers General Atlantic and Silver Lake also participated in the round, which valued the company at more than $1 billion, and added Eoin Duane, managing director at Insight Partners to their board.", "A Place for Mom's service is offered at no charge to families.", "The company derives its revenue from referrals to facilities and providers within its partner network, including residential care homes, assisted living and memory care communities, independent senior apartments, and home care services.", "In December 2017, a class-action lawsuit was brought against A Place for Mom for violations of the Telephone Consumer Protection Act, alleging that the service did not adequately inform users of, or receive written consent for the use of robocalling as part of its services.", "The parties reached a $6 million settlement in September 2019, but it was rejected by a Washington district court for not being based on \"clearly defined objective criteria\"." ]

[ 11, 12 ]

[ "The company provides personal and professional assistance to families in the search of senior care options.", "Their service is free to families.", "They are paid by the senior living communities and homecare providers on its platform." ]

[ "The revolt was spurred by the prosecutions launched by Minh Mạng against southern factions which had opposed his rule and tended to be favourable to Christianity.", "In particular, Minh Mạng prosecuted Lê Văn Duyệt, a former faithful general of Emperor Gia Long, who had opposed his enthronement.", "Since Lê Văn Duyệt had already died in July 1832, his tomb was profaned and inscribed with the words \"This is the place where the infamous Lê Văn Duyệt was punished\".", "Lê Văn Khôi, the adoptive son of general Lê Văn Duyệt, had also been imprisoned, but managed to escape on 10 May 1833.", "Soon, numerous people joined the revolt, in the desire to avenge Lê Văn Duyệt and challenge the legitimacy of the Nguyễn dynasty.", "Lê Văn Khôi declared himself in favour of the restoration of the line of Prince Cảnh, the original heir to Gia Long according to the rule of primogeniture, in the person of his remaining son An-hoa.", "This choice was designed to obtain the support of Catholic missionaries and Vietnamese Catholics, who had supported the line of Prince Cảnh with Lê Văn Duyệt.", "Lê Văn Khôi further promised to protect Catholicism.", "On 18 May 1833, the rebels managed to take the Citadel of Saigon (\"Thanh Phien-an\").", "Lê Văn Khôi was able to conquer six provinces of Gia Dinh in the span of one month.", "The main actors of the revolt were Vietnamese Christians and Chinese settlers who had been suffering from the rule of Minh Mạng.", "As Minh Mạng raised an army to quell the rebellion,", "Lê Văn Khôi fortified himself into the Saigon fortress and asked for the help of the Siamese.", "Rama III, king of Siam, accepted the offer and sent troops to attack the Vietnamese provinces of Ha-tien and An-giang and Vietnamese imperial forces in Laos and Cambodia.", "The Siamese troops were accompanied by 2,000 Vietnamese Catholic troops under the command of Father Nguyen Van Tam.", "These Siamese and Vietnamese forces were repelled in summer 1834 by General Truong Minh Giang.", "Lê Văn Khôi died in 1834, during the siege, and was succeeded by his 8-year-old son Le Van Cu.", "It took three years for Minh Mạng to quell the rebellion and the Siamese offensive.", "When the fortress of Phien", "An was invaded in September 1835, 1,831 people were executed and buried in mass graves (now situated in District 3, Saigon).", "Only six survivors were temporarily spared, among whom were Le Van Cu, but also the French missionary Father Joseph Marchand, of the Paris Foreign Missions Society.", "Marchand had apparently been supporting the cause of Lê Văn Khôi, and asked for the help of the Siamese army, through communications to his counterpart in Siam, Father Taberd.", "This revealed the strong Catholic involvement in the revolt.", "Father Marchand was tortured and executed on 5 November 1835, as was the child Le Van Cu.", "The failure of the revolt had a disastrous effect on the Christian communities of Vietnam.", "New waves of persecutions against Christians followed, and demands were made to find and execute remaining missionaries.", "Anti-Catholic edicts to this effect were issued by Minh Mạng in 1836 and 1838.", "In 1836–1837 six missionaries were executed: Ignacio Delgado, Dominico Henares, Jean-Charles Cornay, José Fernández, François Jaccard, and Bishop Pierre Borie." ]

[ 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ]

[ "The Lê Văn Khôi revolt (, 1833–1835) was an important revolt in 19th-century Vietnam, in which southern Vietnamese, Vietnamese Catholics, French Catholic missionaries and Chinese settlers under the leadership of Lê Văn Khôi opposed the Imperial rule of Emperor Minh Mạng." ]

[ "According to the Migration Theory that was based primarily on comparative linguistics, the proto-Finns migrated from an ancient homeland somewhere in north-western Siberia or western Russia to the shores of the Baltic Sea around 1000 BC, at which time Finns and Estonians separated.", "The Migration Theory has been called into question since 1980 based on genealogy, craniometry and archaeology.", "Recently, a modified form of the Migration Theory has gained new support among the younger generation of linguists, who consider that archaeology, genes and craniometric data cannot supply evidence of prehistoric languages.", "During the last 30 years, scientific research in physical anthropology, craniometric analyses, and mitochondrial and Y-chromosomal DNA frequencies have reduced the likelihood of the Migration Theory—a major westward migration as recently as 3,000 years ago.", "The Settlement Continuity Theory asserts that at least the genetic ancestors of the Finnic peoples were among the earliest indigenous peoples of Europe.", "The origin of the people who lived around the Baltic Sea area during the Mesolithic Era continues to be debated by scientists.", "From the middle of the Neolithic onward, there is a certain extent of agreement among scholars: it has been suggested that Finnic tribes arrived in the Baltic region from the east or south-east around the period 4000–3000 BC and merged with the original inhabitants, who then adopted the proto-Finno-Ugric language and the Pit–Comb Ware culture of the newcomers.", "The members of this new Finno-Ugric-speaking ethnicity are thought to be the ancestors of modern-day Estonians.", "The Y-chromosomal data has also revealed a common Finnic ancestry for the males of the neighbouring Balts, speakers of the Indo-European Baltic languages.", "According to the studies, Baltic males are most closely related to the Volga Finns such as the Mari, rather than to Baltic Finns.", "The results suggest that the territories of Estonia, Latvia and Lithuania have been settled by Finnic-speaking tribes since the early Mesolithic period.", "On the other hand, some linguists do not consider it likely that a Baltic Finnic language form could have existed at such an early date.", "According to these views, the Finnic languages appeared in Finland and the Baltic region only during the Early Bronze Age (ca. 1800 BC), if not later.", "The Finnic peoples share a common cultural heritage: the art of ancient \"rune\" (poem) singing in the Kalevala meter, estimated to be 2,500–3,000 years old.", "The Finnish and Estonian national epics, \"Kalevala\" and \"Kalevipoeg\", are both written in this meter.", "The Veps are the only Baltic Finnish people with no significant corpus of Kalevala meter oral poetry.", "The poetic tradition has included epic poems (known mostly in Karelia and Ingria, perhaps as survivals from an earlier, wider distribution), lyric poems and magic chants.", "The ancient rune singing has inspired the creation of the national epic of Finland, \"Kalevala\" compiled by Elias Lönnrot, and the music of Arvo Pärt, the best-known Estonian composer in the classical field.", "J. R. R. Tolkien has highlighted the importance of Kalevala as a source for his legendarium, including \"The Silmarillion\" and \"The Lord of the Rings\".", "The region has been populated since the end of the last glacial era, about 10,000 BC.", "The earliest traces of human settlement are connected with Suomusjärvi culture and Kunda culture.", "The Early Mesolithic Pulli settlement is located by the Pärnu River.", "It has been dated to the beginning of the 9th millennium BC.", "The Kunda Culture received its name from the Lammasmäe settlement site in northern Estonia, which dates from earlier than 8500.", "Bone and stone artefacts similar to those found at Kunda have been discovered elsewhere in Estonia, as well as in Latvia, northern Lithuania and southern Finland.", "Around 5300 BCE pottery and agriculture entered Finland.", "The earliest representatives belong to the Pit–Comb Ware culture, known for their distinctive decorating patterns.", "This marks the beginning of the Neolithic,", "Until the early 1980s, the arrival of Finnic peoples, the ancestors of the Estonians, Finns, and Livonians on the shores of the Baltic Sea around 3000 BC, was associated with the Pit–Comb Ware culture However, such a linking of archaeologically defined cultural entities with linguistic ones cannot be proven and it has been suggested that the increase of settlement finds in the period is more likely to have been associated with an economic boom related to the warming of climate.", "Some researchers have even argued that a form of Uralic languages may have been spoken in Estonia and Finland since the end of the last glaciation.", "Through archaeogenetics the population has been shown to derive the bulk of its ancestry from Eastern Hunter-Gatherers of Russia.", "The beginning of the Bronze Age in Estonia is dated to approximately 1800 BC, in present-day Finland some time after 1500 BCE.", "The coastal regions of Finland were a part of the Nordic Bronze Culture, whereas in the inland regions the influences came from the bronze-using cultures of Northern Russia.", "The first fortified settlements, Asva and Ridala on the island of Saaremaa and Iru in the Northern Estonia, began to be built.", "The development of shipbuilding facilitated the spread of bronze.", "Changes took place in burial customs, a new type of burial ground spread from Germanic to Estonian areas, stone cist graves and cremation burials became increasingly common beside small numbers of boat-shaped stone graves.", "In terms of genetics, the Bronze Age population of the East Baltic derives most of their ancestry from the Corded Ware culture with an elevated amount of Mesolithic Hunter-Gatherer ancestry, but showing no prevalence of Siberian related ancestry.", "The Pre-Roman Iron Age began in about 500 BC and lasted until the middle of the 1st century.", "The oldest iron items were imported, although since the 1st century iron was smelted from local marsh and lake ore.", "Settlement sites were located mostly in places that offered natural protection.", "Fortresses were built, although used temporarily.", "The appearance of square Celtic fields surrounded by enclosures in Estonia date from the Pre-Roman Iron Age.", "The majority of stones with man-made indents, which presumably were connected with magic designed to increase crop fertility, date from this period.", "A new type of grave, quadrangular burial mounds, began to develop.", "Burial traditions show the clear beginning of social stratification.", "The first reported individuals with the y-DNA haplotype N-M231 in the Baltic are from the Iron Age, alongside Siberian ancestry.", "The Roman Iron Age is roughly dated to between AD 50 and 450, the era that was affected by the influence of the Roman Empire.", "In material culture this is reflected by a few Roman coins, some jewellery and artefacts.", "The abundance of iron artefacts in Southern Estonia speaks of closer mainland ties with southern areas, while coastal Finland and the islands of western and northern Estonia communicated with their neighbours mainly by sea.", "Between 200 and 400 AD, a group of Baltic Sea Finns in southwestern Finland, who had traveled to Finland proper from the areas of nowadays Estonia, began moving inland towards Tavastia.", "Between 200 and 400 AD, the Finns proper themselves became divided geographically in three \nparts:\n# Tavastians: The tribes who went inland to Tavastia;\n# Southwestern Finns: The tribes who stayed in the southern side of the Kokemäenjoki river delta;\n# Southern Ostrobothnians: The tribes who stayed on the northern side of the river delta.", "During the Migration Period in 400–600 AD, the Estonian influence gradually weakened.", "By the end of the period, clearly defined tribal dialectical areas – Finns, Tavastians, Karelians, Northern Estonians, Southern Estonians, and Western Estonians including the islanders—had emerged, the population of each having formed its own understanding of identity.", "The word \"Finn\" is first mentioned in the form \"fenni\" in the 1st century AD by Roman historian Tacitus.", "However, it is possible that he was referring to the people of northern Europe in general, particularly the Lappic or Sami people.", "After that the name \"finni\" is used by Claudius Ptolemaeus (around 150) and the Eastern Roman writer Jordanes in his \"Getica\" (551).", "References to Finnic tribes become much more numerous from the Viking Age (800–1050).", "It was not until about 1171 that the word \"Finni\" was employed to mean the Finns.", "The term \"Eesti\", the name of the Estonians, occurs first again in Tacitus; however, it might have indicated Balts.", "In Northern sagas (13th century), the term started to be used to indicate the Estonians.", "In a Norwegian text (11th–12th century), the name \"Kiriali\", referring to Karelians, and the term \"cornuti Finni\", interpreted as referring to the Lapps or Sami people, first appear.", "The opening chapter of the Old East Slavic Primary Chronicle (early 12th century) lists the following peoples living \"in the share of Japheth\" among others: Chud, Merya, Muroma, Ves, Mordvin (Moksha and Erzya), Chud beyond the portages, Perm, Pechera, Yam, Ugra and Liv.\nThe name \"Sum\", possibly meaning \"Suomi\" (Finland in Finnish), is found in the Primary Chronicle.", "The names of other Finnic tribes are also listed, including Veps, Cheremis, Mordvins (Moksha and Erzya) and Permians.", "The Chudes, as mentioned in the earliest East Slavic chronicles, are in a 12th-century context usually considered to be Estonians, although the name sometimes referred to all Finnic peoples in north-western Rus.", "According to the East Slavic Primary Chronicle, the Chudes' lands were bounded by the Varangian Sea (Baltic Sea).", "In 1030 Yaroslav I the Wise invaded the country of the Chudes and laid the foundations of Yuriev (the historical Russian name of Tartu, Estonia).", "They remained until 1061 when, according to chronicles, Yuryev was burned down by the Chudes.", "According to Old East Slavic chronicles, the Chudes were one of the founders of the Rus' state.", "The Northern (or eastern) Chudes were also a mythical people in folklore among Northern Russians and their neighbours.", "In Komi mythology, the Northern Chudes represent the mythic ancestors of the Komi people.", "In the 13th century the east Baltic world was transformed by military conquest: first the Livs and Estonians, then the Finns underwent defeat, baptism, military occupation and sometimes extermination by groups of Germans, Danes and Swedes.", "Finland was governed as a part of Sweden, while Estonia was under a Baltic German knightly brotherhood.", "Finland and Estonia became independent at the beginning of the modern age in 1917–1918 (see history of Finland and history of Estonia).", "The Karelians remained under Russian and then Soviet rule, and their absolute and relative numbers dwindled.", "When urbanization was peaking, less-numerous peoples rapidly lost capacity to maintain their village-based cultures and so were often assimilated to the mainstream society." ]

[ 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74 ]

[ "The bulk of the Finnic peoples (more than 98%) are ethnic Finns and Estonians, who reside in the only two independent Finnic nation states—Finland and Estonia." ]

[ "The \"MG XPower\" brand was created by MG Rover for their motorsport subsidiary MG Sport & Racing Ltd. in April 2001.", "The brand \"MG XPower\" was subsequently used for the sports car MG XPower SV in October 2002.", "William Riley bought the rights to the \"MG XPower\" brand from the administrators in October 2008, following the collapse of MG Rover three years earlier in April 2005." ]

[ 0, 1, 2 ]

[ "MG XPower is a British automotive brand which was created by MG Rover Group in April 2001 and is now owned by MG Sports and Racing Europe based in Tenbury Wells." ]

[ "Organized by the Lithuanian Football Federation (LFF), I Lyga is contested by 14-16 teams, with the top team gaining promotion to A Lyga and replaced by the lowest-placed team in top division and the bottom 4 clubs being relegated to the II Lyga.", "Starting with the 2016 season, the second-placed team qualifies to promotion play-offs with A Lyga's next-to-last team.", "The final list of participants often does not correlate to the final results of the previous season, as the participation is finalized through the Lithuanian Football Federation league licensing process.", "There were 15 teams competing in the 2017 season.", "At the end of this season, three teams withdrew from all competitions.", "In 2018, there were 14 teams that started the championship.", "However, FK Koralas Klaipėda withdrew in the mid-season.", "After the end of the season, two more teams have withdrawn from participation in the next season.", "The 2019 season saw 16 teams starting the championship.", "In June FC Stumbras ran into financial difficulties, its license was withdrawn from the A Lyga, along with Stumbras B license in the I Lyga.", "In July Stumbras B was removed from the league, with all results annulled as the team played less than half of all season games.", "At the end of the season an investigation into match-fixing was launched.", "As a result, FK Atlantas and FK Palanga were expelled from A Lyga and demoted to II Lyga.", "An appeal to allow to participate in I Lyga was rejected.", "As the investigation continued, I Lyga side FC Kupiškis was also found to be involved in match-fixing, and subsequently fined and demoted to II Lyga.", "Although the 2019 I Lyga winners FC Džiugas Telšiai won promotion to A lyga, the club failed to meet 2020 A Lyga licensing criteria, and had their promotion forfeited.", "Only FK Banga Gargždai had advanced to A Lyga after the 2019 season, having won the promotion playoff against the A lyga 7-th placed FK Palanga before its expulsion from the A Lyga.\nThe 2020 season was affected by the COVID-19 pandemic, and was shortened to 1.5 rounds.", "14 teams participated in the tournament, with four teams offered promotion to A Lyga.", "The last-placed team was meant to be relegated, but in the end stayed up in I Lyga.", "2021 season ran in full despite some COVID-19 threats.", "As four teams advanced to the A Lyga, and one club withdrew, five teams joined from the II Lyga.", "Previous season winner FK Jonava were denied A Lyga license because of allegations of match-fixing.", "The league consisted of 14 teams, with an expectation to expand the league to 16 the next season.", "FA Šiauliai won the 2021 title, beating FK Jonava in the last round.", "Both clubs finished with 66 points, and the top position had to be decided by additional match at a neutral stadium.", "FA Šiauliai had won both matches this season - 3:1 and 1:0.", "And also won additional match on penalties to become champions.", "Match was played in Kėdainiai.", "For the last several years, the second-placed team contested with A Lyga's next-to-last team in a play-off for a spot in A Lyga.\nSince 2020 season saw A Lyga reduced to 6 teams, the LFF announced that 4 teams will gain promotion from I Lyga this season.", "The play-off match was not mentioned.", "At the 2021 season end, it is expected that two teams will be relegated directly from A Lyga, without a play-off game." ]

[ 0, 1, 2 ]

[ "The I Lyga, LFF I Lyga, Pirma Lyga, is the second tier of professional Lithuanian football championship." ]

[ "The fishing sector in Portugal faced deep structural changes in terms of both the volume of its business and its working conditions since adhesion to the European Economic Community in 1986.", "The fishing fleet dropped from 12,299 vessels of all kinds in 1994 to 10,933 in 1999, while the number of registered fishing workers fell from 31,721 to 27,191.", "The volume of imported fish increased by 31% from 1990 to 1999, whereas exports decreased by 0.4% over the same period.", "In 1997, 4,932 people were registered as employees in the fishing sector.", "In 2004, there were 10,089 vessels registered with a total size of 112,978 GT and a total power of 391 006 kW. These numbers indicate a reduction in overall fleet size since 1998 of approximately 9.9% in number, 1.5% in GT and 0.8% in power.", "Total catches fell from 224,000 tonnes in 1998 to 140,000 tonnes in 2004, a 38% decrease.", "As laid out in its Common Fisheries Policy, the European Union is seeking to establish a policy that determines priorities which will contribute to a sustainable balance between fisheries resources and their exploitation; increase the competitiveness of fishing enterprises and organisations; and develop viable enterprises.", "The EU has been paying special attention to the situation in Portugal both because of the characteristics of the Portuguese coastal area and the type of vessel used there.", "The Portuguese fishing fleet has changed significantly, both in size and in character, in order to adjust fishing capacity to the potential of national, EU, non-EU and international waters.", "Reflecting the current status of the national resources and restricted access to foreign fishing grounds, re-dimensioning of the fleet is part of the renovation and modernization process.", "During the 1990s and 2000s, new fishing vessels, with improved on-board fish conservation methods, automated work systems, and electronic navigation and fish detection systems, were gradually introduced to replace the ageing fishing vessels from the 1980s and before.", "Roman ruins of fish processing facilities were found across the Portuguese coast.", "Garum (a type of fermented fish sauce) of Lusitania (present-day Portugal) was highly prized in Rome.", "It was shipped to Rome directly from the harbour of Lacobriga (present-day Lagos).", "The fishing and fish processing industry was so important in the territory that ruins of a former Roman garum factory can be even visited today in the downtown of Lisbon's old quarter.", "Fish has been an important staple for the entire Portuguese population at least since the Portuguese Age of Discovery.", "The Portuguese population is among the world's largest per capita fish consumers.", "Portuguese cuisine includes a variety of fish and other seafood-based dishes, some of them renowned internationally.", "The main institution responsible for fisheries management is the Directorate-General of Fisheries and Aquaculture (DGPA), in association with the Assistant-Secretariat of State and the Ministry of Agriculture, Fisheries and Forests.", "The \"Instituto Nacional dos Recursos Biológicos\" (INRB), as well as the Producer Organizations and Shipowner's Associations, are consulted and have an advisory role in the decision-making process.", "INRB is also responsible for fish stock assessments within the International Council for the Exploration of the Sea (ICES) and the Northwest Atlantic Fisheries Organization (NAFO) frameworks.", "INRB uses information collected during research surveys and in fishing ports, and also the catch statistics provided by DGPA.", "At a national level, INRB has also the role of proposing technical measures to protect and maintain fish stocks.", "The Portuguese fishing industry is fairly large and diversified.", "Fishing vessels classified according to the area in which they operate, can be divided into local fishing vessels, coastal fishing vessels and long-distance fishing vessels.", "The local fleet is mainly composed of small traditional vessels (less than 5 GT), comprising, in 2004, 87% of the total fishing fleet and accounting for 8% of the total tonnage.", "These vessels are usually equipped to use more than one fishing method, such as hooks, gill nets and traps, and constitute the so-called polyvalent segment of the fleet.", "Their physical output is low but reasonable levels of income are attained by virtue of the high commercial value of the species they capture: octopus, black scabbardfish, conger, pouting, hake and anglerfish.", "Purse seine fishing is also part of the local fleet and has, on the mainland, only one target species: the sardine.", "This fishery represents 37% of total landings.", "The coastal fishing fleet accounted for only 13% of vessels but had the largest GT (93%).", "These vessels operate in areas farther from the coast, and even outside the Portugal's Exclusive Economic Zone.", "The coastal fishing fleet comprises polyvalent, purse seine and trawl fishing vessels.", "The trawlers operate only on the mainland shelf and target demersal species such as horse mackerel, blue whiting, octopus and crustaceans.", "The crustacean trawling fishery targets Norway lobster, red shrimp and deepwater rose shrimp.", "The most important fish species landed in Portugal in 2004 were sardine, mackerel and horse mackerel, representing 37%, 9% and 8% of total landings by weight, and 13%, 1% and 8% of total value, respectively.", "Molluscs accounted for only 12% of total landings in weight, but 22% of total landings in value.", "Crustaceans were 0.6% of the total landings by weight and 5% by value.", "Fishing in foreign waters has decreased considerably since 1998, after the end of the fisheries agreement with Morocco and the renegotiation of the agreement with Mauritania.", "A new fisheries agreement between EU and Morocco has been reached, and started in March 2006, after a 7-year interval.", "In 1999, 40 Portuguese vessels were fishing in Moroccan waters, making Morocco the second-largest foreign fisheries ground at that time.", "In 2004, 15% of the total landings were from international waters from 59 registered vessels, mainly from the northwest Atlantic, northeast Atlantic (Norway, Svalbard, Spain and Greenland since 2003) and the central Atlantic (Guinea-Bissau, Cape Verde, Senegal, Mauritania).", "In the northwest Atlantic, redfish was the most important species, with 50% of total catches, while in Spain it was sardine and horse mackerel, with 36%.", "Off Norway and Svalbard, cod (\"bacalhau\" in Portuguese) was the most important species, accounting for 82% of total catches, while from Greenland, redfish was the only species landed.", "\"Bacalhau\" is indeed one of the most popular fishes used in Portuguese cuisine, along with sardine and tuna.", "The main landing sites in Portugal (including Azores and Madeira), according to total landings in weight by year, are the harbours of Matosinhos, Peniche, Olhão, Sesimbra, Figueira da Foz, Sines, Portimão and Madeira.", "The main objective of the national fisheries policy, particularly since 2002, is to maintain the sustainability of the sector and reverse the negative tendency of recent years.", "To achieve this objective, several measures have been adopted to promote recovery and stabilization of the fishing industry.", "At the same time, fleet renewal and modernization has been promoted in order to reduce production costs and improve work safety.", "Structural modernization of the fishing industry, as well as the processing industry and the aquaculture sector, are also promoted within the present fisheries management plan.", "These objectives are in accordance with those established by the EU in the Common Fishery Policy.", "The present national management system includes the establishment of annual quotas for some species and fishing areas, the application of technical conservation measures, and limitation of fishing effort.", "Fishing effort is controlled by a licensing system, where acquisition, construction or modification of vessels requires prior authorization.", "The use of certain fishing methods is also subject to prior authorization and annual licensing.", "The objective is to allow the modernization of the fishing fleet without increased fishing effort, by authorizing the construction of new vessels only as replacement of others; improving working conditions; and promoting conservation measures by encourage the use of less predatory fishing gear.", "There are species subject to quotas in national waters.", "Quotas can be allocated to individual vessels, as is the case for vessels operating in North Atlantic Fishery Organization (NAFO) and Norwegian fishing grounds; or to groups of vessels, as is the case for the purse seine fishery, where sardine catch limits are divided among Producer Organizations.", "Individual vessel quotas are also transferable within a shipowner's fleet to facilitate flexible management and therefore maximum utilization of these quotas.", "In 2004, 63 t of fish were landed by inland fisheries, with a value of US$642 000.", "The main species landed were shad (Alosa sp.), lamprey (Lampetra fluviatilis) and eels, with 49%, 29% and 16% of total landings from this fishery, respectively.", "Regarding fisheries management, purse-seine nets, bottom trawl, gill nets (except when targeting lamprey) and gear that uses tidal movements are prohibited in inland waters.", "There are also limitations on fishing areas and gear characteristics (mesh and gear size, amongst others).", "Recreational fishing is common and popular in inland fresh water streams, lakes, reservoirs and rivers.", "Every recreational fishing enthusiast desiring to use those kinds of national water resources for fishing, must respect rules and be aware of several limitations.", "A yearly individual fee must be paid to the state for fishing in suitable inland or oceanic waters.", "Until the mid-1980s, aquaculture production consisted of freshwater trout and bivalves bottom culture in tidal estuaries.", "However, marine aquaculture production showed an overall increase at the beginning of the 1990s, followed by a period of some fluctuation.", "Total production was 7 829 t in 2003, and consisted mainly of grooved carpet shell (\"Ruditapes decussatus\") (3 007 t), mussels (280 t), oyster (425 t), seabream (1 429 t) and seabass (1 384 t) from marine units; and trout (333 t) from freshwater units.", "Nowadays, both freshwater and marine aquaculture is well-established in Portugal producing from marine fin-fish and shellfish to micro-algae and trout.", "The objective of the national fisheries policy regarding aquaculture is to increase production and product diversity, but also to increase product quality, in order to improve the competitive position of the sector.", "Structural modernization of the aquaculture sector is also promoted within the present fisheries management plan.", "These objectives are in accordance with those established by the European Union in the Common Fisheries Policy, and in particular with the 2002 Strategy for the Sustainable Development of European Aquaculture, which promotes environmental, economic and social sustainability.", "One of the main aquaculture projects of Portugal is the Pescanova's production centre in Mira, Centro region.", "The southern Portuguese region of the Algarve is also a major aquaculture centre.", "In 2017, aquaculture production reached 12,549 tonnes, with a value of 83.2 million euros.", "These values correspond to an increase of 11.5% in quantity and to an increase of 10.6% in value, compared to the values of the previous year.", "There are many canned fish processing plants across Portugal, producing under different trademarked brands which are mostly exported.", "The mainland's principal ports specialized in canning small pelagic fish, most of which sardine, are Matosinhos-Póvoa de Varzim area, Peniche, and Olhão.", "In the Azores, the canned tuna fish industry is predominant, and most of the production is almost exclusively exported.", "A diversification drive is being attempted with the development of black scabbardfish canning industry, a barely exploited resource on the islands.", "Major fish processing companies include Briosa, Cofaco, Cofisa, Conserveira do Sul, Conservas Ramirez (the world's oldest canned fish producer still in operation), Fábrica de Conservas da Murtosa, Conservas Portugal Norte and the Portuguese branch of Pescanova.", "Portuguese processed fish products are exported through several companies under a number of different brands and registered trademarks like Ramirez, Bom Petisco, Briosa Gourmet, Combate, Comur, Conserveira, General, Inês, Líder, Manná, Murtosa, Pescador, Pitéu, Porthos, Tenório, Torreira, and Vasco da Gama.", "Portugal, as an Atlantic country and an historical seafaring nation, has a long tradition in the sector of fishing.", "It is among the countries in the world with the highest fish consumption per capita.", "Species like the sardine, Atlantic mackerel, tuna, and the European hake are important for the Portuguese commercial capture fisheries.", "Other, widely used species in Portuguese cuisine is the cod, known in Portugal as \"bacalhau\".", "Salt cod has been produced for at least 500 years, since the time of the European discoveries.", "Before refrigeration, there was a need to preserve the codfish; drying and salting are ancient techniques to keep many nutrients and the process makes the codfish tastier.", "The Portuguese tried to use this method of drying and salting several fishes from their waters, but the ideal fish came from much further north.", "With the \"discovery\" of Newfoundland in 1497, Portuguese fishermen started fishing its cod-rich Grand Banks.", "Thus, ' became a staple of the Portuguese cuisine, nicknamed ' (faithful friend).", "From the 18th century the town of Kristiansund in Norway became an important place of producing bacalao or klippfish, which is also exported to Portugal.", "In Portugal, there are several vocational and higher education institutions devoted to the teaching of fishing, fisheries, oceanography, marine biology and marine science in general.", "For example, the state-run polytechnic institute \"Instituto Politécnico de Leiria\" at Peniche, through its \"Escola Superior de Turismo e Tecnologia do Mar de Peniche\", has a school of marine technologies awarding bachelor's and master's degrees in these subjects.", "There are also a number of universities awarding bachelor's, masters' and doctorate degrees in varied marine science subfields, as well as making research and development work.", "The marine biology and marine sciences degrees awarded by the Marine and Environmental Sciences Faculty of the University of the Algarve are among the most prestigious in the country.", "The Instituto Nacional dos Recursos Biológicos (INRB) is the national research institute for agriculture and fisheries." ]

[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]

[ "Fishing is a major economic activity in Portugal." ]

[ "The fishing sector in Portugal faced deep structural changes in terms of both the volume of its business and its working conditions since adhesion to the European Economic Community in 1986.", "The fishing fleet dropped from 12,299 vessels of all kinds in 1994 to 10,933 in 1999, while the number of registered fishing workers fell from 31,721 to 27,191.", "The volume of imported fish increased by 31% from 1990 to 1999, whereas exports decreased by 0.4% over the same period.", "In 1997, 4,932 people were registered as employees in the fishing sector.", "In 2004, there were 10,089 vessels registered with a total size of 112,978 GT and a total power of 391 006 kW. These numbers indicate a reduction in overall fleet size since 1998 of approximately 9.9% in number, 1.5% in GT and 0.8% in power.", "Total catches fell from 224,000 tonnes in 1998 to 140,000 tonnes in 2004, a 38% decrease.", "As laid out in its Common Fisheries Policy, the European Union is seeking to establish a policy that determines priorities which will contribute to a sustainable balance between fisheries resources and their exploitation; increase the competitiveness of fishing enterprises and organisations; and develop viable enterprises.", "The EU has been paying special attention to the situation in Portugal both because of the characteristics of the Portuguese coastal area and the type of vessel used there.", "The Portuguese fishing fleet has changed significantly, both in size and in character, in order to adjust fishing capacity to the potential of national, EU, non-EU and international waters.", "Reflecting the current status of the national resources and restricted access to foreign fishing grounds, re-dimensioning of the fleet is part of the renovation and modernization process.", "During the 1990s and 2000s, new fishing vessels, with improved on-board fish conservation methods, automated work systems, and electronic navigation and fish detection systems, were gradually introduced to replace the ageing fishing vessels from the 1980s and before.", "Roman ruins of fish processing facilities were found across the Portuguese coast.", "Garum (a type of fermented fish sauce) of Lusitania (present-day Portugal) was highly prized in Rome.", "It was shipped to Rome directly from the harbour of Lacobriga (present-day Lagos).", "The fishing and fish processing industry was so important in the territory that ruins of a former Roman garum factory can be even visited today in the downtown of Lisbon's old quarter.", "Fish has been an important staple for the entire Portuguese population at least since the Portuguese Age of Discovery.", "The Portuguese population is among the world's largest per capita fish consumers.", "Portuguese cuisine includes a variety of fish and other seafood-based dishes, some of them renowned internationally.", "The main institution responsible for fisheries management is the Directorate-General of Fisheries and Aquaculture (DGPA), in association with the Assistant-Secretariat of State and the Ministry of Agriculture, Fisheries and Forests.", "The \"Instituto Nacional dos Recursos Biológicos\" (INRB), as well as the Producer Organizations and Shipowner's Associations, are consulted and have an advisory role in the decision-making process.", "INRB is also responsible for fish stock assessments within the International Council for the Exploration of the Sea (ICES) and the Northwest Atlantic Fisheries Organization (NAFO) frameworks.", "INRB uses information collected during research surveys and in fishing ports, and also the catch statistics provided by DGPA.", "At a national level, INRB has also the role of proposing technical measures to protect and maintain fish stocks.", "The Portuguese fishing industry is fairly large and diversified.", "Fishing vessels classified according to the area in which they operate, can be divided into local fishing vessels, coastal fishing vessels and long-distance fishing vessels.", "The local fleet is mainly composed of small traditional vessels (less than 5 GT), comprising, in 2004, 87% of the total fishing fleet and accounting for 8% of the total tonnage.", "These vessels are usually equipped to use more than one fishing method, such as hooks, gill nets and traps, and constitute the so-called polyvalent segment of the fleet.", "Their physical output is low but reasonable levels of income are attained by virtue of the high commercial value of the species they capture: octopus, black scabbardfish, conger, pouting, hake and anglerfish.", "Purse seine fishing is also part of the local fleet and has, on the mainland, only one target species: the sardine.", "This fishery represents 37% of total landings.", "The coastal fishing fleet accounted for only 13% of vessels but had the largest GT (93%).", "These vessels operate in areas farther from the coast, and even outside the Portugal's Exclusive Economic Zone.", "The coastal fishing fleet comprises polyvalent, purse seine and trawl fishing vessels.", "The trawlers operate only on the mainland shelf and target demersal species such as horse mackerel, blue whiting, octopus and crustaceans.", "The crustacean trawling fishery targets Norway lobster, red shrimp and deepwater rose shrimp.", "The most important fish species landed in Portugal in 2004 were sardine, mackerel and horse mackerel, representing 37%, 9% and 8% of total landings by weight, and 13%, 1% and 8% of total value, respectively.", "Molluscs accounted for only 12% of total landings in weight, but 22% of total landings in value.", "Crustaceans were 0.6% of the total landings by weight and 5% by value.", "Fishing in foreign waters has decreased considerably since 1998, after the end of the fisheries agreement with Morocco and the renegotiation of the agreement with Mauritania.", "A new fisheries agreement between EU and Morocco has been reached, and started in March 2006, after a 7-year interval.", "In 1999, 40 Portuguese vessels were fishing in Moroccan waters, making Morocco the second-largest foreign fisheries ground at that time.", "In 2004, 15% of the total landings were from international waters from 59 registered vessels, mainly from the northwest Atlantic, northeast Atlantic (Norway, Svalbard, Spain and Greenland since 2003) and the central Atlantic (Guinea-Bissau, Cape Verde, Senegal, Mauritania).", "In the northwest Atlantic, redfish was the most important species, with 50% of total catches, while in Spain it was sardine and horse mackerel, with 36%.", "Off Norway and Svalbard, cod (\"bacalhau\" in Portuguese) was the most important species, accounting for 82% of total catches, while from Greenland, redfish was the only species landed.", "\"Bacalhau\" is indeed one of the most popular fishes used in Portuguese cuisine, along with sardine and tuna.", "The main landing sites in Portugal (including Azores and Madeira), according to total landings in weight by year, are the harbours of Matosinhos, Peniche, Olhão, Sesimbra, Figueira da Foz, Sines, Portimão and Madeira.", "The main objective of the national fisheries policy, particularly since 2002, is to maintain the sustainability of the sector and reverse the negative tendency of recent years.", "To achieve this objective, several measures have been adopted to promote recovery and stabilization of the fishing industry.", "At the same time, fleet renewal and modernization has been promoted in order to reduce production costs and improve work safety.", "Structural modernization of the fishing industry, as well as the processing industry and the aquaculture sector, are also promoted within the present fisheries management plan.", "These objectives are in accordance with those established by the EU in the Common Fishery Policy.", "The present national management system includes the establishment of annual quotas for some species and fishing areas, the application of technical conservation measures, and limitation of fishing effort.", "Fishing effort is controlled by a licensing system, where acquisition, construction or modification of vessels requires prior authorization.", "The use of certain fishing methods is also subject to prior authorization and annual licensing.", "The objective is to allow the modernization of the fishing fleet without increased fishing effort, by authorizing the construction of new vessels only as replacement of others; improving working conditions; and promoting conservation measures by encourage the use of less predatory fishing gear.", "There are species subject to quotas in national waters.", "Quotas can be allocated to individual vessels, as is the case for vessels operating in North Atlantic Fishery Organization (NAFO) and Norwegian fishing grounds; or to groups of vessels, as is the case for the purse seine fishery, where sardine catch limits are divided among Producer Organizations.", "Individual vessel quotas are also transferable within a shipowner's fleet to facilitate flexible management and therefore maximum utilization of these quotas.", "In 2004, 63 t of fish were landed by inland fisheries, with a value of US$642 000.", "The main species landed were shad (Alosa sp.), lamprey (Lampetra fluviatilis) and eels, with 49%, 29% and 16% of total landings from this fishery, respectively.", "Regarding fisheries management, purse-seine nets, bottom trawl, gill nets (except when targeting lamprey) and gear that uses tidal movements are prohibited in inland waters.", "There are also limitations on fishing areas and gear characteristics (mesh and gear size, amongst others).", "Recreational fishing is common and popular in inland fresh water streams, lakes, reservoirs and rivers.", "Every recreational fishing enthusiast desiring to use those kinds of national water resources for fishing, must respect rules and be aware of several limitations.", "A yearly individual fee must be paid to the state for fishing in suitable inland or oceanic waters.", "Until the mid-1980s, aquaculture production consisted of freshwater trout and bivalves bottom culture in tidal estuaries.", "However, marine aquaculture production showed an overall increase at the beginning of the 1990s, followed by a period of some fluctuation.", "Total production was 7 829 t in 2003, and consisted mainly of grooved carpet shell (\"Ruditapes decussatus\") (3 007 t), mussels (280 t), oyster (425 t), seabream (1 429 t) and seabass (1 384 t) from marine units; and trout (333 t) from freshwater units.", "Nowadays, both freshwater and marine aquaculture is well-established in Portugal producing from marine fin-fish and shellfish to micro-algae and trout.", "The objective of the national fisheries policy regarding aquaculture is to increase production and product diversity, but also to increase product quality, in order to improve the competitive position of the sector.", "Structural modernization of the aquaculture sector is also promoted within the present fisheries management plan.", "These objectives are in accordance with those established by the European Union in the Common Fisheries Policy, and in particular with the 2002 Strategy for the Sustainable Development of European Aquaculture, which promotes environmental, economic and social sustainability.", "One of the main aquaculture projects of Portugal is the Pescanova's production centre in Mira, Centro region.", "The southern Portuguese region of the Algarve is also a major aquaculture centre.", "In 2017, aquaculture production reached 12,549 tonnes, with a value of 83.2 million euros.", "These values correspond to an increase of 11.5% in quantity and to an increase of 10.6% in value, compared to the values of the previous year.", "There are many canned fish processing plants across Portugal, producing under different trademarked brands which are mostly exported.", "The mainland's principal ports specialized in canning small pelagic fish, most of which sardine, are Matosinhos-Póvoa de Varzim area, Peniche, and Olhão.", "In the Azores, the canned tuna fish industry is predominant, and most of the production is almost exclusively exported.", "A diversification drive is being attempted with the development of black scabbardfish canning industry, a barely exploited resource on the islands.", "Major fish processing companies include Briosa, Cofaco, Cofisa, Conserveira do Sul, Conservas Ramirez (the world's oldest canned fish producer still in operation), Fábrica de Conservas da Murtosa, Conservas Portugal Norte and the Portuguese branch of Pescanova.", "Portuguese processed fish products are exported through several companies under a number of different brands and registered trademarks like Ramirez, Bom Petisco, Briosa Gourmet, Combate, Comur, Conserveira, General, Inês, Líder, Manná, Murtosa, Pescador, Pitéu, Porthos, Tenório, Torreira, and Vasco da Gama.", "Portugal, as an Atlantic country and an historical seafaring nation, has a long tradition in the sector of fishing.", "It is among the countries in the world with the highest fish consumption per capita.", "Species like the sardine, Atlantic mackerel, tuna, and the European hake are important for the Portuguese commercial capture fisheries.", "Other, widely used species in Portuguese cuisine is the cod, known in Portugal as \"bacalhau\".", "Salt cod has been produced for at least 500 years, since the time of the European discoveries.", "Before refrigeration, there was a need to preserve the codfish; drying and salting are ancient techniques to keep many nutrients and the process makes the codfish tastier.", "The Portuguese tried to use this method of drying and salting several fishes from their waters, but the ideal fish came from much further north.", "With the \"discovery\" of Newfoundland in 1497, Portuguese fishermen started fishing its cod-rich Grand Banks.", "Thus, ' became a staple of the Portuguese cuisine, nicknamed ' (faithful friend).", "From the 18th century the town of Kristiansund in Norway became an important place of producing bacalao or klippfish, which is also exported to Portugal.", "In Portugal, there are several vocational and higher education institutions devoted to the teaching of fishing, fisheries, oceanography, marine biology and marine science in general.", "For example, the state-run polytechnic institute \"Instituto Politécnico de Leiria\" at Peniche, through its \"Escola Superior de Turismo e Tecnologia do Mar de Peniche\", has a school of marine technologies awarding bachelor's and master's degrees in these subjects.", "There are also a number of universities awarding bachelor's, masters' and doctorate degrees in varied marine science subfields, as well as making research and development work.", "The marine biology and marine sciences degrees awarded by the Marine and Environmental Sciences Faculty of the University of the Algarve are among the most prestigious in the country.", "The Instituto Nacional dos Recursos Biológicos (INRB) is the national research institute for agriculture and fisheries." ]

[ 11, 12, 13, 14, 15, 16, 17 ]

[ "Roman ruins of fish processing facilities were found across the Portuguese coast.", "Fish has been an important staple for the entire Portuguese population, at least since the Portuguese Age of Discovery." ]

[ "The fishing sector in Portugal faced deep structural changes in terms of both the volume of its business and its working conditions since adhesion to the European Economic Community in 1986.", "The fishing fleet dropped from 12,299 vessels of all kinds in 1994 to 10,933 in 1999, while the number of registered fishing workers fell from 31,721 to 27,191.", "The volume of imported fish increased by 31% from 1990 to 1999, whereas exports decreased by 0.4% over the same period.", "In 1997, 4,932 people were registered as employees in the fishing sector.", "In 2004, there were 10,089 vessels registered with a total size of 112,978 GT and a total power of 391 006 kW. These numbers indicate a reduction in overall fleet size since 1998 of approximately 9.9% in number, 1.5% in GT and 0.8% in power.", "Total catches fell from 224,000 tonnes in 1998 to 140,000 tonnes in 2004, a 38% decrease.", "As laid out in its Common Fisheries Policy, the European Union is seeking to establish a policy that determines priorities which will contribute to a sustainable balance between fisheries resources and their exploitation; increase the competitiveness of fishing enterprises and organisations; and develop viable enterprises.", "The EU has been paying special attention to the situation in Portugal both because of the characteristics of the Portuguese coastal area and the type of vessel used there.", "The Portuguese fishing fleet has changed significantly, both in size and in character, in order to adjust fishing capacity to the potential of national, EU, non-EU and international waters.", "Reflecting the current status of the national resources and restricted access to foreign fishing grounds, re-dimensioning of the fleet is part of the renovation and modernization process.", "During the 1990s and 2000s, new fishing vessels, with improved on-board fish conservation methods, automated work systems, and electronic navigation and fish detection systems, were gradually introduced to replace the ageing fishing vessels from the 1980s and before.", "Roman ruins of fish processing facilities were found across the Portuguese coast.", "Garum (a type of fermented fish sauce) of Lusitania (present-day Portugal) was highly prized in Rome.", "It was shipped to Rome directly from the harbour of Lacobriga (present-day Lagos).", "The fishing and fish processing industry was so important in the territory that ruins of a former Roman garum factory can be even visited today in the downtown of Lisbon's old quarter.", "Fish has been an important staple for the entire Portuguese population at least since the Portuguese Age of Discovery.", "The Portuguese population is among the world's largest per capita fish consumers.", "Portuguese cuisine includes a variety of fish and other seafood-based dishes, some of them renowned internationally.", "The main institution responsible for fisheries management is the Directorate-General of Fisheries and Aquaculture (DGPA), in association with the Assistant-Secretariat of State and the Ministry of Agriculture, Fisheries and Forests.", "The \"Instituto Nacional dos Recursos Biológicos\" (INRB), as well as the Producer Organizations and Shipowner's Associations, are consulted and have an advisory role in the decision-making process.", "INRB is also responsible for fish stock assessments within the International Council for the Exploration of the Sea (ICES) and the Northwest Atlantic Fisheries Organization (NAFO) frameworks.", "INRB uses information collected during research surveys and in fishing ports, and also the catch statistics provided by DGPA.", "At a national level, INRB has also the role of proposing technical measures to protect and maintain fish stocks.", "The Portuguese fishing industry is fairly large and diversified.", "Fishing vessels classified according to the area in which they operate, can be divided into local fishing vessels, coastal fishing vessels and long-distance fishing vessels.", "The local fleet is mainly composed of small traditional vessels (less than 5 GT), comprising, in 2004, 87% of the total fishing fleet and accounting for 8% of the total tonnage.", "These vessels are usually equipped to use more than one fishing method, such as hooks, gill nets and traps, and constitute the so-called polyvalent segment of the fleet.", "Their physical output is low but reasonable levels of income are attained by virtue of the high commercial value of the species they capture: octopus, black scabbardfish, conger, pouting, hake and anglerfish.", "Purse seine fishing is also part of the local fleet and has, on the mainland, only one target species: the sardine.", "This fishery represents 37% of total landings.", "The coastal fishing fleet accounted for only 13% of vessels but had the largest GT (93%).", "These vessels operate in areas farther from the coast, and even outside the Portugal's Exclusive Economic Zone.", "The coastal fishing fleet comprises polyvalent, purse seine and trawl fishing vessels.", "The trawlers operate only on the mainland shelf and target demersal species such as horse mackerel, blue whiting, octopus and crustaceans.", "The crustacean trawling fishery targets Norway lobster, red shrimp and deepwater rose shrimp.", "The most important fish species landed in Portugal in 2004 were sardine, mackerel and horse mackerel, representing 37%, 9% and 8% of total landings by weight, and 13%, 1% and 8% of total value, respectively.", "Molluscs accounted for only 12% of total landings in weight, but 22% of total landings in value.", "Crustaceans were 0.6% of the total landings by weight and 5% by value.", "Fishing in foreign waters has decreased considerably since 1998, after the end of the fisheries agreement with Morocco and the renegotiation of the agreement with Mauritania.", "A new fisheries agreement between EU and Morocco has been reached, and started in March 2006, after a 7-year interval.", "In 1999, 40 Portuguese vessels were fishing in Moroccan waters, making Morocco the second-largest foreign fisheries ground at that time.", "In 2004, 15% of the total landings were from international waters from 59 registered vessels, mainly from the northwest Atlantic, northeast Atlantic (Norway, Svalbard, Spain and Greenland since 2003) and the central Atlantic (Guinea-Bissau, Cape Verde, Senegal, Mauritania).", "In the northwest Atlantic, redfish was the most important species, with 50% of total catches, while in Spain it was sardine and horse mackerel, with 36%.", "Off Norway and Svalbard, cod (\"bacalhau\" in Portuguese) was the most important species, accounting for 82% of total catches, while from Greenland, redfish was the only species landed.", "\"Bacalhau\" is indeed one of the most popular fishes used in Portuguese cuisine, along with sardine and tuna.", "The main landing sites in Portugal (including Azores and Madeira), according to total landings in weight by year, are the harbours of Matosinhos, Peniche, Olhão, Sesimbra, Figueira da Foz, Sines, Portimão and Madeira.", "The main objective of the national fisheries policy, particularly since 2002, is to maintain the sustainability of the sector and reverse the negative tendency of recent years.", "To achieve this objective, several measures have been adopted to promote recovery and stabilization of the fishing industry.", "At the same time, fleet renewal and modernization has been promoted in order to reduce production costs and improve work safety.", "Structural modernization of the fishing industry, as well as the processing industry and the aquaculture sector, are also promoted within the present fisheries management plan.", "These objectives are in accordance with those established by the EU in the Common Fishery Policy.", "The present national management system includes the establishment of annual quotas for some species and fishing areas, the application of technical conservation measures, and limitation of fishing effort.", "Fishing effort is controlled by a licensing system, where acquisition, construction or modification of vessels requires prior authorization.", "The use of certain fishing methods is also subject to prior authorization and annual licensing.", "The objective is to allow the modernization of the fishing fleet without increased fishing effort, by authorizing the construction of new vessels only as replacement of others; improving working conditions; and promoting conservation measures by encourage the use of less predatory fishing gear.", "There are species subject to quotas in national waters.", "Quotas can be allocated to individual vessels, as is the case for vessels operating in North Atlantic Fishery Organization (NAFO) and Norwegian fishing grounds; or to groups of vessels, as is the case for the purse seine fishery, where sardine catch limits are divided among Producer Organizations.", "Individual vessel quotas are also transferable within a shipowner's fleet to facilitate flexible management and therefore maximum utilization of these quotas.", "In 2004, 63 t of fish were landed by inland fisheries, with a value of US$642 000.", "The main species landed were shad (Alosa sp.), lamprey (Lampetra fluviatilis) and eels, with 49%, 29% and 16% of total landings from this fishery, respectively.", "Regarding fisheries management, purse-seine nets, bottom trawl, gill nets (except when targeting lamprey) and gear that uses tidal movements are prohibited in inland waters.", "There are also limitations on fishing areas and gear characteristics (mesh and gear size, amongst others).", "Recreational fishing is common and popular in inland fresh water streams, lakes, reservoirs and rivers.", "Every recreational fishing enthusiast desiring to use those kinds of national water resources for fishing, must respect rules and be aware of several limitations.", "A yearly individual fee must be paid to the state for fishing in suitable inland or oceanic waters.", "Until the mid-1980s, aquaculture production consisted of freshwater trout and bivalves bottom culture in tidal estuaries.", "However, marine aquaculture production showed an overall increase at the beginning of the 1990s, followed by a period of some fluctuation.", "Total production was 7 829 t in 2003, and consisted mainly of grooved carpet shell (\"Ruditapes decussatus\") (3 007 t), mussels (280 t), oyster (425 t), seabream (1 429 t) and seabass (1 384 t) from marine units; and trout (333 t) from freshwater units.", "Nowadays, both freshwater and marine aquaculture is well-established in Portugal producing from marine fin-fish and shellfish to micro-algae and trout.", "The objective of the national fisheries policy regarding aquaculture is to increase production and product diversity, but also to increase product quality, in order to improve the competitive position of the sector.", "Structural modernization of the aquaculture sector is also promoted within the present fisheries management plan.", "These objectives are in accordance with those established by the European Union in the Common Fisheries Policy, and in particular with the 2002 Strategy for the Sustainable Development of European Aquaculture, which promotes environmental, economic and social sustainability.", "One of the main aquaculture projects of Portugal is the Pescanova's production centre in Mira, Centro region.", "The southern Portuguese region of the Algarve is also a major aquaculture centre.", "In 2017, aquaculture production reached 12,549 tonnes, with a value of 83.2 million euros.", "These values correspond to an increase of 11.5% in quantity and to an increase of 10.6% in value, compared to the values of the previous year.", "There are many canned fish processing plants across Portugal, producing under different trademarked brands which are mostly exported.", "The mainland's principal ports specialized in canning small pelagic fish, most of which sardine, are Matosinhos-Póvoa de Varzim area, Peniche, and Olhão.", "In the Azores, the canned tuna fish industry is predominant, and most of the production is almost exclusively exported.", "A diversification drive is being attempted with the development of black scabbardfish canning industry, a barely exploited resource on the islands.", "Major fish processing companies include Briosa, Cofaco, Cofisa, Conserveira do Sul, Conservas Ramirez (the world's oldest canned fish producer still in operation), Fábrica de Conservas da Murtosa, Conservas Portugal Norte and the Portuguese branch of Pescanova.", "Portuguese processed fish products are exported through several companies under a number of different brands and registered trademarks like Ramirez, Bom Petisco, Briosa Gourmet, Combate, Comur, Conserveira, General, Inês, Líder, Manná, Murtosa, Pescador, Pitéu, Porthos, Tenório, Torreira, and Vasco da Gama.", "Portugal, as an Atlantic country and an historical seafaring nation, has a long tradition in the sector of fishing.", "It is among the countries in the world with the highest fish consumption per capita.", "Species like the sardine, Atlantic mackerel, tuna, and the European hake are important for the Portuguese commercial capture fisheries.", "Other, widely used species in Portuguese cuisine is the cod, known in Portugal as \"bacalhau\".", "Salt cod has been produced for at least 500 years, since the time of the European discoveries.", "Before refrigeration, there was a need to preserve the codfish; drying and salting are ancient techniques to keep many nutrients and the process makes the codfish tastier.", "The Portuguese tried to use this method of drying and salting several fishes from their waters, but the ideal fish came from much further north.", "With the \"discovery\" of Newfoundland in 1497, Portuguese fishermen started fishing its cod-rich Grand Banks.", "Thus, ' became a staple of the Portuguese cuisine, nicknamed ' (faithful friend).", "From the 18th century the town of Kristiansund in Norway became an important place of producing bacalao or klippfish, which is also exported to Portugal.", "In Portugal, there are several vocational and higher education institutions devoted to the teaching of fishing, fisheries, oceanography, marine biology and marine science in general.", "For example, the state-run polytechnic institute \"Instituto Politécnico de Leiria\" at Peniche, through its \"Escola Superior de Turismo e Tecnologia do Mar de Peniche\", has a school of marine technologies awarding bachelor's and master's degrees in these subjects.", "There are also a number of universities awarding bachelor's, masters' and doctorate degrees in varied marine science subfields, as well as making research and development work.", "The marine biology and marine sciences degrees awarded by the Marine and Environmental Sciences Faculty of the University of the Algarve are among the most prestigious in the country.", "The Instituto Nacional dos Recursos Biológicos (INRB) is the national research institute for agriculture and fisheries." ]

[ 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57 ]

[ "The Portuguese fishing sector is divided into various subsectors, which in turn are divided between industrial fishing and artisanal fishing." ]

[ "The fishing sector in Portugal faced deep structural changes in terms of both the volume of its business and its working conditions since adhesion to the European Economic Community in 1986.", "The fishing fleet dropped from 12,299 vessels of all kinds in 1994 to 10,933 in 1999, while the number of registered fishing workers fell from 31,721 to 27,191.", "The volume of imported fish increased by 31% from 1990 to 1999, whereas exports decreased by 0.4% over the same period.", "In 1997, 4,932 people were registered as employees in the fishing sector.", "In 2004, there were 10,089 vessels registered with a total size of 112,978 GT and a total power of 391 006 kW. These numbers indicate a reduction in overall fleet size since 1998 of approximately 9.9% in number, 1.5% in GT and 0.8% in power.", "Total catches fell from 224,000 tonnes in 1998 to 140,000 tonnes in 2004, a 38% decrease.", "As laid out in its Common Fisheries Policy, the European Union is seeking to establish a policy that determines priorities which will contribute to a sustainable balance between fisheries resources and their exploitation; increase the competitiveness of fishing enterprises and organisations; and develop viable enterprises.", "The EU has been paying special attention to the situation in Portugal both because of the characteristics of the Portuguese coastal area and the type of vessel used there.", "The Portuguese fishing fleet has changed significantly, both in size and in character, in order to adjust fishing capacity to the potential of national, EU, non-EU and international waters.", "Reflecting the current status of the national resources and restricted access to foreign fishing grounds, re-dimensioning of the fleet is part of the renovation and modernization process.", "During the 1990s and 2000s, new fishing vessels, with improved on-board fish conservation methods, automated work systems, and electronic navigation and fish detection systems, were gradually introduced to replace the ageing fishing vessels from the 1980s and before.", "Roman ruins of fish processing facilities were found across the Portuguese coast.", "Garum (a type of fermented fish sauce) of Lusitania (present-day Portugal) was highly prized in Rome.", "It was shipped to Rome directly from the harbour of Lacobriga (present-day Lagos).", "The fishing and fish processing industry was so important in the territory that ruins of a former Roman garum factory can be even visited today in the downtown of Lisbon's old quarter.", "Fish has been an important staple for the entire Portuguese population at least since the Portuguese Age of Discovery.", "The Portuguese population is among the world's largest per capita fish consumers.", "Portuguese cuisine includes a variety of fish and other seafood-based dishes, some of them renowned internationally.", "The main institution responsible for fisheries management is the Directorate-General of Fisheries and Aquaculture (DGPA), in association with the Assistant-Secretariat of State and the Ministry of Agriculture, Fisheries and Forests.", "The \"Instituto Nacional dos Recursos Biológicos\" (INRB), as well as the Producer Organizations and Shipowner's Associations, are consulted and have an advisory role in the decision-making process.", "INRB is also responsible for fish stock assessments within the International Council for the Exploration of the Sea (ICES) and the Northwest Atlantic Fisheries Organization (NAFO) frameworks.", "INRB uses information collected during research surveys and in fishing ports, and also the catch statistics provided by DGPA.", "At a national level, INRB has also the role of proposing technical measures to protect and maintain fish stocks.", "The Portuguese fishing industry is fairly large and diversified.", "Fishing vessels classified according to the area in which they operate, can be divided into local fishing vessels, coastal fishing vessels and long-distance fishing vessels.", "The local fleet is mainly composed of small traditional vessels (less than 5 GT), comprising, in 2004, 87% of the total fishing fleet and accounting for 8% of the total tonnage.", "These vessels are usually equipped to use more than one fishing method, such as hooks, gill nets and traps, and constitute the so-called polyvalent segment of the fleet.", "Their physical output is low but reasonable levels of income are attained by virtue of the high commercial value of the species they capture: octopus, black scabbardfish, conger, pouting, hake and anglerfish.", "Purse seine fishing is also part of the local fleet and has, on the mainland, only one target species: the sardine.", "This fishery represents 37% of total landings.", "The coastal fishing fleet accounted for only 13% of vessels but had the largest GT (93%).", "These vessels operate in areas farther from the coast, and even outside the Portugal's Exclusive Economic Zone.", "The coastal fishing fleet comprises polyvalent, purse seine and trawl fishing vessels.", "The trawlers operate only on the mainland shelf and target demersal species such as horse mackerel, blue whiting, octopus and crustaceans.", "The crustacean trawling fishery targets Norway lobster, red shrimp and deepwater rose shrimp.", "The most important fish species landed in Portugal in 2004 were sardine, mackerel and horse mackerel, representing 37%, 9% and 8% of total landings by weight, and 13%, 1% and 8% of total value, respectively.", "Molluscs accounted for only 12% of total landings in weight, but 22% of total landings in value.", "Crustaceans were 0.6% of the total landings by weight and 5% by value.", "Fishing in foreign waters has decreased considerably since 1998, after the end of the fisheries agreement with Morocco and the renegotiation of the agreement with Mauritania.", "A new fisheries agreement between EU and Morocco has been reached, and started in March 2006, after a 7-year interval.", "In 1999, 40 Portuguese vessels were fishing in Moroccan waters, making Morocco the second-largest foreign fisheries ground at that time.", "In 2004, 15% of the total landings were from international waters from 59 registered vessels, mainly from the northwest Atlantic, northeast Atlantic (Norway, Svalbard, Spain and Greenland since 2003) and the central Atlantic (Guinea-Bissau, Cape Verde, Senegal, Mauritania).", "In the northwest Atlantic, redfish was the most important species, with 50% of total catches, while in Spain it was sardine and horse mackerel, with 36%.", "Off Norway and Svalbard, cod (\"bacalhau\" in Portuguese) was the most important species, accounting for 82% of total catches, while from Greenland, redfish was the only species landed.", "\"Bacalhau\" is indeed one of the most popular fishes used in Portuguese cuisine, along with sardine and tuna.", "The main landing sites in Portugal (including Azores and Madeira), according to total landings in weight by year, are the harbours of Matosinhos, Peniche, Olhão, Sesimbra, Figueira da Foz, Sines, Portimão and Madeira.", "The main objective of the national fisheries policy, particularly since 2002, is to maintain the sustainability of the sector and reverse the negative tendency of recent years.", "To achieve this objective, several measures have been adopted to promote recovery and stabilization of the fishing industry.", "At the same time, fleet renewal and modernization has been promoted in order to reduce production costs and improve work safety.", "Structural modernization of the fishing industry, as well as the processing industry and the aquaculture sector, are also promoted within the present fisheries management plan.", "These objectives are in accordance with those established by the EU in the Common Fishery Policy.", "The present national management system includes the establishment of annual quotas for some species and fishing areas, the application of technical conservation measures, and limitation of fishing effort.", "Fishing effort is controlled by a licensing system, where acquisition, construction or modification of vessels requires prior authorization.", "The use of certain fishing methods is also subject to prior authorization and annual licensing.", "The objective is to allow the modernization of the fishing fleet without increased fishing effort, by authorizing the construction of new vessels only as replacement of others; improving working conditions; and promoting conservation measures by encourage the use of less predatory fishing gear.", "There are species subject to quotas in national waters.", "Quotas can be allocated to individual vessels, as is the case for vessels operating in North Atlantic Fishery Organization (NAFO) and Norwegian fishing grounds; or to groups of vessels, as is the case for the purse seine fishery, where sardine catch limits are divided among Producer Organizations.", "Individual vessel quotas are also transferable within a shipowner's fleet to facilitate flexible management and therefore maximum utilization of these quotas.", "In 2004, 63 t of fish were landed by inland fisheries, with a value of US$642 000.", "The main species landed were shad (Alosa sp.), lamprey (Lampetra fluviatilis) and eels, with 49%, 29% and 16% of total landings from this fishery, respectively.", "Regarding fisheries management, purse-seine nets, bottom trawl, gill nets (except when targeting lamprey) and gear that uses tidal movements are prohibited in inland waters.", "There are also limitations on fishing areas and gear characteristics (mesh and gear size, amongst others).", "Recreational fishing is common and popular in inland fresh water streams, lakes, reservoirs and rivers.", "Every recreational fishing enthusiast desiring to use those kinds of national water resources for fishing, must respect rules and be aware of several limitations.", "A yearly individual fee must be paid to the state for fishing in suitable inland or oceanic waters.", "Until the mid-1980s, aquaculture production consisted of freshwater trout and bivalves bottom culture in tidal estuaries.", "However, marine aquaculture production showed an overall increase at the beginning of the 1990s, followed by a period of some fluctuation.", "Total production was 7 829 t in 2003, and consisted mainly of grooved carpet shell (\"Ruditapes decussatus\") (3 007 t), mussels (280 t), oyster (425 t), seabream (1 429 t) and seabass (1 384 t) from marine units; and trout (333 t) from freshwater units.", "Nowadays, both freshwater and marine aquaculture is well-established in Portugal producing from marine fin-fish and shellfish to micro-algae and trout.", "The objective of the national fisheries policy regarding aquaculture is to increase production and product diversity, but also to increase product quality, in order to improve the competitive position of the sector.", "Structural modernization of the aquaculture sector is also promoted within the present fisheries management plan.", "These objectives are in accordance with those established by the European Union in the Common Fisheries Policy, and in particular with the 2002 Strategy for the Sustainable Development of European Aquaculture, which promotes environmental, economic and social sustainability.", "One of the main aquaculture projects of Portugal is the Pescanova's production centre in Mira, Centro region.", "The southern Portuguese region of the Algarve is also a major aquaculture centre.", "In 2017, aquaculture production reached 12,549 tonnes, with a value of 83.2 million euros.", "These values correspond to an increase of 11.5% in quantity and to an increase of 10.6% in value, compared to the values of the previous year.", "There are many canned fish processing plants across Portugal, producing under different trademarked brands which are mostly exported.", "The mainland's principal ports specialized in canning small pelagic fish, most of which sardine, are Matosinhos-Póvoa de Varzim area, Peniche, and Olhão.", "In the Azores, the canned tuna fish industry is predominant, and most of the production is almost exclusively exported.", "A diversification drive is being attempted with the development of black scabbardfish canning industry, a barely exploited resource on the islands.", "Major fish processing companies include Briosa, Cofaco, Cofisa, Conserveira do Sul, Conservas Ramirez (the world's oldest canned fish producer still in operation), Fábrica de Conservas da Murtosa, Conservas Portugal Norte and the Portuguese branch of Pescanova.", "Portuguese processed fish products are exported through several companies under a number of different brands and registered trademarks like Ramirez, Bom Petisco, Briosa Gourmet, Combate, Comur, Conserveira, General, Inês, Líder, Manná, Murtosa, Pescador, Pitéu, Porthos, Tenório, Torreira, and Vasco da Gama.", "Portugal, as an Atlantic country and an historical seafaring nation, has a long tradition in the sector of fishing.", "It is among the countries in the world with the highest fish consumption per capita.", "Species like the sardine, Atlantic mackerel, tuna, and the European hake are important for the Portuguese commercial capture fisheries.", "Other, widely used species in Portuguese cuisine is the cod, known in Portugal as \"bacalhau\".", "Salt cod has been produced for at least 500 years, since the time of the European discoveries.", "Before refrigeration, there was a need to preserve the codfish; drying and salting are ancient techniques to keep many nutrients and the process makes the codfish tastier.", "The Portuguese tried to use this method of drying and salting several fishes from their waters, but the ideal fish came from much further north.", "With the \"discovery\" of Newfoundland in 1497, Portuguese fishermen started fishing its cod-rich Grand Banks.", "Thus, ' became a staple of the Portuguese cuisine, nicknamed ' (faithful friend).", "From the 18th century the town of Kristiansund in Norway became an important place of producing bacalao or klippfish, which is also exported to Portugal.", "In Portugal, there are several vocational and higher education institutions devoted to the teaching of fishing, fisheries, oceanography, marine biology and marine science in general.", "For example, the state-run polytechnic institute \"Instituto Politécnico de Leiria\" at Peniche, through its \"Escola Superior de Turismo e Tecnologia do Mar de Peniche\", has a school of marine technologies awarding bachelor's and master's degrees in these subjects.", "There are also a number of universities awarding bachelor's, masters' and doctorate degrees in varied marine science subfields, as well as making research and development work.", "The marine biology and marine sciences degrees awarded by the Marine and Environmental Sciences Faculty of the University of the Algarve are among the most prestigious in the country.", "The Instituto Nacional dos Recursos Biológicos (INRB) is the national research institute for agriculture and fisheries." ]

[ 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75 ]

[ "Both freshwater and marine aquaculture is well-established in Portugal producing from marine fin-fish and shellfish to micro-algae and trout." ]

[ "The fishing sector in Portugal faced deep structural changes in terms of both the volume of its business and its working conditions since adhesion to the European Economic Community in 1986.", "The fishing fleet dropped from 12,299 vessels of all kinds in 1994 to 10,933 in 1999, while the number of registered fishing workers fell from 31,721 to 27,191.", "The volume of imported fish increased by 31% from 1990 to 1999, whereas exports decreased by 0.4% over the same period.", "In 1997, 4,932 people were registered as employees in the fishing sector.", "In 2004, there were 10,089 vessels registered with a total size of 112,978 GT and a total power of 391 006 kW. These numbers indicate a reduction in overall fleet size since 1998 of approximately 9.9% in number, 1.5% in GT and 0.8% in power.", "Total catches fell from 224,000 tonnes in 1998 to 140,000 tonnes in 2004, a 38% decrease.", "As laid out in its Common Fisheries Policy, the European Union is seeking to establish a policy that determines priorities which will contribute to a sustainable balance between fisheries resources and their exploitation; increase the competitiveness of fishing enterprises and organisations; and develop viable enterprises.", "The EU has been paying special attention to the situation in Portugal both because of the characteristics of the Portuguese coastal area and the type of vessel used there.", "The Portuguese fishing fleet has changed significantly, both in size and in character, in order to adjust fishing capacity to the potential of national, EU, non-EU and international waters.", "Reflecting the current status of the national resources and restricted access to foreign fishing grounds, re-dimensioning of the fleet is part of the renovation and modernization process.", "During the 1990s and 2000s, new fishing vessels, with improved on-board fish conservation methods, automated work systems, and electronic navigation and fish detection systems, were gradually introduced to replace the ageing fishing vessels from the 1980s and before.", "Roman ruins of fish processing facilities were found across the Portuguese coast.", "Garum (a type of fermented fish sauce) of Lusitania (present-day Portugal) was highly prized in Rome.", "It was shipped to Rome directly from the harbour of Lacobriga (present-day Lagos).", "The fishing and fish processing industry was so important in the territory that ruins of a former Roman garum factory can be even visited today in the downtown of Lisbon's old quarter.", "Fish has been an important staple for the entire Portuguese population at least since the Portuguese Age of Discovery.", "The Portuguese population is among the world's largest per capita fish consumers.", "Portuguese cuisine includes a variety of fish and other seafood-based dishes, some of them renowned internationally.", "The main institution responsible for fisheries management is the Directorate-General of Fisheries and Aquaculture (DGPA), in association with the Assistant-Secretariat of State and the Ministry of Agriculture, Fisheries and Forests.", "The \"Instituto Nacional dos Recursos Biológicos\" (INRB), as well as the Producer Organizations and Shipowner's Associations, are consulted and have an advisory role in the decision-making process.", "INRB is also responsible for fish stock assessments within the International Council for the Exploration of the Sea (ICES) and the Northwest Atlantic Fisheries Organization (NAFO) frameworks.", "INRB uses information collected during research surveys and in fishing ports, and also the catch statistics provided by DGPA.", "At a national level, INRB has also the role of proposing technical measures to protect and maintain fish stocks.", "The Portuguese fishing industry is fairly large and diversified.", "Fishing vessels classified according to the area in which they operate, can be divided into local fishing vessels, coastal fishing vessels and long-distance fishing vessels.", "The local fleet is mainly composed of small traditional vessels (less than 5 GT), comprising, in 2004, 87% of the total fishing fleet and accounting for 8% of the total tonnage.", "These vessels are usually equipped to use more than one fishing method, such as hooks, gill nets and traps, and constitute the so-called polyvalent segment of the fleet.", "Their physical output is low but reasonable levels of income are attained by virtue of the high commercial value of the species they capture: octopus, black scabbardfish, conger, pouting, hake and anglerfish.", "Purse seine fishing is also part of the local fleet and has, on the mainland, only one target species: the sardine.", "This fishery represents 37% of total landings.", "The coastal fishing fleet accounted for only 13% of vessels but had the largest GT (93%).", "These vessels operate in areas farther from the coast, and even outside the Portugal's Exclusive Economic Zone.", "The coastal fishing fleet comprises polyvalent, purse seine and trawl fishing vessels.", "The trawlers operate only on the mainland shelf and target demersal species such as horse mackerel, blue whiting, octopus and crustaceans.", "The crustacean trawling fishery targets Norway lobster, red shrimp and deepwater rose shrimp.", "The most important fish species landed in Portugal in 2004 were sardine, mackerel and horse mackerel, representing 37%, 9% and 8% of total landings by weight, and 13%, 1% and 8% of total value, respectively.", "Molluscs accounted for only 12% of total landings in weight, but 22% of total landings in value.", "Crustaceans were 0.6% of the total landings by weight and 5% by value.", "Fishing in foreign waters has decreased considerably since 1998, after the end of the fisheries agreement with Morocco and the renegotiation of the agreement with Mauritania.", "A new fisheries agreement between EU and Morocco has been reached, and started in March 2006, after a 7-year interval.", "In 1999, 40 Portuguese vessels were fishing in Moroccan waters, making Morocco the second-largest foreign fisheries ground at that time.", "In 2004, 15% of the total landings were from international waters from 59 registered vessels, mainly from the northwest Atlantic, northeast Atlantic (Norway, Svalbard, Spain and Greenland since 2003) and the central Atlantic (Guinea-Bissau, Cape Verde, Senegal, Mauritania).", "In the northwest Atlantic, redfish was the most important species, with 50% of total catches, while in Spain it was sardine and horse mackerel, with 36%.", "Off Norway and Svalbard, cod (\"bacalhau\" in Portuguese) was the most important species, accounting for 82% of total catches, while from Greenland, redfish was the only species landed.", "\"Bacalhau\" is indeed one of the most popular fishes used in Portuguese cuisine, along with sardine and tuna.", "The main landing sites in Portugal (including Azores and Madeira), according to total landings in weight by year, are the harbours of Matosinhos, Peniche, Olhão, Sesimbra, Figueira da Foz, Sines, Portimão and Madeira.", "The main objective of the national fisheries policy, particularly since 2002, is to maintain the sustainability of the sector and reverse the negative tendency of recent years.", "To achieve this objective, several measures have been adopted to promote recovery and stabilization of the fishing industry.", "At the same time, fleet renewal and modernization has been promoted in order to reduce production costs and improve work safety.", "Structural modernization of the fishing industry, as well as the processing industry and the aquaculture sector, are also promoted within the present fisheries management plan.", "These objectives are in accordance with those established by the EU in the Common Fishery Policy.", "The present national management system includes the establishment of annual quotas for some species and fishing areas, the application of technical conservation measures, and limitation of fishing effort.", "Fishing effort is controlled by a licensing system, where acquisition, construction or modification of vessels requires prior authorization.", "The use of certain fishing methods is also subject to prior authorization and annual licensing.", "The objective is to allow the modernization of the fishing fleet without increased fishing effort, by authorizing the construction of new vessels only as replacement of others; improving working conditions; and promoting conservation measures by encourage the use of less predatory fishing gear.", "There are species subject to quotas in national waters.", "Quotas can be allocated to individual vessels, as is the case for vessels operating in North Atlantic Fishery Organization (NAFO) and Norwegian fishing grounds; or to groups of vessels, as is the case for the purse seine fishery, where sardine catch limits are divided among Producer Organizations.", "Individual vessel quotas are also transferable within a shipowner's fleet to facilitate flexible management and therefore maximum utilization of these quotas.", "In 2004, 63 t of fish were landed by inland fisheries, with a value of US$642 000.", "The main species landed were shad (Alosa sp.), lamprey (Lampetra fluviatilis) and eels, with 49%, 29% and 16% of total landings from this fishery, respectively.", "Regarding fisheries management, purse-seine nets, bottom trawl, gill nets (except when targeting lamprey) and gear that uses tidal movements are prohibited in inland waters.", "There are also limitations on fishing areas and gear characteristics (mesh and gear size, amongst others).", "Recreational fishing is common and popular in inland fresh water streams, lakes, reservoirs and rivers.", "Every recreational fishing enthusiast desiring to use those kinds of national water resources for fishing, must respect rules and be aware of several limitations.", "A yearly individual fee must be paid to the state for fishing in suitable inland or oceanic waters.", "Until the mid-1980s, aquaculture production consisted of freshwater trout and bivalves bottom culture in tidal estuaries.", "However, marine aquaculture production showed an overall increase at the beginning of the 1990s, followed by a period of some fluctuation.", "Total production was 7 829 t in 2003, and consisted mainly of grooved carpet shell (\"Ruditapes decussatus\") (3 007 t), mussels (280 t), oyster (425 t), seabream (1 429 t) and seabass (1 384 t) from marine units; and trout (333 t) from freshwater units.", "Nowadays, both freshwater and marine aquaculture is well-established in Portugal producing from marine fin-fish and shellfish to micro-algae and trout.", "The objective of the national fisheries policy regarding aquaculture is to increase production and product diversity, but also to increase product quality, in order to improve the competitive position of the sector.", "Structural modernization of the aquaculture sector is also promoted within the present fisheries management plan.", "These objectives are in accordance with those established by the European Union in the Common Fisheries Policy, and in particular with the 2002 Strategy for the Sustainable Development of European Aquaculture, which promotes environmental, economic and social sustainability.", "One of the main aquaculture projects of Portugal is the Pescanova's production centre in Mira, Centro region.", "The southern Portuguese region of the Algarve is also a major aquaculture centre.", "In 2017, aquaculture production reached 12,549 tonnes, with a value of 83.2 million euros.", "These values correspond to an increase of 11.5% in quantity and to an increase of 10.6% in value, compared to the values of the previous year.", "There are many canned fish processing plants across Portugal, producing under different trademarked brands which are mostly exported.", "The mainland's principal ports specialized in canning small pelagic fish, most of which sardine, are Matosinhos-Póvoa de Varzim area, Peniche, and Olhão.", "In the Azores, the canned tuna fish industry is predominant, and most of the production is almost exclusively exported.", "A diversification drive is being attempted with the development of black scabbardfish canning industry, a barely exploited resource on the islands.", "Major fish processing companies include Briosa, Cofaco, Cofisa, Conserveira do Sul, Conservas Ramirez (the world's oldest canned fish producer still in operation), Fábrica de Conservas da Murtosa, Conservas Portugal Norte and the Portuguese branch of Pescanova.", "Portuguese processed fish products are exported through several companies under a number of different brands and registered trademarks like Ramirez, Bom Petisco, Briosa Gourmet, Combate, Comur, Conserveira, General, Inês, Líder, Manná, Murtosa, Pescador, Pitéu, Porthos, Tenório, Torreira, and Vasco da Gama.", "Portugal, as an Atlantic country and an historical seafaring nation, has a long tradition in the sector of fishing.", "It is among the countries in the world with the highest fish consumption per capita.", "Species like the sardine, Atlantic mackerel, tuna, and the European hake are important for the Portuguese commercial capture fisheries.", "Other, widely used species in Portuguese cuisine is the cod, known in Portugal as \"bacalhau\".", "Salt cod has been produced for at least 500 years, since the time of the European discoveries.", "Before refrigeration, there was a need to preserve the codfish; drying and salting are ancient techniques to keep many nutrients and the process makes the codfish tastier.", "The Portuguese tried to use this method of drying and salting several fishes from their waters, but the ideal fish came from much further north.", "With the \"discovery\" of Newfoundland in 1497, Portuguese fishermen started fishing its cod-rich Grand Banks.", "Thus, ' became a staple of the Portuguese cuisine, nicknamed ' (faithful friend).", "From the 18th century the town of Kristiansund in Norway became an important place of producing bacalao or klippfish, which is also exported to Portugal.", "In Portugal, there are several vocational and higher education institutions devoted to the teaching of fishing, fisheries, oceanography, marine biology and marine science in general.", "For example, the state-run polytechnic institute \"Instituto Politécnico de Leiria\" at Peniche, through its \"Escola Superior de Turismo e Tecnologia do Mar de Peniche\", has a school of marine technologies awarding bachelor's and master's degrees in these subjects.", "There are also a number of universities awarding bachelor's, masters' and doctorate degrees in varied marine science subfields, as well as making research and development work.", "The marine biology and marine sciences degrees awarded by the Marine and Environmental Sciences Faculty of the University of the Algarve are among the most prestigious in the country.", "The Instituto Nacional dos Recursos Biológicos (INRB) is the national research institute for agriculture and fisheries." ]

[ 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75 ]

[ "Both freshwater and marine aquaculture is well-established in Portugal producing from marine fin-fish and shellfish to micro-algae and trout." ]

[ "The fishing sector in Portugal faced deep structural changes in terms of both the volume of its business and its working conditions since adhesion to the European Economic Community in 1986.", "The fishing fleet dropped from 12,299 vessels of all kinds in 1994 to 10,933 in 1999, while the number of registered fishing workers fell from 31,721 to 27,191.", "The volume of imported fish increased by 31% from 1990 to 1999, whereas exports decreased by 0.4% over the same period.", "In 1997, 4,932 people were registered as employees in the fishing sector.", "In 2004, there were 10,089 vessels registered with a total size of 112,978 GT and a total power of 391 006 kW. These numbers indicate a reduction in overall fleet size since 1998 of approximately 9.9% in number, 1.5% in GT and 0.8% in power.", "Total catches fell from 224,000 tonnes in 1998 to 140,000 tonnes in 2004, a 38% decrease.", "As laid out in its Common Fisheries Policy, the European Union is seeking to establish a policy that determines priorities which will contribute to a sustainable balance between fisheries resources and their exploitation; increase the competitiveness of fishing enterprises and organisations; and develop viable enterprises.", "The EU has been paying special attention to the situation in Portugal both because of the characteristics of the Portuguese coastal area and the type of vessel used there.", "The Portuguese fishing fleet has changed significantly, both in size and in character, in order to adjust fishing capacity to the potential of national, EU, non-EU and international waters.", "Reflecting the current status of the national resources and restricted access to foreign fishing grounds, re-dimensioning of the fleet is part of the renovation and modernization process.", "During the 1990s and 2000s, new fishing vessels, with improved on-board fish conservation methods, automated work systems, and electronic navigation and fish detection systems, were gradually introduced to replace the ageing fishing vessels from the 1980s and before.", "Roman ruins of fish processing facilities were found across the Portuguese coast.", "Garum (a type of fermented fish sauce) of Lusitania (present-day Portugal) was highly prized in Rome.", "It was shipped to Rome directly from the harbour of Lacobriga (present-day Lagos).", "The fishing and fish processing industry was so important in the territory that ruins of a former Roman garum factory can be even visited today in the downtown of Lisbon's old quarter.", "Fish has been an important staple for the entire Portuguese population at least since the Portuguese Age of Discovery.", "The Portuguese population is among the world's largest per capita fish consumers.", "Portuguese cuisine includes a variety of fish and other seafood-based dishes, some of them renowned internationally.", "The main institution responsible for fisheries management is the Directorate-General of Fisheries and Aquaculture (DGPA), in association with the Assistant-Secretariat of State and the Ministry of Agriculture, Fisheries and Forests.", "The \"Instituto Nacional dos Recursos Biológicos\" (INRB), as well as the Producer Organizations and Shipowner's Associations, are consulted and have an advisory role in the decision-making process.", "INRB is also responsible for fish stock assessments within the International Council for the Exploration of the Sea (ICES) and the Northwest Atlantic Fisheries Organization (NAFO) frameworks.", "INRB uses information collected during research surveys and in fishing ports, and also the catch statistics provided by DGPA.", "At a national level, INRB has also the role of proposing technical measures to protect and maintain fish stocks.", "The Portuguese fishing industry is fairly large and diversified.", "Fishing vessels classified according to the area in which they operate, can be divided into local fishing vessels, coastal fishing vessels and long-distance fishing vessels.", "The local fleet is mainly composed of small traditional vessels (less than 5 GT), comprising, in 2004, 87% of the total fishing fleet and accounting for 8% of the total tonnage.", "These vessels are usually equipped to use more than one fishing method, such as hooks, gill nets and traps, and constitute the so-called polyvalent segment of the fleet.", "Their physical output is low but reasonable levels of income are attained by virtue of the high commercial value of the species they capture: octopus, black scabbardfish, conger, pouting, hake and anglerfish.", "Purse seine fishing is also part of the local fleet and has, on the mainland, only one target species: the sardine.", "This fishery represents 37% of total landings.", "The coastal fishing fleet accounted for only 13% of vessels but had the largest GT (93%).", "These vessels operate in areas farther from the coast, and even outside the Portugal's Exclusive Economic Zone.", "The coastal fishing fleet comprises polyvalent, purse seine and trawl fishing vessels.", "The trawlers operate only on the mainland shelf and target demersal species such as horse mackerel, blue whiting, octopus and crustaceans.", "The crustacean trawling fishery targets Norway lobster, red shrimp and deepwater rose shrimp.", "The most important fish species landed in Portugal in 2004 were sardine, mackerel and horse mackerel, representing 37%, 9% and 8% of total landings by weight, and 13%, 1% and 8% of total value, respectively.", "Molluscs accounted for only 12% of total landings in weight, but 22% of total landings in value.", "Crustaceans were 0.6% of the total landings by weight and 5% by value.", "Fishing in foreign waters has decreased considerably since 1998, after the end of the fisheries agreement with Morocco and the renegotiation of the agreement with Mauritania.", "A new fisheries agreement between EU and Morocco has been reached, and started in March 2006, after a 7-year interval.", "In 1999, 40 Portuguese vessels were fishing in Moroccan waters, making Morocco the second-largest foreign fisheries ground at that time.", "In 2004, 15% of the total landings were from international waters from 59 registered vessels, mainly from the northwest Atlantic, northeast Atlantic (Norway, Svalbard, Spain and Greenland since 2003) and the central Atlantic (Guinea-Bissau, Cape Verde, Senegal, Mauritania).", "In the northwest Atlantic, redfish was the most important species, with 50% of total catches, while in Spain it was sardine and horse mackerel, with 36%.", "Off Norway and Svalbard, cod (\"bacalhau\" in Portuguese) was the most important species, accounting for 82% of total catches, while from Greenland, redfish was the only species landed.", "\"Bacalhau\" is indeed one of the most popular fishes used in Portuguese cuisine, along with sardine and tuna.", "The main landing sites in Portugal (including Azores and Madeira), according to total landings in weight by year, are the harbours of Matosinhos, Peniche, Olhão, Sesimbra, Figueira da Foz, Sines, Portimão and Madeira.", "The main objective of the national fisheries policy, particularly since 2002, is to maintain the sustainability of the sector and reverse the negative tendency of recent years.", "To achieve this objective, several measures have been adopted to promote recovery and stabilization of the fishing industry.", "At the same time, fleet renewal and modernization has been promoted in order to reduce production costs and improve work safety.", "Structural modernization of the fishing industry, as well as the processing industry and the aquaculture sector, are also promoted within the present fisheries management plan.", "These objectives are in accordance with those established by the EU in the Common Fishery Policy.", "The present national management system includes the establishment of annual quotas for some species and fishing areas, the application of technical conservation measures, and limitation of fishing effort.", "Fishing effort is controlled by a licensing system, where acquisition, construction or modification of vessels requires prior authorization.", "The use of certain fishing methods is also subject to prior authorization and annual licensing.", "The objective is to allow the modernization of the fishing fleet without increased fishing effort, by authorizing the construction of new vessels only as replacement of others; improving working conditions; and promoting conservation measures by encourage the use of less predatory fishing gear.", "There are species subject to quotas in national waters.", "Quotas can be allocated to individual vessels, as is the case for vessels operating in North Atlantic Fishery Organization (NAFO) and Norwegian fishing grounds; or to groups of vessels, as is the case for the purse seine fishery, where sardine catch limits are divided among Producer Organizations.", "Individual vessel quotas are also transferable within a shipowner's fleet to facilitate flexible management and therefore maximum utilization of these quotas.", "In 2004, 63 t of fish were landed by inland fisheries, with a value of US$642 000.", "The main species landed were shad (Alosa sp.), lamprey (Lampetra fluviatilis) and eels, with 49%, 29% and 16% of total landings from this fishery, respectively.", "Regarding fisheries management, purse-seine nets, bottom trawl, gill nets (except when targeting lamprey) and gear that uses tidal movements are prohibited in inland waters.", "There are also limitations on fishing areas and gear characteristics (mesh and gear size, amongst others).", "Recreational fishing is common and popular in inland fresh water streams, lakes, reservoirs and rivers.", "Every recreational fishing enthusiast desiring to use those kinds of national water resources for fishing, must respect rules and be aware of several limitations.", "A yearly individual fee must be paid to the state for fishing in suitable inland or oceanic waters.", "Until the mid-1980s, aquaculture production consisted of freshwater trout and bivalves bottom culture in tidal estuaries.", "However, marine aquaculture production showed an overall increase at the beginning of the 1990s, followed by a period of some fluctuation.", "Total production was 7 829 t in 2003, and consisted mainly of grooved carpet shell (\"Ruditapes decussatus\") (3 007 t), mussels (280 t), oyster (425 t), seabream (1 429 t) and seabass (1 384 t) from marine units; and trout (333 t) from freshwater units.", "Nowadays, both freshwater and marine aquaculture is well-established in Portugal producing from marine fin-fish and shellfish to micro-algae and trout.", "The objective of the national fisheries policy regarding aquaculture is to increase production and product diversity, but also to increase product quality, in order to improve the competitive position of the sector.", "Structural modernization of the aquaculture sector is also promoted within the present fisheries management plan.", "These objectives are in accordance with those established by the European Union in the Common Fisheries Policy, and in particular with the 2002 Strategy for the Sustainable Development of European Aquaculture, which promotes environmental, economic and social sustainability.", "One of the main aquaculture projects of Portugal is the Pescanova's production centre in Mira, Centro region.", "The southern Portuguese region of the Algarve is also a major aquaculture centre.", "In 2017, aquaculture production reached 12,549 tonnes, with a value of 83.2 million euros.", "These values correspond to an increase of 11.5% in quantity and to an increase of 10.6% in value, compared to the values of the previous year.", "There are many canned fish processing plants across Portugal, producing under different trademarked brands which are mostly exported.", "The mainland's principal ports specialized in canning small pelagic fish, most of which sardine, are Matosinhos-Póvoa de Varzim area, Peniche, and Olhão.", "In the Azores, the canned tuna fish industry is predominant, and most of the production is almost exclusively exported.", "A diversification drive is being attempted with the development of black scabbardfish canning industry, a barely exploited resource on the islands.", "Major fish processing companies include Briosa, Cofaco, Cofisa, Conserveira do Sul, Conservas Ramirez (the world's oldest canned fish producer still in operation), Fábrica de Conservas da Murtosa, Conservas Portugal Norte and the Portuguese branch of Pescanova.", "Portuguese processed fish products are exported through several companies under a number of different brands and registered trademarks like Ramirez, Bom Petisco, Briosa Gourmet, Combate, Comur, Conserveira, General, Inês, Líder, Manná, Murtosa, Pescador, Pitéu, Porthos, Tenório, Torreira, and Vasco da Gama.", "Portugal, as an Atlantic country and an historical seafaring nation, has a long tradition in the sector of fishing.", "It is among the countries in the world with the highest fish consumption per capita.", "Species like the sardine, Atlantic mackerel, tuna, and the European hake are important for the Portuguese commercial capture fisheries.", "Other, widely used species in Portuguese cuisine is the cod, known in Portugal as \"bacalhau\".", "Salt cod has been produced for at least 500 years, since the time of the European discoveries.", "Before refrigeration, there was a need to preserve the codfish; drying and salting are ancient techniques to keep many nutrients and the process makes the codfish tastier.", "The Portuguese tried to use this method of drying and salting several fishes from their waters, but the ideal fish came from much further north.", "With the \"discovery\" of Newfoundland in 1497, Portuguese fishermen started fishing its cod-rich Grand Banks.", "Thus, ' became a staple of the Portuguese cuisine, nicknamed ' (faithful friend).", "From the 18th century the town of Kristiansund in Norway became an important place of producing bacalao or klippfish, which is also exported to Portugal.", "In Portugal, there are several vocational and higher education institutions devoted to the teaching of fishing, fisheries, oceanography, marine biology and marine science in general.", "For example, the state-run polytechnic institute \"Instituto Politécnico de Leiria\" at Peniche, through its \"Escola Superior de Turismo e Tecnologia do Mar de Peniche\", has a school of marine technologies awarding bachelor's and master's degrees in these subjects.", "There are also a number of universities awarding bachelor's, masters' and doctorate degrees in varied marine science subfields, as well as making research and development work.", "The marine biology and marine sciences degrees awarded by the Marine and Environmental Sciences Faculty of the University of the Algarve are among the most prestigious in the country.", "The Instituto Nacional dos Recursos Biológicos (INRB) is the national research institute for agriculture and fisheries." ]

[ 82, 83, 84, 85, 86, 87, 88, 89, 90, 91 ]

[ "The country has a long tradition in the sector, and is among the countries in the world with the highest fish consumption per capita." ]

[ "Following the announcement of their separation, RBD said that they planned a last tour to say goodbye.", "The tour included about 20 shows in countries such as Argentina, Venezuela, Ecuador, Paraguay, Chile, and Brazil.", "In the month of November 2008, the group began the tour in the following cities: La Paz (Bolivia), Buenos Aires, Cordoba and Rosario (Argentina), Fortaleza, Porto Alegre, Rio de Janeiro, São Paulo and Brasília (Brazil).", "In December, shows by RBD were presented in the cities of Los Angeles (United States), then back to Brazil for two extra concerts in São Paulo and Rio de Janeiro; Guayaquil, Quito (Ecuador ), Lima (Peru), Santiago (Chile), Ljubljana (Slovenia), Belgrade (Serbia), and Madrid Spain.", "The special \"O Adeus\" was broadcast by television network Rede Record (Brazil).", "The group officially disbanded on March 10, 2009 with the launch of its latest studio album of (\"Para Olvidarte De Mí\"), but with one last special, \"O Adeus\" (\"The Goodbye\"), the \"Turnê Do Adeus\" (Gira Del Adiós or Tour Del Adiós).", "#\"Cariño Mío\"\n#\"Aún Hay Algo\"\n#\"Celestial\"\n#\"Un Poco de tu Amor\"\n#\"Otro Día que Va\"\n#\"Ser o Parecer\"\n#\"Hoy Que Te Vas\"\n#\"Solo Quédate en Silencio\"\n#\"Inalcanzable\"\n#\"Y No Puedo Olvidarte\"\n#\"Light up The World Tonight\"\n#\"Sálvame\"\n#\"Este Corazón\"\n#\"Tu Amor\"\n#\"No Pares\"\n#\"Empezar Desde Cero\"\n#\"Solo Para Ti\"\n#\"Me Voy\"\n#\"Qué Hay Detrás\"\n#\"Bésame Sin Miedo\"\n#\"Nuestro Amor\"\n#\"Tras de Mí\"\n#\"Rebelde\"" ]

[ 4, 5 ]

[ "Gira Del Adiós (Turnê Do Adeus in Brazil) is the fifth and final world tour by Mexican group RBD." ]

[ "Born in Toronto, Ontario, Vernace grew up playing most of his minor hockey in the Greater Toronto Hockey League, finishing his minor career with the 2001–02 Mississauga Reps Bantams.", "After that season, Vernace was a 9th round choice (163rd overall) in the 2001 OHL Priority Selection by the Brampton Battalion.", "The following season, Vernace was assigned by the Battalion to the OHA Jr.A. Bramalea Blues.", "Vernace was drafted 201st overall by the San Jose Sharks in the 2004 NHL Entry Draft from the Brampton Battalion of the Ontario Hockey League.", "He attended Chaminade College School for his high school education.", "On June 1, 2006, Vernace was traded by the Sharks to the Colorado Avalanche for a 6th round drafts pick and was signed to an entry level contract.", "Vernace made his professional debut with the Arizona Sundogs of the CHL before joining the Avalanche's affiliate the Albany River Rats of the AHL in the 2006–07 season.", "Vernace joined new Avalanche affiliate, the Lake Erie Monsters, for their inaugural season in the 2007–08 season, leading the Monsters in games played with 79.", "After spending the majority of the 2008–09 season with the Monsters, Vernace received his first NHL call-up on March 16, 2009.", "He made his NHL debut with the Avalanche in a 3–2 shootout loss to the Minnesota Wild on March 17, 2009.", "After not being offered a contract with the Avalanche, Vernace a free agent, signed a one-year deal with the Atlanta Thrashers on July 30, 2009.", "On September 26, 2009, Vernace was assigned to AHL affiliate, the Chicago Wolves, for the beginning of the 2009–10 season.", "After 47 games with the Wolves, Vernace was then reassigned to the Hamilton Bulldogs on March 10, 2010.", "He recorded 4 assists in 18 post season games to help the Bulldogs reach the Western Conference finals.", "On June 23, 2010, Vernace was traded by the Thrashers, along with Brett Sterling and a 7th round selection in 2010 NHL Entry Draft, back to the Sharks for future considerations in order to help the Thrashers facilitate an earlier trade of Dustin Byfuglien from the Chicago Blackhawks.", "Unable to come to terms with San Jose, Vernace signed as a free agent with the Tampa Bay Lightning on July 29, 2010, to a one-year, two-way contract.", "In the 2011–12 season, on December 2, 2011, Vernace was traded by the Lightning, along with James Wright, to the Florida Panthers for Mike Kostka and Evan Oberg.", "Assigned to AHL affiliate, the San Antonio Rampage, his tenure was short lived when on February 25, 2012, Vernace was traded by the Panthers to the New York Rangers, along with a third round pick in the 2013 NHL Entry Draft, for Wojtek Wolski, Vernace's former teammate from the Brampton Battalion.", "After two seasons within the Rangers organization, Vernace left as a free agent to sign his first European contract in Germany on a one-year deal with Adler Mannheim of the Deutsche Eishockey Liga on August 8, 2013.", "After 18 points in 51 games with Mannheim, Vernace belatedly signed in the Swedish second division the following season, signing for the remainder of the 2014–15 season with Rögle BK on December 11, 2014.", "Vernace played two seasons in Europe, before opting for a return to North America and with the 2015–16 season underway, signed a contract with the Brampton Beast of the ECHL on October 28, 2015." ]

[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ]

[ "Michael Vernace (born May 26, 1986) is a Canadian former professional ice hockey defenseman.", "He played in the National Hockey League with the Colorado Avalanche and the Tampa Bay Lightning." ]

[ "The House and Senate Afterschool Caucuses were founded on March 3, 2005.", "In addition to the co-chairs, the founding members of Senate and House Afterschool Caucuses are Senators Barbara Boxer (D-CA) and Susan Collins (R-ME) and Representative Dale Kildee (D-MI).", "Today, these Caucuses serve as a voice on the issue of strengthening and increasing the availability of afterschool programs.", "The Caucuses were formed in response to the finding that 14.3 million children go home alone after the school day ends, including more than 40,000 kindergartners and almost four million middle school students in grades six to eight.", "The Caucuses act to promote the availability of afterschool programs, with a special emphasis on the 21st Century Community Learning Center (CCLC) program, for every American school-age child by increasing public awareness of such programs and supporting increased federal resources.", "In each chamber, the Caucuses have conducted a variety of activities supporting the goal of quality, affordable programs for all children.", "This has included organizing congressional briefings on specific topics such as the role of the STEM fields in afterschool (science, technology, engineering and mathematics) education; disseminating letters in support of increased resources for afterschool to the President as well as congressional colleagues; sharing new research on effective programs; and organizing press events around the Afterschool Challenge with celebrity supporters.", "The Afterschool Caucuses seek to educate the public on the role that afterschool programs play in the lives of families, and promote the expansion of federal, state, and local support in order to make access to these programs a reality for all interested children and families.", "The Afterschool Caucuses are nonpartisan.", "As of March 2021 there were a total of 40 members in the House Afterschool Caucus with 37 Democrats and 3 Republicans and 25 members of the Senate Afterschool Caucus with 6 Republicans and 19 Democrats." ]

[ 3, 4, 5, 6, 7 ]

[ "The Afterschool Caucuses in the United States Senate and House of Representatives were established in order to build support for afterschool programs and increase resources for afterschool care." ]

[ "Hutton was born 6 May 1955, in London, though his family moved to Westcliff-on-Sea, Essex when he was 8.", "He was educated at Westcliff High School for Boys and Magdalen College, Oxford, where he joined the Conservative, Liberal and Labour Associations and gained a BA in 1976 and a BCL 1978.", "He worked for a year as a bus driver.", "For two years he was a legal adviser to the CBI.", "From 1980–81, he was a research associate for Templeton College, Oxford.", "He went on to become a senior law lecturer at the Newcastle Polytechnic from 1981–92 before turning back to politics.", "Hutton first stood for election in the Penrith and the Borders seat in 1987.", "Two years later, he also failed to be elected as a Member of the European Parliament (MEP) for the Cumbria and North Lancashire region.", "His election to the Barrow and Furness seat in the 1992 general election saw him replace Cecil Franks as MP with a majority of 3,578.", "His majority increased to 14,497 in the Labour landslide of the 1997 Election.", "After being a part of the Department of Health from 1998, he was made a member of the Privy Council in 2001.", "In the reshuffle following the 2005 general election (in which his majority fell to just over 6,000), he was made Chancellor of the Duchy of Lancaster and Minister for the Cabinet Office, replacing his close friend and former flatmate, Alan Milburn.", "His position in this role was short lived, however.", "Following the second resignation of David Blunkett, Hutton was appointed as his replacement in the role of Secretary of State for Work and Pensions on 2 November 2005.", "Hutton was seen as one of Tony Blair's closest supporters but survived in cabinet following Blair's resignation in June 2007 and was moved by new Prime Minister Gordon Brown to be Secretary of State for Business, Enterprise and Regulatory Reform, which incorporated the bulk of portfolios from the now dissolved Department of Trade and Industry, including Energy security issues which many had expected to be ceded to DEFRA.", "In September 2006, while discussing the forthcoming Labour Party leadership election, Hutton gave an anonymous quote to BBC journalist Nick Robinson that Gordon Brown would be a \"fucking disaster\" as prime minister.", "He was moved into the role of Secretary of State for Defence in the cabinet reshuffle on 3 October 2008.", "On 5 June 2009, Hutton resigned his Cabinet position and announced his intention to stand down as an MP at the next general election.", "Hutton gave evidence to the Iraq Inquiry about his role as Defence Secretary on 25 January 2010, the same day as his predecessor, Des Browne.", "On 27 June 2010, he was created a life peer as Baron Hutton of Furness, \"of Aldingham in the County of Cumbria\", and was introduced in the House of Lords on 1 July 2010, where he sits on the Labour benches.", "In June 2010, it was announced that Hutton had joined the board of US nuclear power company Hyperion Power Generation.", "The Advisory Committee on Business Appointments stipulated that he should not lobby his former department for 12 months.", "It was also announced in June 2010, that the Conservative –", "Lib Dem coalition had asked him to head a commission into public sector pensions.", "His initial report was published in October 2010.", "The final report was published in March 2011.", "On 19 June 2011, Hutton rejected claims by trade unionists and Labour colleagues that he had been used as a 'stooge' by the government and dismissed speculation regarding his motives for accepting the coalition's invitation.", "Hutton became Chairman of the Nuclear Industry Association in June 2011.", "John Hutton married Rosemary Caroline Little in 1978 in Oxford.", "They had three sons, Jack, George, and Edward, author of the NHS's 'Urgent Care:", "Case For Change' project, as well as a daughter, Freya, before divorcing in 1993.", "John has multiple grandchildren from his sons Jack and Edward, and his daughter, Freya.", "He married civil servant Heather Rogers in 2004.", "He is a member of Cemetery Cottages Working Men's Club, Barrow.", "In 2008 John Hutton's first book was published, a non-fiction book with the title \"Kitchener's Men – The King's Own Royal Lancasters on the Western Front 1915–18\".", "In it, Hutton gives a \"graphic insight into the daily routine and grim reality of warfare on the Western Front for men who were mostly recruited from the Furness area of the North-West.", "This was followed in 2010 by 'August 1914, Surrender at St. Quentin'.", "He has also co-authored the book 'How to be a minister – a 21st-century guide' with Sir Leigh Lewis.", "It was published in September 2014." ]

[ 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 ]

[ "John Matthew Patrick Hutton, Baron Hutton of Furness, (born 6 May 1955) is a British Labour Party politician who was Member of Parliament (MP) for Barrow and Furness from 1992 to 2010 and served in a number of Cabinet offices, including Defence Secretary and Business Secretary." ]

[ "Lysine is a proteinaceous diamino acid (i.e. a component of proteins), and is accordingly coded by codons of the genetic material.", "In the pH range found inside living cells, both the amino groups are protonated, and they can be classified therefore as cationic amino acids.", "Ornithine is a non-proteinaceous diamino acid.", "In biochemistry, diamino acids are of particular interest.", "Diamino acids are used for the synthesis of specific peptide nucleic acids, such as daPNA.", "Artificial peptide nucleic acids are capable of forming duplex structures with individual DNA- and RNA-strands and are, therefore, not only called DNA-analog, but also they are considered as candidates for the first genetic material on Earth.", "The corresponding diamino acids such as 2,3-diaminopropanoic acid were detected in the Murchison meteorite and in a simulated comet." ]

[ 0, 1, 2, 3, 4, 5, 6 ]

[ "Diamino acids belong to the class of amino acids." ]

[ "Guachochi is one of the 67 municipalities of Chihuahua, in northern Mexico.", "The municipal seat lies at Guachochi.", "The municipality covers an area of 4,340.35 km².", "It was created by the State Congress on 31 December 1962, with its excision from the municipality of Batopilas.", "As of 2010, the municipality had a total population of 49,689, up from 45,881 as of 2005.", "As of 2010, the city of Guachochi had a population of 14,513.", "Other than the city of Guachochi, the municipality had 1,508 localities, the largest of which (with 2010 populations in parentheses) was: Samachique (1,241), classified as rural.", "The municipality has 1,134 localities.", "The largest are:", "The settlement was founded by Jesuit missionaries in the mid-18th century.", "In 1952 Guachochi, then only a small village, was chosen as the location of one of the first two Indigenous Centres of the National Institute of Indigenous Peoples (INI).", "It is the seat of the Roman Catholic Diocese of Tarahumara.", "The area around Guachochi is rich in history, and old Jesuit missions are kept in several communities.", "Guachochi was established in the middle of the 18th century as part of a mission, whose name was Guachochi.", "The original mission buildings no longer exist.", "Tónachi, Yoquivo, the temple of Our Lady of Loreto of Yoquivo, and the temple of Our Lady of Pilar de Norogachi, in Norogachi are places where old Jesuit buildings are still conserved.", "Guachochi is home to XETAR-AM, a government-run community radio station that broadcasts to the local area in Spanish, Rarámuri and Tepehuano." ]

[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]

[ "Guachochi is a city in the south-western portion of the Mexican state of Chihuahua.", "The city of Guachochi serves as the municipal seat for the surrounding municipality of the same name.", "As of 2010, the city of Guachochi had a population of 14,513, up from 12,385 in 2005." ]

[ "It operates the Boeing KC-135 Stratotanker aircraft conducting aerial refueling missions.", "Activated in late 1943 as a Douglas C-47 Skytrain troop carrier squadron, trained under I Troop Carrier Command in the United States.", "Was not deployed until the spring of 1945 to England, being assigned to the IX Troop Carrier Command.", "Was not used in combat operations, however did transport supplies and equipment to the front-line ground forces primarily into Germany and evacuated casualties to rear areas.", "Returned to the United States in September 1945 and was a transport squadron for Continental Air Forces until its inactivation in September 1946.", "It trained in the reserve for troop carrier missions from, 1949–1951, for fighter-bomber missions from, 1952–1957, and resumed its current role as an airlift squadron in 1957 until 1976.", "The squadron has performed air refueling missions worldwide since 1977 and maintained an alert responsibility for Strategic Air Command until the command's inactivation in June 1992.", "It deployed aircraft and personnel to Saudi Arabia and European locations in support of the Gulf War and later contingency operations in Somalia and the Balkans.", "The squadron was inactivated in 2009 pursuant to 2005 Base Realignment and Closure Commission action that eliminated the 940th Air Refueling Wing's KC-135 flying mission and redesignated it as the 940th Wing as an associate unit to the 9th Reconnaissance Wing in support of RQ-4 Global Hawk remotely piloted (e.g., unmanned) aircraft operations.", "In 2016, the wing returned to its former designation as an air refueling wing and reacquired its manned flying mission and KC-135R aircraft, with the reactivation of the squadron occurring the same year.", "Activated on 1 November 1943\n Inactivated on 31 July 1946\n Activated in the reserve on 27 June 1949\n Ordered to active service on 1 April 1951\n Inactivated on 2 April 1951\n Activated in the reserve on 13 June 1952\n Redesignated 314th Troop Carrier Squadron, Medium on 1 September 1957\n Ordered to active service on 28 October 1962\n Released from active service on 28 November 1962\n Redesignated 314th Troop Carrier Squadron, Heavy on 1 April 1965\n Redesignated 314th Air Transport Squadron, Heavy on 1 December 1965\n Redesignated 314th Military Airlift Squadron on 1 January 1966\n Redesignated 314th Tactical Airlift Squadron on 1 April 1972\n Redesignated 314th Air Refueling Squadron, Heavy on 1 January 1977\n Redesignated 314th Air Refueling Squadron on 1 February 1992\n Inactivated on 1 July 2009", "Notes" ]

[ 1, 2, 3, 4, 5, 6, 7, 8, 9 ]

[ "It is currently assigned to the 940th Air Refueling Wing, based at Beale Air Force Base, California." ]

[ "It operates the Boeing KC-135 Stratotanker aircraft conducting aerial refueling missions.", "Activated in late 1943 as a Douglas C-47 Skytrain troop carrier squadron, trained under I Troop Carrier Command in the United States.", "Was not deployed until the spring of 1945 to England, being assigned to the IX Troop Carrier Command.", "Was not used in combat operations, however did transport supplies and equipment to the front-line ground forces primarily into Germany and evacuated casualties to rear areas.", "Returned to the United States in September 1945 and was a transport squadron for Continental Air Forces until its inactivation in September 1946.", "It trained in the reserve for troop carrier missions from, 1949–1951, for fighter-bomber missions from, 1952–1957, and resumed its current role as an airlift squadron in 1957 until 1976.", "The squadron has performed air refueling missions worldwide since 1977 and maintained an alert responsibility for Strategic Air Command until the command's inactivation in June 1992.", "It deployed aircraft and personnel to Saudi Arabia and European locations in support of the Gulf War and later contingency operations in Somalia and the Balkans.", "The squadron was inactivated in 2009 pursuant to 2005 Base Realignment and Closure Commission action that eliminated the 940th Air Refueling Wing's KC-135 flying mission and redesignated it as the 940th Wing as an associate unit to the 9th Reconnaissance Wing in support of RQ-4 Global Hawk remotely piloted (e.g., unmanned) aircraft operations.", "In 2016, the wing returned to its former designation as an air refueling wing and reacquired its manned flying mission and KC-135R aircraft, with the reactivation of the squadron occurring the same year.", "Activated on 1 November 1943\n Inactivated on 31 July 1946\n Activated in the reserve on 27 June 1949\n Ordered to active service on 1 April 1951\n Inactivated on 2 April 1951\n Activated in the reserve on 13 June 1952\n Redesignated 314th Troop Carrier Squadron, Medium on 1 September 1957\n Ordered to active service on 28 October 1962\n Released from active service on 28 November 1962\n Redesignated 314th Troop Carrier Squadron, Heavy on 1 April 1965\n Redesignated 314th Air Transport Squadron, Heavy on 1 December 1965\n Redesignated 314th Military Airlift Squadron on 1 January 1966\n Redesignated 314th Tactical Airlift Squadron on 1 April 1972\n Redesignated 314th Air Refueling Squadron, Heavy on 1 January 1977\n Redesignated 314th Air Refueling Squadron on 1 February 1992\n Inactivated on 1 July 2009", "Notes" ]

[ 10, 11 ]

[ "The 314th Air Refueling Squadron is an active United States Air Force unit within the Air Force Reserve Command.", "It was inactivated on 1 July 2009 and reactivated on 1 June 2016." ]

[ "In 1742, Swedish astronomer Anders Celsius (1701–1744) created a temperature scale that was the reverse of the scale now known as \"Celsius\": 0 represented the boiling point of water, while 100 represented the freezing point of water.", "In his paper \"Observations of two persistent degrees on a thermometer\", he recounted his experiments showing that the melting point of ice is essentially unaffected by pressure.", "He also determined with remarkable precision how the boiling point of water varied as a function of atmospheric pressure.", "He proposed that the zero point of his temperature scale, being the boiling point, would be calibrated at the mean barometric pressure at mean sea level.", "This pressure is known as one standard atmosphere.", "The BIPM's 10th General Conference on Weights and Measures (CGPM) in 1954 defined one standard atmosphere to equal precisely 1,013,250 dynes per square centimeter (101.325 kPa).", "In 1743, the Lyonnais physicist Jean-Pierre Christin, permanent secretary of the Academy of Lyon, inverted the Celsius scale so that 0 represented the freezing point of water and 100 represented the boiling point of water.", "Some credit Christin for independently inventing the reverse of Celsius' original scale, while others believe Christin merely reversed Celsius' scale.", "On 19 May 1743 he published the design of a mercury thermometer, the \"Thermometer of Lyon\" built by the craftsman Pierre Casati that used this scale.", "In 1744, coincident with the death of Anders Celsius, the Swedish botanist Carl Linnaeus (1707–1778) reversed Celsius's scale.", "His custom-made \"linnaeus-thermometer\", for use in his greenhouses, was made by Daniel Ekström, Sweden's leading maker of scientific instruments at the time, whose workshop was located in the basement of the Stockholm observatory.", "As often happened in this age before modern communications, numerous physicists, scientists, and instrument makers are credited with having independently developed this same scale; among them were Pehr Elvius, the secretary of the Royal Swedish Academy of Sciences (which had an instrument workshop) and with whom Linnaeus had been corresponding; , the instrument maker; and Mårten Strömer (1707–1770) who had studied astronomy under Anders Celsius.", "The first known Swedish document reporting temperatures in this modern \"forward\" Celsius scale is the paper \"Hortus Upsaliensis\" dated 16 December 1745 that Linnaeus wrote to a student of his, Samuel Nauclér.", "In it, Linnaeus recounted the temperatures inside the orangery at the University of Uppsala Botanical Garden:", "Since the 19th century, the scientific and thermometry communities worldwide have used the phrase \"centigrade scale\" and temperatures were often reported simply as \"degrees\" or, when greater specificity was desired, as \"degrees centigrade\", with the symbol °C.", "In the French language, the term \"centigrade\" also means one hundredth of a gradian, when used for angular measurement.", "The term \"centesimal degree\" was later introduced for temperatures but was also problematic, as it means gradian (one hundredth of a right angle) in the French and Spanish languages.", "The risk of confusion between temperature and angular measurement was eliminated in 1948 when the 9th meeting of the General Conference on Weights and Measures and the Comité International des Poids et Mesures (CIPM) formally adopted \"degree Celsius\" for temperature.", "While \"Celsius\" is the term commonly used in scientific work, \"centigrade\" remains in common use in English-speaking countries, especially in informal contexts.", "While in Australia from 1 September 1972, only Celsius measurements were given for temperature in weather reports/forecasts, it was not until February 1985 that the weather forecasts issued by the BBC switched from \"centigrade\" to \"Celsius\".", "Some key temperatures relating the Celsius scale to other temperature scales are shown in the table below.", "The \"degree Celsius\" has been the only SI unit whose full unit name contains an uppercase letter since 1967, when the SI base unit for temperature became the kelvin, replacing the capitalized term \"degrees Kelvin\".", "The plural form is \"degrees Celsius\".", "The general rule of the International Bureau of Weights and Measures (BIPM) is that the numerical value always precedes the unit, and a space is always used to separate the unit from the number, (not \" or \").", "The only exceptions to this rule are for the unit symbols for degree, minute, and second for plane angle (°, ′, and ″, respectively), for which no space is left between the numerical value and the unit symbol.", "Other languages, and various publishing houses, may follow different typographical rules.", "Unicode provides the Celsius symbol at code point .", "However, this is a compatibility character provided for roundtrip compatibility with legacy encodings.", "It easily allows correct rendering for vertically written East Asian scripts, such as Chinese.", "The Unicode standard explicitly discourages the use of this character: \"In normal use, it is better to represent degrees Celsius \"°C\" with a sequence of + , rather than .", "For searching, treat these two sequences as identical.", "\"", "The degree Celsius is subject to the same rules as the kelvin with regard to the use of its unit name and symbol.", "Thus, besides expressing specific temperatures along its scale (e.g. \"Gallium melts at 29.7646 °C\" and \"The temperature outside is 23 degrees Celsius\"), the degree Celsius is also suitable for expressing temperature \"intervals\": differences between temperatures or their uncertainties (e.g. \"The output of the heat exchanger is hotter by 40 degrees Celsius\", and \"Our standard uncertainty is ±3 °C\").", "Because of this dual usage, one must not rely upon the unit name or its symbol to denote that a quantity is a temperature interval; it must be unambiguous through context or explicit statement that the quantity is an interval.", "This is sometimes solved by using the symbol °C (pronounced \"degrees Celsius\") for a temperature, and C° (pronounced \"Celsius degrees\") for a temperature interval, although this usage is non-standard.", "Another way to express the same is , which can be commonly found in literature.", "Celsius measurement follows an interval system but not a ratio system; and it follows a relative scale not an absolute scale.", "For example, an object at 20 °C does not have twice the energy of when it is 10 °C; and 0 °C is not the lowest Celsius value.", "Thus, degrees Celsius is a useful interval measurement but does not possess the characteristics of ratio measures like weight or distance.", "In science and in engineering, the Celsius scale and the Kelvin scale are often used in combination in close contexts, e.g. \"a measured value was 0.01023 °C with an uncertainty of 70 μK\".", "This practice is permissible because the magnitude of the degree Celsius is equal to that of the kelvin.", "Notwithstanding the official endorsement provided by decision no. 3 of Resolution 3 of the 13th CGPM, which stated \"a temperature interval may also be expressed in degrees Celsius\", the practice of simultaneously using both °C and K remains widespread throughout the scientific world as the use of SI-prefixed forms of the degree Celsius (such as \"μ°C\" or \"microdegrees Celsius\") to express a temperature interval has not been well adopted.", "The melting and boiling points of water are no longer part of the definition of the Celsius scale.", "In 1948, the definition was changed to use the triple point of water.", "In 2005 the definition was further refined to use water with precisely defined isotopic composition (VSMOW) for the triple point.", "In 2019, the definition was changed to use the Boltzmann constant, completely decoupling the definition of the kelvin from the properties of water.", "Each of these formal definitions left the numerical values of the Celsius scale identical to the prior definition to within the limits of accuracy of the metrology of the time.", "When the melting and boiling points of water ceased being part of the definition, they became measured quantities instead.", "This is also true of the triple point.", "In 1948 when the 9th General Conference on Weights and Measures (CGPM) in Resolution 3 first considered using the triple point of water as a defining point, the triple point was so close to being 0.01 °C greater than water's known melting point, it was simply defined as precisely 0.01 °C.", "However, later measurements showed that the difference between the triple and melting points of VSMOW is actually very slightly (<0.001 °C) greater than 0.01 °C.", "Thus, the actual melting point of ice is very slightly (less than a thousandth of a degree) below 0 °C.", "Also, defining water's triple point at 273.16 K precisely defined the magnitude of each 1 °C increment in terms of the absolute thermodynamic temperature scale (referencing absolute zero).", "Now decoupled from the actual boiling point of water, the value \"100 °C\" is hotter than 0 °C – in absolute terms – by a factor of \"precisely\" (approximately 36.61% thermodynamically hotter).", "When adhering \"strictly\" to the two-point definition for calibration, the boiling point of VSMOW under one standard atmosphere of pressure was actually 373.1339 K (99.9839 °C).", "When calibrated to ITS-90 (a calibration standard comprising many definition points and commonly used for high-precision instrumentation), the boiling point of VSMOW was slightly less, about 99.974 °C.", "This boiling-point difference of 16.1 millikelvins between the Celsius scale's original definition and the previous one (based on absolute zero and the triple point) has little practical meaning in common daily applications because water's boiling point is very sensitive to variations in barometric pressure.", "For example, an altitude change of only 28 cm (11 in) causes the boiling point to change by one millikelvin." ]

[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ]

[ "The degree Celsius is a unit of temperature on the Celsius scale, a temperature scale originally known as the centigrade scale.", "It is named after the Swedish astronomer Anders Celsius (1701–1744), who developed a similar temperature scale in 1742.", "Since 1743 the Celsius scale has been based on 0 °C for the freezing point of water and 100 °C for the boiling point of water at 1 atm pressure.", "Prior to 1743 the values were reversed (i.e. the boiling point was 0 degrees and the freezing point was 100 degrees).", "The 1743 scale reversal was proposed by Jean-Pierre Christin." ]

[ "In 1742, Swedish astronomer Anders Celsius (1701–1744) created a temperature scale that was the reverse of the scale now known as \"Celsius\": 0 represented the boiling point of water, while 100 represented the freezing point of water.", "In his paper \"Observations of two persistent degrees on a thermometer\", he recounted his experiments showing that the melting point of ice is essentially unaffected by pressure.", "He also determined with remarkable precision how the boiling point of water varied as a function of atmospheric pressure.", "He proposed that the zero point of his temperature scale, being the boiling point, would be calibrated at the mean barometric pressure at mean sea level.", "This pressure is known as one standard atmosphere.", "The BIPM's 10th General Conference on Weights and Measures (CGPM) in 1954 defined one standard atmosphere to equal precisely 1,013,250 dynes per square centimeter (101.325 kPa).", "In 1743, the Lyonnais physicist Jean-Pierre Christin, permanent secretary of the Academy of Lyon, inverted the Celsius scale so that 0 represented the freezing point of water and 100 represented the boiling point of water.", "Some credit Christin for independently inventing the reverse of Celsius' original scale, while others believe Christin merely reversed Celsius' scale.", "On 19 May 1743 he published the design of a mercury thermometer, the \"Thermometer of Lyon\" built by the craftsman Pierre Casati that used this scale.", "In 1744, coincident with the death of Anders Celsius, the Swedish botanist Carl Linnaeus (1707–1778) reversed Celsius's scale.", "His custom-made \"linnaeus-thermometer\", for use in his greenhouses, was made by Daniel Ekström, Sweden's leading maker of scientific instruments at the time, whose workshop was located in the basement of the Stockholm observatory.", "As often happened in this age before modern communications, numerous physicists, scientists, and instrument makers are credited with having independently developed this same scale; among them were Pehr Elvius, the secretary of the Royal Swedish Academy of Sciences (which had an instrument workshop) and with whom Linnaeus had been corresponding; , the instrument maker; and Mårten Strömer (1707–1770) who had studied astronomy under Anders Celsius.", "The first known Swedish document reporting temperatures in this modern \"forward\" Celsius scale is the paper \"Hortus Upsaliensis\" dated 16 December 1745 that Linnaeus wrote to a student of his, Samuel Nauclér.", "In it, Linnaeus recounted the temperatures inside the orangery at the University of Uppsala Botanical Garden:", "Since the 19th century, the scientific and thermometry communities worldwide have used the phrase \"centigrade scale\" and temperatures were often reported simply as \"degrees\" or, when greater specificity was desired, as \"degrees centigrade\", with the symbol °C.", "In the French language, the term \"centigrade\" also means one hundredth of a gradian, when used for angular measurement.", "The term \"centesimal degree\" was later introduced for temperatures but was also problematic, as it means gradian (one hundredth of a right angle) in the French and Spanish languages.", "The risk of confusion between temperature and angular measurement was eliminated in 1948 when the 9th meeting of the General Conference on Weights and Measures and the Comité International des Poids et Mesures (CIPM) formally adopted \"degree Celsius\" for temperature.", "While \"Celsius\" is the term commonly used in scientific work, \"centigrade\" remains in common use in English-speaking countries, especially in informal contexts.", "While in Australia from 1 September 1972, only Celsius measurements were given for temperature in weather reports/forecasts, it was not until February 1985 that the weather forecasts issued by the BBC switched from \"centigrade\" to \"Celsius\".", "Some key temperatures relating the Celsius scale to other temperature scales are shown in the table below.", "The \"degree Celsius\" has been the only SI unit whose full unit name contains an uppercase letter since 1967, when the SI base unit for temperature became the kelvin, replacing the capitalized term \"degrees Kelvin\".", "The plural form is \"degrees Celsius\".", "The general rule of the International Bureau of Weights and Measures (BIPM) is that the numerical value always precedes the unit, and a space is always used to separate the unit from the number, (not \" or \").", "The only exceptions to this rule are for the unit symbols for degree, minute, and second for plane angle (°, ′, and ″, respectively), for which no space is left between the numerical value and the unit symbol.", "Other languages, and various publishing houses, may follow different typographical rules.", "Unicode provides the Celsius symbol at code point .", "However, this is a compatibility character provided for roundtrip compatibility with legacy encodings.", "It easily allows correct rendering for vertically written East Asian scripts, such as Chinese.", "The Unicode standard explicitly discourages the use of this character: \"In normal use, it is better to represent degrees Celsius \"°C\" with a sequence of + , rather than .", "For searching, treat these two sequences as identical.", "\"", "The degree Celsius is subject to the same rules as the kelvin with regard to the use of its unit name and symbol.", "Thus, besides expressing specific temperatures along its scale (e.g. \"Gallium melts at 29.7646 °C\" and \"The temperature outside is 23 degrees Celsius\"), the degree Celsius is also suitable for expressing temperature \"intervals\": differences between temperatures or their uncertainties (e.g. \"The output of the heat exchanger is hotter by 40 degrees Celsius\", and \"Our standard uncertainty is ±3 °C\").", "Because of this dual usage, one must not rely upon the unit name or its symbol to denote that a quantity is a temperature interval; it must be unambiguous through context or explicit statement that the quantity is an interval.", "This is sometimes solved by using the symbol °C (pronounced \"degrees Celsius\") for a temperature, and C° (pronounced \"Celsius degrees\") for a temperature interval, although this usage is non-standard.", "Another way to express the same is , which can be commonly found in literature.", "Celsius measurement follows an interval system but not a ratio system; and it follows a relative scale not an absolute scale.", "For example, an object at 20 °C does not have twice the energy of when it is 10 °C; and 0 °C is not the lowest Celsius value.", "Thus, degrees Celsius is a useful interval measurement but does not possess the characteristics of ratio measures like weight or distance.", "In science and in engineering, the Celsius scale and the Kelvin scale are often used in combination in close contexts, e.g. \"a measured value was 0.01023 °C with an uncertainty of 70 μK\".", "This practice is permissible because the magnitude of the degree Celsius is equal to that of the kelvin.", "Notwithstanding the official endorsement provided by decision no. 3 of Resolution 3 of the 13th CGPM, which stated \"a temperature interval may also be expressed in degrees Celsius\", the practice of simultaneously using both °C and K remains widespread throughout the scientific world as the use of SI-prefixed forms of the degree Celsius (such as \"μ°C\" or \"microdegrees Celsius\") to express a temperature interval has not been well adopted.", "The melting and boiling points of water are no longer part of the definition of the Celsius scale.", "In 1948, the definition was changed to use the triple point of water.", "In 2005 the definition was further refined to use water with precisely defined isotopic composition (VSMOW) for the triple point.", "In 2019, the definition was changed to use the Boltzmann constant, completely decoupling the definition of the kelvin from the properties of water.", "Each of these formal definitions left the numerical values of the Celsius scale identical to the prior definition to within the limits of accuracy of the metrology of the time.", "When the melting and boiling points of water ceased being part of the definition, they became measured quantities instead.", "This is also true of the triple point.", "In 1948 when the 9th General Conference on Weights and Measures (CGPM) in Resolution 3 first considered using the triple point of water as a defining point, the triple point was so close to being 0.01 °C greater than water's known melting point, it was simply defined as precisely 0.01 °C.", "However, later measurements showed that the difference between the triple and melting points of VSMOW is actually very slightly (<0.001 °C) greater than 0.01 °C.", "Thus, the actual melting point of ice is very slightly (less than a thousandth of a degree) below 0 °C.", "Also, defining water's triple point at 273.16 K precisely defined the magnitude of each 1 °C increment in terms of the absolute thermodynamic temperature scale (referencing absolute zero).", "Now decoupled from the actual boiling point of water, the value \"100 °C\" is hotter than 0 °C – in absolute terms – by a factor of \"precisely\" (approximately 36.61% thermodynamically hotter).", "When adhering \"strictly\" to the two-point definition for calibration, the boiling point of VSMOW under one standard atmosphere of pressure was actually 373.1339 K (99.9839 °C).", "When calibrated to ITS-90 (a calibration standard comprising many definition points and commonly used for high-precision instrumentation), the boiling point of VSMOW was slightly less, about 99.974 °C.", "This boiling-point difference of 16.1 millikelvins between the Celsius scale's original definition and the previous one (based on absolute zero and the triple point) has little practical meaning in common daily applications because water's boiling point is very sensitive to variations in barometric pressure.", "For example, an altitude change of only 28 cm (11 in) causes the boiling point to change by one millikelvin." ]

[ 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 ]

[ "This means that a temperature difference of one degree Celsius and that of one kelvin are exactly the same." ]

[ "In 1742, Swedish astronomer Anders Celsius (1701–1744) created a temperature scale that was the reverse of the scale now known as \"Celsius\": 0 represented the boiling point of water, while 100 represented the freezing point of water.", "In his paper \"Observations of two persistent degrees on a thermometer\", he recounted his experiments showing that the melting point of ice is essentially unaffected by pressure.", "He also determined with remarkable precision how the boiling point of water varied as a function of atmospheric pressure.", "He proposed that the zero point of his temperature scale, being the boiling point, would be calibrated at the mean barometric pressure at mean sea level.", "This pressure is known as one standard atmosphere.", "The BIPM's 10th General Conference on Weights and Measures (CGPM) in 1954 defined one standard atmosphere to equal precisely 1,013,250 dynes per square centimeter (101.325 kPa).", "In 1743, the Lyonnais physicist Jean-Pierre Christin, permanent secretary of the Academy of Lyon, inverted the Celsius scale so that 0 represented the freezing point of water and 100 represented the boiling point of water.", "Some credit Christin for independently inventing the reverse of Celsius' original scale, while others believe Christin merely reversed Celsius' scale.", "On 19 May 1743 he published the design of a mercury thermometer, the \"Thermometer of Lyon\" built by the craftsman Pierre Casati that used this scale.", "In 1744, coincident with the death of Anders Celsius, the Swedish botanist Carl Linnaeus (1707–1778) reversed Celsius's scale.", "His custom-made \"linnaeus-thermometer\", for use in his greenhouses, was made by Daniel Ekström, Sweden's leading maker of scientific instruments at the time, whose workshop was located in the basement of the Stockholm observatory.", "As often happened in this age before modern communications, numerous physicists, scientists, and instrument makers are credited with having independently developed this same scale; among them were Pehr Elvius, the secretary of the Royal Swedish Academy of Sciences (which had an instrument workshop) and with whom Linnaeus had been corresponding; , the instrument maker; and Mårten Strömer (1707–1770) who had studied astronomy under Anders Celsius.", "The first known Swedish document reporting temperatures in this modern \"forward\" Celsius scale is the paper \"Hortus Upsaliensis\" dated 16 December 1745 that Linnaeus wrote to a student of his, Samuel Nauclér.", "In it, Linnaeus recounted the temperatures inside the orangery at the University of Uppsala Botanical Garden:", "Since the 19th century, the scientific and thermometry communities worldwide have used the phrase \"centigrade scale\" and temperatures were often reported simply as \"degrees\" or, when greater specificity was desired, as \"degrees centigrade\", with the symbol °C.", "In the French language, the term \"centigrade\" also means one hundredth of a gradian, when used for angular measurement.", "The term \"centesimal degree\" was later introduced for temperatures but was also problematic, as it means gradian (one hundredth of a right angle) in the French and Spanish languages.", "The risk of confusion between temperature and angular measurement was eliminated in 1948 when the 9th meeting of the General Conference on Weights and Measures and the Comité International des Poids et Mesures (CIPM) formally adopted \"degree Celsius\" for temperature.", "While \"Celsius\" is the term commonly used in scientific work, \"centigrade\" remains in common use in English-speaking countries, especially in informal contexts.", "While in Australia from 1 September 1972, only Celsius measurements were given for temperature in weather reports/forecasts, it was not until February 1985 that the weather forecasts issued by the BBC switched from \"centigrade\" to \"Celsius\".", "Some key temperatures relating the Celsius scale to other temperature scales are shown in the table below.", "The \"degree Celsius\" has been the only SI unit whose full unit name contains an uppercase letter since 1967, when the SI base unit for temperature became the kelvin, replacing the capitalized term \"degrees Kelvin\".", "The plural form is \"degrees Celsius\".", "The general rule of the International Bureau of Weights and Measures (BIPM) is that the numerical value always precedes the unit, and a space is always used to separate the unit from the number, (not \" or \").", "The only exceptions to this rule are for the unit symbols for degree, minute, and second for plane angle (°, ′, and ″, respectively), for which no space is left between the numerical value and the unit symbol.", "Other languages, and various publishing houses, may follow different typographical rules.", "Unicode provides the Celsius symbol at code point .", "However, this is a compatibility character provided for roundtrip compatibility with legacy encodings.", "It easily allows correct rendering for vertically written East Asian scripts, such as Chinese.", "The Unicode standard explicitly discourages the use of this character: \"In normal use, it is better to represent degrees Celsius \"°C\" with a sequence of + , rather than .", "For searching, treat these two sequences as identical.", "\"", "The degree Celsius is subject to the same rules as the kelvin with regard to the use of its unit name and symbol.", "Thus, besides expressing specific temperatures along its scale (e.g. \"Gallium melts at 29.7646 °C\" and \"The temperature outside is 23 degrees Celsius\"), the degree Celsius is also suitable for expressing temperature \"intervals\": differences between temperatures or their uncertainties (e.g. \"The output of the heat exchanger is hotter by 40 degrees Celsius\", and \"Our standard uncertainty is ±3 °C\").", "Because of this dual usage, one must not rely upon the unit name or its symbol to denote that a quantity is a temperature interval; it must be unambiguous through context or explicit statement that the quantity is an interval.", "This is sometimes solved by using the symbol °C (pronounced \"degrees Celsius\") for a temperature, and C° (pronounced \"Celsius degrees\") for a temperature interval, although this usage is non-standard.", "Another way to express the same is , which can be commonly found in literature.", "Celsius measurement follows an interval system but not a ratio system; and it follows a relative scale not an absolute scale.", "For example, an object at 20 °C does not have twice the energy of when it is 10 °C; and 0 °C is not the lowest Celsius value.", "Thus, degrees Celsius is a useful interval measurement but does not possess the characteristics of ratio measures like weight or distance.", "In science and in engineering, the Celsius scale and the Kelvin scale are often used in combination in close contexts, e.g. \"a measured value was 0.01023 °C with an uncertainty of 70 μK\".", "This practice is permissible because the magnitude of the degree Celsius is equal to that of the kelvin.", "Notwithstanding the official endorsement provided by decision no. 3 of Resolution 3 of the 13th CGPM, which stated \"a temperature interval may also be expressed in degrees Celsius\", the practice of simultaneously using both °C and K remains widespread throughout the scientific world as the use of SI-prefixed forms of the degree Celsius (such as \"μ°C\" or \"microdegrees Celsius\") to express a temperature interval has not been well adopted.", "The melting and boiling points of water are no longer part of the definition of the Celsius scale.", "In 1948, the definition was changed to use the triple point of water.", "In 2005 the definition was further refined to use water with precisely defined isotopic composition (VSMOW) for the triple point.", "In 2019, the definition was changed to use the Boltzmann constant, completely decoupling the definition of the kelvin from the properties of water.", "Each of these formal definitions left the numerical values of the Celsius scale identical to the prior definition to within the limits of accuracy of the metrology of the time.", "When the melting and boiling points of water ceased being part of the definition, they became measured quantities instead.", "This is also true of the triple point.", "In 1948 when the 9th General Conference on Weights and Measures (CGPM) in Resolution 3 first considered using the triple point of water as a defining point, the triple point was so close to being 0.01 °C greater than water's known melting point, it was simply defined as precisely 0.01 °C.", "However, later measurements showed that the difference between the triple and melting points of VSMOW is actually very slightly (<0.001 °C) greater than 0.01 °C.", "Thus, the actual melting point of ice is very slightly (less than a thousandth of a degree) below 0 °C.", "Also, defining water's triple point at 273.16 K precisely defined the magnitude of each 1 °C increment in terms of the absolute thermodynamic temperature scale (referencing absolute zero).", "Now decoupled from the actual boiling point of water, the value \"100 °C\" is hotter than 0 °C – in absolute terms – by a factor of \"precisely\" (approximately 36.61% thermodynamically hotter).", "When adhering \"strictly\" to the two-point definition for calibration, the boiling point of VSMOW under one standard atmosphere of pressure was actually 373.1339 K (99.9839 °C).", "When calibrated to ITS-90 (a calibration standard comprising many definition points and commonly used for high-precision instrumentation), the boiling point of VSMOW was slightly less, about 99.974 °C.", "This boiling-point difference of 16.1 millikelvins between the Celsius scale's original definition and the previous one (based on absolute zero and the triple point) has little practical meaning in common daily applications because water's boiling point is very sensitive to variations in barometric pressure.", "For example, an altitude change of only 28 cm (11 in) causes the boiling point to change by one millikelvin." ]

[ 32, 33, 34, 35, 36, 37, 38, 39 ]

[ "The degree Celsius (symbol: °C) can refer to a specific temperature on the Celsius scale or a unit to indicate a difference or range between two temperatures." ]

[ "In 1742, Swedish astronomer Anders Celsius (1701–1744) created a temperature scale that was the reverse of the scale now known as \"Celsius\": 0 represented the boiling point of water, while 100 represented the freezing point of water.", "In his paper \"Observations of two persistent degrees on a thermometer\", he recounted his experiments showing that the melting point of ice is essentially unaffected by pressure.", "He also determined with remarkable precision how the boiling point of water varied as a function of atmospheric pressure.", "He proposed that the zero point of his temperature scale, being the boiling point, would be calibrated at the mean barometric pressure at mean sea level.", "This pressure is known as one standard atmosphere.", "The BIPM's 10th General Conference on Weights and Measures (CGPM) in 1954 defined one standard atmosphere to equal precisely 1,013,250 dynes per square centimeter (101.325 kPa).", "In 1743, the Lyonnais physicist Jean-Pierre Christin, permanent secretary of the Academy of Lyon, inverted the Celsius scale so that 0 represented the freezing point of water and 100 represented the boiling point of water.", "Some credit Christin for independently inventing the reverse of Celsius' original scale, while others believe Christin merely reversed Celsius' scale.", "On 19 May 1743 he published the design of a mercury thermometer, the \"Thermometer of Lyon\" built by the craftsman Pierre Casati that used this scale.", "In 1744, coincident with the death of Anders Celsius, the Swedish botanist Carl Linnaeus (1707–1778) reversed Celsius's scale.", "His custom-made \"linnaeus-thermometer\", for use in his greenhouses, was made by Daniel Ekström, Sweden's leading maker of scientific instruments at the time, whose workshop was located in the basement of the Stockholm observatory.", "As often happened in this age before modern communications, numerous physicists, scientists, and instrument makers are credited with having independently developed this same scale; among them were Pehr Elvius, the secretary of the Royal Swedish Academy of Sciences (which had an instrument workshop) and with whom Linnaeus had been corresponding; , the instrument maker; and Mårten Strömer (1707–1770) who had studied astronomy under Anders Celsius.", "The first known Swedish document reporting temperatures in this modern \"forward\" Celsius scale is the paper \"Hortus Upsaliensis\" dated 16 December 1745 that Linnaeus wrote to a student of his, Samuel Nauclér.", "In it, Linnaeus recounted the temperatures inside the orangery at the University of Uppsala Botanical Garden:", "Since the 19th century, the scientific and thermometry communities worldwide have used the phrase \"centigrade scale\" and temperatures were often reported simply as \"degrees\" or, when greater specificity was desired, as \"degrees centigrade\", with the symbol °C.", "In the French language, the term \"centigrade\" also means one hundredth of a gradian, when used for angular measurement.", "The term \"centesimal degree\" was later introduced for temperatures but was also problematic, as it means gradian (one hundredth of a right angle) in the French and Spanish languages.", "The risk of confusion between temperature and angular measurement was eliminated in 1948 when the 9th meeting of the General Conference on Weights and Measures and the Comité International des Poids et Mesures (CIPM) formally adopted \"degree Celsius\" for temperature.", "While \"Celsius\" is the term commonly used in scientific work, \"centigrade\" remains in common use in English-speaking countries, especially in informal contexts.", "While in Australia from 1 September 1972, only Celsius measurements were given for temperature in weather reports/forecasts, it was not until February 1985 that the weather forecasts issued by the BBC switched from \"centigrade\" to \"Celsius\".", "Some key temperatures relating the Celsius scale to other temperature scales are shown in the table below.", "The \"degree Celsius\" has been the only SI unit whose full unit name contains an uppercase letter since 1967, when the SI base unit for temperature became the kelvin, replacing the capitalized term \"degrees Kelvin\".", "The plural form is \"degrees Celsius\".", "The general rule of the International Bureau of Weights and Measures (BIPM) is that the numerical value always precedes the unit, and a space is always used to separate the unit from the number, (not \" or \").", "The only exceptions to this rule are for the unit symbols for degree, minute, and second for plane angle (°, ′, and ″, respectively), for which no space is left between the numerical value and the unit symbol.", "Other languages, and various publishing houses, may follow different typographical rules.", "Unicode provides the Celsius symbol at code point .", "However, this is a compatibility character provided for roundtrip compatibility with legacy encodings.", "It easily allows correct rendering for vertically written East Asian scripts, such as Chinese.", "The Unicode standard explicitly discourages the use of this character: \"In normal use, it is better to represent degrees Celsius \"°C\" with a sequence of + , rather than .", "For searching, treat these two sequences as identical.", "\"", "The degree Celsius is subject to the same rules as the kelvin with regard to the use of its unit name and symbol.", "Thus, besides expressing specific temperatures along its scale (e.g. \"Gallium melts at 29.7646 °C\" and \"The temperature outside is 23 degrees Celsius\"), the degree Celsius is also suitable for expressing temperature \"intervals\": differences between temperatures or their uncertainties (e.g. \"The output of the heat exchanger is hotter by 40 degrees Celsius\", and \"Our standard uncertainty is ±3 °C\").", "Because of this dual usage, one must not rely upon the unit name or its symbol to denote that a quantity is a temperature interval; it must be unambiguous through context or explicit statement that the quantity is an interval.", "This is sometimes solved by using the symbol °C (pronounced \"degrees Celsius\") for a temperature, and C° (pronounced \"Celsius degrees\") for a temperature interval, although this usage is non-standard.", "Another way to express the same is , which can be commonly found in literature.", "Celsius measurement follows an interval system but not a ratio system; and it follows a relative scale not an absolute scale.", "For example, an object at 20 °C does not have twice the energy of when it is 10 °C; and 0 °C is not the lowest Celsius value.", "Thus, degrees Celsius is a useful interval measurement but does not possess the characteristics of ratio measures like weight or distance.", "In science and in engineering, the Celsius scale and the Kelvin scale are often used in combination in close contexts, e.g. \"a measured value was 0.01023 °C with an uncertainty of 70 μK\".", "This practice is permissible because the magnitude of the degree Celsius is equal to that of the kelvin.", "Notwithstanding the official endorsement provided by decision no. 3 of Resolution 3 of the 13th CGPM, which stated \"a temperature interval may also be expressed in degrees Celsius\", the practice of simultaneously using both °C and K remains widespread throughout the scientific world as the use of SI-prefixed forms of the degree Celsius (such as \"μ°C\" or \"microdegrees Celsius\") to express a temperature interval has not been well adopted.", "The melting and boiling points of water are no longer part of the definition of the Celsius scale.", "In 1948, the definition was changed to use the triple point of water.", "In 2005 the definition was further refined to use water with precisely defined isotopic composition (VSMOW) for the triple point.", "In 2019, the definition was changed to use the Boltzmann constant, completely decoupling the definition of the kelvin from the properties of water.", "Each of these formal definitions left the numerical values of the Celsius scale identical to the prior definition to within the limits of accuracy of the metrology of the time.", "When the melting and boiling points of water ceased being part of the definition, they became measured quantities instead.", "This is also true of the triple point.", "In 1948 when the 9th General Conference on Weights and Measures (CGPM) in Resolution 3 first considered using the triple point of water as a defining point, the triple point was so close to being 0.01 °C greater than water's known melting point, it was simply defined as precisely 0.01 °C.", "However, later measurements showed that the difference between the triple and melting points of VSMOW is actually very slightly (<0.001 °C) greater than 0.01 °C.", "Thus, the actual melting point of ice is very slightly (less than a thousandth of a degree) below 0 °C.", "Also, defining water's triple point at 273.16 K precisely defined the magnitude of each 1 °C increment in terms of the absolute thermodynamic temperature scale (referencing absolute zero).", "Now decoupled from the actual boiling point of water, the value \"100 °C\" is hotter than 0 °C – in absolute terms – by a factor of \"precisely\" (approximately 36.61% thermodynamically hotter).", "When adhering \"strictly\" to the two-point definition for calibration, the boiling point of VSMOW under one standard atmosphere of pressure was actually 373.1339 K (99.9839 °C).", "When calibrated to ITS-90 (a calibration standard comprising many definition points and commonly used for high-precision instrumentation), the boiling point of VSMOW was slightly less, about 99.974 °C.", "This boiling-point difference of 16.1 millikelvins between the Celsius scale's original definition and the previous one (based on absolute zero and the triple point) has little practical meaning in common daily applications because water's boiling point is very sensitive to variations in barometric pressure.", "For example, an altitude change of only 28 cm (11 in) causes the boiling point to change by one millikelvin." ]

[ 40, 41, 42 ]

[ "The Kelvin scale is of use in the sciences, with 0 K (-273.15 °C) representing absolute zero.", "The degree Celsius remains exactly equal to the kelvin, and 0 K remains exactly −273.15 °C." ]

[ "In 1742, Swedish astronomer Anders Celsius (1701–1744) created a temperature scale that was the reverse of the scale now known as \"Celsius\": 0 represented the boiling point of water, while 100 represented the freezing point of water.", "In his paper \"Observations of two persistent degrees on a thermometer\", he recounted his experiments showing that the melting point of ice is essentially unaffected by pressure.", "He also determined with remarkable precision how the boiling point of water varied as a function of atmospheric pressure.", "He proposed that the zero point of his temperature scale, being the boiling point, would be calibrated at the mean barometric pressure at mean sea level.", "This pressure is known as one standard atmosphere.", "The BIPM's 10th General Conference on Weights and Measures (CGPM) in 1954 defined one standard atmosphere to equal precisely 1,013,250 dynes per square centimeter (101.325 kPa).", "In 1743, the Lyonnais physicist Jean-Pierre Christin, permanent secretary of the Academy of Lyon, inverted the Celsius scale so that 0 represented the freezing point of water and 100 represented the boiling point of water.", "Some credit Christin for independently inventing the reverse of Celsius' original scale, while others believe Christin merely reversed Celsius' scale.", "On 19 May 1743 he published the design of a mercury thermometer, the \"Thermometer of Lyon\" built by the craftsman Pierre Casati that used this scale.", "In 1744, coincident with the death of Anders Celsius, the Swedish botanist Carl Linnaeus (1707–1778) reversed Celsius's scale.", "His custom-made \"linnaeus-thermometer\", for use in his greenhouses, was made by Daniel Ekström, Sweden's leading maker of scientific instruments at the time, whose workshop was located in the basement of the Stockholm observatory.", "As often happened in this age before modern communications, numerous physicists, scientists, and instrument makers are credited with having independently developed this same scale; among them were Pehr Elvius, the secretary of the Royal Swedish Academy of Sciences (which had an instrument workshop) and with whom Linnaeus had been corresponding; , the instrument maker; and Mårten Strömer (1707–1770) who had studied astronomy under Anders Celsius.", "The first known Swedish document reporting temperatures in this modern \"forward\" Celsius scale is the paper \"Hortus Upsaliensis\" dated 16 December 1745 that Linnaeus wrote to a student of his, Samuel Nauclér.", "In it, Linnaeus recounted the temperatures inside the orangery at the University of Uppsala Botanical Garden:", "Since the 19th century, the scientific and thermometry communities worldwide have used the phrase \"centigrade scale\" and temperatures were often reported simply as \"degrees\" or, when greater specificity was desired, as \"degrees centigrade\", with the symbol °C.", "In the French language, the term \"centigrade\" also means one hundredth of a gradian, when used for angular measurement.", "The term \"centesimal degree\" was later introduced for temperatures but was also problematic, as it means gradian (one hundredth of a right angle) in the French and Spanish languages.", "The risk of confusion between temperature and angular measurement was eliminated in 1948 when the 9th meeting of the General Conference on Weights and Measures and the Comité International des Poids et Mesures (CIPM) formally adopted \"degree Celsius\" for temperature.", "While \"Celsius\" is the term commonly used in scientific work, \"centigrade\" remains in common use in English-speaking countries, especially in informal contexts.", "While in Australia from 1 September 1972, only Celsius measurements were given for temperature in weather reports/forecasts, it was not until February 1985 that the weather forecasts issued by the BBC switched from \"centigrade\" to \"Celsius\".", "Some key temperatures relating the Celsius scale to other temperature scales are shown in the table below.", "The \"degree Celsius\" has been the only SI unit whose full unit name contains an uppercase letter since 1967, when the SI base unit for temperature became the kelvin, replacing the capitalized term \"degrees Kelvin\".", "The plural form is \"degrees Celsius\".", "The general rule of the International Bureau of Weights and Measures (BIPM) is that the numerical value always precedes the unit, and a space is always used to separate the unit from the number, (not \" or \").", "The only exceptions to this rule are for the unit symbols for degree, minute, and second for plane angle (°, ′, and ″, respectively), for which no space is left between the numerical value and the unit symbol.", "Other languages, and various publishing houses, may follow different typographical rules.", "Unicode provides the Celsius symbol at code point .", "However, this is a compatibility character provided for roundtrip compatibility with legacy encodings.", "It easily allows correct rendering for vertically written East Asian scripts, such as Chinese.", "The Unicode standard explicitly discourages the use of this character: \"In normal use, it is better to represent degrees Celsius \"°C\" with a sequence of + , rather than .", "For searching, treat these two sequences as identical.", "\"", "The degree Celsius is subject to the same rules as the kelvin with regard to the use of its unit name and symbol.", "Thus, besides expressing specific temperatures along its scale (e.g. \"Gallium melts at 29.7646 °C\" and \"The temperature outside is 23 degrees Celsius\"), the degree Celsius is also suitable for expressing temperature \"intervals\": differences between temperatures or their uncertainties (e.g. \"The output of the heat exchanger is hotter by 40 degrees Celsius\", and \"Our standard uncertainty is ±3 °C\").", "Because of this dual usage, one must not rely upon the unit name or its symbol to denote that a quantity is a temperature interval; it must be unambiguous through context or explicit statement that the quantity is an interval.", "This is sometimes solved by using the symbol °C (pronounced \"degrees Celsius\") for a temperature, and C° (pronounced \"Celsius degrees\") for a temperature interval, although this usage is non-standard.", "Another way to express the same is , which can be commonly found in literature.", "Celsius measurement follows an interval system but not a ratio system; and it follows a relative scale not an absolute scale.", "For example, an object at 20 °C does not have twice the energy of when it is 10 °C; and 0 °C is not the lowest Celsius value.", "Thus, degrees Celsius is a useful interval measurement but does not possess the characteristics of ratio measures like weight or distance.", "In science and in engineering, the Celsius scale and the Kelvin scale are often used in combination in close contexts, e.g. \"a measured value was 0.01023 °C with an uncertainty of 70 μK\".", "This practice is permissible because the magnitude of the degree Celsius is equal to that of the kelvin.", "Notwithstanding the official endorsement provided by decision no. 3 of Resolution 3 of the 13th CGPM, which stated \"a temperature interval may also be expressed in degrees Celsius\", the practice of simultaneously using both °C and K remains widespread throughout the scientific world as the use of SI-prefixed forms of the degree Celsius (such as \"μ°C\" or \"microdegrees Celsius\") to express a temperature interval has not been well adopted.", "The melting and boiling points of water are no longer part of the definition of the Celsius scale.", "In 1948, the definition was changed to use the triple point of water.", "In 2005 the definition was further refined to use water with precisely defined isotopic composition (VSMOW) for the triple point.", "In 2019, the definition was changed to use the Boltzmann constant, completely decoupling the definition of the kelvin from the properties of water.", "Each of these formal definitions left the numerical values of the Celsius scale identical to the prior definition to within the limits of accuracy of the metrology of the time.", "When the melting and boiling points of water ceased being part of the definition, they became measured quantities instead.", "This is also true of the triple point.", "In 1948 when the 9th General Conference on Weights and Measures (CGPM) in Resolution 3 first considered using the triple point of water as a defining point, the triple point was so close to being 0.01 °C greater than water's known melting point, it was simply defined as precisely 0.01 °C.", "However, later measurements showed that the difference between the triple and melting points of VSMOW is actually very slightly (<0.001 °C) greater than 0.01 °C.", "Thus, the actual melting point of ice is very slightly (less than a thousandth of a degree) below 0 °C.", "Also, defining water's triple point at 273.16 K precisely defined the magnitude of each 1 °C increment in terms of the absolute thermodynamic temperature scale (referencing absolute zero).", "Now decoupled from the actual boiling point of water, the value \"100 °C\" is hotter than 0 °C – in absolute terms – by a factor of \"precisely\" (approximately 36.61% thermodynamically hotter).", "When adhering \"strictly\" to the two-point definition for calibration, the boiling point of VSMOW under one standard atmosphere of pressure was actually 373.1339 K (99.9839 °C).", "When calibrated to ITS-90 (a calibration standard comprising many definition points and commonly used for high-precision instrumentation), the boiling point of VSMOW was slightly less, about 99.974 °C.", "This boiling-point difference of 16.1 millikelvins between the Celsius scale's original definition and the previous one (based on absolute zero and the triple point) has little practical meaning in common daily applications because water's boiling point is very sensitive to variations in barometric pressure.", "For example, an altitude change of only 28 cm (11 in) causes the boiling point to change by one millikelvin." ]

[ 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58 ]

[ "The Kelvin scale is of use in the sciences, with 0 K (-273.15 °C) representing absolute zero.", "Since 1743 the Celsius scale has been based on 0 °C for the freezing point of water and 100 °C for the boiling point of water at 1 atm pressure.", "By international agreement, between 1954 and 2019 the unit and the Celsius scale were defined by absolute zero and the triple point of water.", "This definition also precisely related the Celsius scale to the Kelvin scale, which defines the SI base unit of thermodynamic temperature with symbol K. Absolute zero, the lowest temperature possible, is defined as being exactly 0 K and −273.15 °C.", "Until 19 May 2019, the temperature of the triple point of water was defined as exactly .", "On 20 May 2019, the kelvin was redefined so that its value is now determined by the definition of the Boltzmann constant rather than being defined by the triple point of VSMOW.", "This means that the triple point is now a measured value, not a defined value.", "The newly-defined exact value of the Boltzmann constant was selected so that the measured value of the VSMOW triple point is exactly the same as the older defined value to within the limits of accuracy of contemporary metrology." ]

[ "Lost Nation has a popular golf course, called \"Lost Nation Golf Course\" that has 18 holes, watered fairways, and a pro shop as well as a cocktail lounge." ]

[ 0 ]

[ "Lost Nation has an area of ; of this is land, and is water." ]

[ "During the 18th century multiple temperature scales were developed, most notably Fahrenheit and centigrade (later Celsius).", "These scales predated much of the modern science of thermodynamics, including the scientific consensus in favour of atomic theory and the kinetic theory of gases that underpin the concept of absolute zero.", "Instead, they chose defining points inside the range of human experience at the time that could be easily and reasonably accurately reproduced, but did not necessarily have any deep significance in thermal physics.", "In the case of the Celsius scale (and the long since defunct Newton scale and Réaumur scale) the melting point of water served as such a semi-arbitrary starting point, with Celsius being defined, from the 1740s up until the 1940s, by calibrating a thermometer such that:\n\nThis referring to pure water at a set pressure designed to approximate the natural air pressure at sea level.", "An implication of this was that an increment of 1 °C was equal to an increment of of the temperature difference between the melting and boiling points.", "This temperature interval would go on to become the template for the kelvin.", "In October 1848, William Thomson, a 24 year old professor of Natural Philosophy at the University of Glasgow, published a paper \"On an Absolute Thermometric Scale\".", "Using the soon-to-be-defunct caloric theory, he proposed an \"absolute\" scale based on the following parameters:\n\n\"The arbitrary points which coincide on the two scales are 0° and 100°\"\n\"The characteristic property of the scale which I now propose is, that all degrees have the same value; that is, that a unit of heat descending from a body \"A\" at the temperature \"T\"° of this scale, to a body \"B\" at the temperature (\"T\" − 1)°, would give out the same mechanical effect, whatever be the number \"T\".", "This may justly be termed an absolute scale, since its characteristic is quite independent of the physical properties of any specific substance.", "\"\nAs Carnot's theorem is understood in modern thermodynamics to simply describe the maximum efficiency with which thermal energy can be converted to mechanical energy and the predicted maximum efficiency is a function of the \"ratio\" between the absolute temperatures of the heat source and heat sink:\nIt follows that increments of equal numbers of degrees on this scale must always represent equal \"proportional\" increases in absolute temperature.", "The numerical value of an absolute temperature, , on the 1848 scale is related to the absolute temperature of the melting point of water, , and the absolute temperature of the boiling point of water, , by:\nOn this scale, an increase of 222 degrees always means an approximate doubling of absolute temperature regardless of the starting temperature.", "In a footnote Thomson calculated that \"infinite cold\" (absolute zero, which would have a numerical value of negative infinity on this scale) was equivalent to −273 °C using the air thermometers of the time.", "This value of \"−273\" was the negative reciprocal of 0.00366—the accepted expansion coefficient of gas per degree Celsius relative to the ice point, giving a remarkable consistency to the currently accepted value.", "Within a decade, Thomson had abandoned caloric theory and superseded the 1848 scale with a new one based on the 2 features that would characterise all future versions of the kelvin scale:\n\nIn 1892 Thomson was awarded the noble title 1st", "Baron Kelvin of Largs, or more succinctly Lord Kelvin.", "This name was a reference to the River Kelvin which flows through the grounds of Glasgow University.", "In the early decades of the 20th century, the Kelvin scale was often called the \"absolute Celsius\" scale, indicating Celsius degrees counted from absolute zero rather than the freezing point of water, and using the same symbol for regular Celsius degrees, °C.", "In 1873 William Thomson's older brother James coined the term \"triple point\" to describe the combination of temperature and pressure at which the solid, liquid, and gas phases of a substance were capable of coexisting in thermodynamic equilibrium.", "While any two phases could coexist along a range of temperature-pressure combinations (e.g. the boiling point of water can be affected quite dramatically by raising or lowering the pressure), the triple point condition for a given substance can occur only at 1 pressure and only at 1 temperature.", "By the 1940s, the triple point of water had been experimentally measured to be about 0.6% of standard atmospheric pressure and very close to 0.01 °C per the historical definition of Celsius then in use.", "In 1948, the Celsius scale was recalibrated by assigning the triple point temperature of water the value of 0.01 °C exactly and allowing the melting point at standard atmospheric pressure to have an empirically determined value (and the actual melting point at ambient pressure to have a fluctuating value) close to 0 °C.", "This was justified on the grounds that the triple point was judged to give a more accurately reproducible reference temperature than the melting point.", "In 1954, with absolute zero having been experimentally determined to be about −273.15 °C per the definition of °C then in use, Resolution 3 of the 10th General Conference on Weights and Measures (CGPM) introduced a new internationally standardised Kelvin scale which defined the triple point as exactly:\n273.15 + 0.01 = 273.16 \"degrees Kelvin\"\nIn 1967/1968, Resolution 3 of the 13th CGPM renamed the unit increment of thermodynamic temperature \"kelvin\", symbol K, replacing \"degree Kelvin\", symbol °K.", "Furthermore, feeling it useful to more explicitly define the magnitude of the unit increment, the 13th CGPM also held in Resolution 4 that \"The kelvin, unit of thermodynamic temperature, is equal to the fraction of the thermodynamic temperature of the triple point of water.", "\"\nAfter the 1983 redefinition of the metre, this left the kelvin, the second, and the kilogram as the only SI units not defined with reference to any other unit.", "Hydrogen has 2 stable isotopes (and one trace radioisotope) and oxygen has 3 stable isotopes.", "In 2005, noting that the triple point could be influenced by the isotopic ratio of the hydrogen and oxygen making up a water sample and that this was \"now one of the major sources of the observed variability between different realizations of the water triple point\", the International Committee for Weights and Measures (CIPM), a committee of the CGPM, affirmed that for the purposes of delineating the temperature of the triple point of water, the definition of the kelvin would refer to water having the isotopic composition specified for Vienna Standard Mean Ocean Water:", "In 2005 the CIPM began a programme to redefine the kelvin (along with the other SI units) using a more experimentally rigorous method.", "In particular, the committee proposed redefining the kelvin such that the Boltzmann constant takes the exact value .", "The committee had hoped that the program would be completed in time for its adoption by the CGPM at its 2011 meeting, but at the 2011 meeting the decision was postponed to the 2014 meeting when it would be considered as part of a larger program.", "The redefinition was further postponed in 2014, pending more accurate measurements of Boltzmann's constant in terms of the current definition,\nbut was finally adopted at the 26th CGPM in late 2018, with a value of  = \nFor scientific purposes, the main advantage is that this allows measurements at very low and very high temperatures to be made more accurately, as the techniques used depend on the Boltzmann constant.", "It also has the philosophical advantage of being independent of any particular substance.", "The unit J/K is equal to kg⋅m2⋅s−2⋅K−1, where the kilogram, metre and second are defined in terms of the Planck constant, the speed of light, and the duration of the caesium-133 ground-state hyperfine transition respectively.", "Thus, this definition depends only on universal constants, and not on any physical artifacts as practiced previously, such as the International Prototype of the Kilogram, whose mass diverged over time from the original value.", "The challenge was to avoid degrading the accuracy of measurements close to the triple point.", "For practical purposes, the redefinition was unnoticed; water still freezes at 273.15 K (0 °C), and the triple point of water continues to be a commonly used laboratory reference temperature.", "The difference is that, before the redefinition, the triple point of water was exact and the Boltzmann constant had a measured value of , with a relative standard uncertainty of .", "Afterward, the Boltzmann constant is exact and the uncertainty is transferred to the triple point of water, which is now .", "For legal metrology purposes, the new definition officially came into force on 20 May 2019, the 144th anniversary of the Metre Convention.", "The post-2019 definition is based on fixing the value of the Boltzmann constant , expressed in SI units, at joules per kelvin.", "This constant appears in (some formulations of) the ideal gas law, which links the pressure, , of an ideal gas, its volume, , its temperature, , and the number of gas particles making it up, , via the relationship:\nSubstituting in the defined value of gives:\nWhich can be rearranged to give:\nOr:\nWhere (K) is the numerical value of the temperature expressed in kelvins, and (J) is the numerical value of the product of the pressure and the average volume per gas particle expressed in joules.", "It is worth emphasising that in dimensional analysis terms the product of a pressure and a volume is an energy.", "This can be seen by considering that pressure, volume, and energy have the dimensions force/length2, length3 and force × length, respectively.", "Another context where this relationship becomes intuitive is in the case of a pump or a water turbine, where the minimum energy demand and maximum energy available, respectively, is given by the volume of fluid passing through the component multiplied by the pressure differential across it.", "The above temperature equation holds exactly for an ideal gas, a hypothetical substance composed of point particles affected only by elastic collisions with their container, but is closely approximated by a real gas that is well above its boiling or sublimation point and well below its critical pressure.", "Using the metric prefix system this can be given as:\nBecause the average kinetic energy per degree of freedom is and gas particles have 3 translational degrees of freedom, the temperature in kelvins is also related to the mean kinetic energy per degree of freedom by:\nAnd to the mean translational kinetic energy by:\nExpressed in terms of the SI defining constants 1 kelvin is:\nWhere is the Planck constant and is the caesium-133 hyperfine transition frequency.", "Because the term is equal to the photon energy of the caesium-133 hyperfine transition radiation, , and 1/ is equal to for an ideal gas:\nWhich can be rearranged to give:\nOr:\nExpressed in terms of mean kinetic energy, this becomes:\nAnd:", "Although the kelvin is an SI base unit, its only use in fundamental physics is the Boltzmann constant.", "This allows a natural unit definition that makes kelvins and joules different units for the same dimension, .", "Such a definition is already in use in some textbooks.", "However, such a definition is unlikely to have a practical use in an experiment due to the large orders of magnitude involved.", "Several physical constants are defined in terms of the Boltzmann constant and other SI defining constants, for example the universal gas constant, , is defined as the product of the Boltzmann constant, , and the Avogadro constant, A. Prior to 2019, its value in SI units could only be empirically estimated, with a small but inevitable degree of experimental uncertainty.", "After 2019, the kelvin was redefined by giving an exact value to the Boltzmann constant and the mole was redefined by assigning an exact value to the Avogadro constant, meaning the value of the universal gas constant in SI units could be calculated exactly as:\nSimilarly, the Stefan-Boltzmann constant, \"σ\", not to be confused with the Boltzmann constant, relates the temperature of a black body to the rate at which thermal energy is electromagnetically radiated from its surface and is equal to:\nWhere is the Planck constant, whose value now defines the kilogram, and is the speed of light, whose value now defines the metre (and had been implicit in the definition of the metre since 1983).", "The exact value of \"σ\" in SI units is therefore:\nThe second radiation constant in Planck's law, 2, is equal to:\nWhich means its exact value in SI units is:", "1 kelvin is the approximate temperature of the Boomerang Nebula, the coldest known natural environment in the universe.", "Because 1 K is colder than the effective temperature of the cosmic microwave background (about 2.7 K), it cannot be reached simply by moving a previously warm object far away from point sources of heat (e.g. stars) and requires additional cooling mechanisms, such as evaporative cooling, laser cooling, or adiabatic cooling to achieve in the current universe, though in the far future the ongoing expansion of the universe may cause the average temperature of the universe to drop below 1 K. Temperatures significantly colder than 1 K are not known to occur in nature, but have been produced in laboratories and, from the perspective of an external observer, black holes may appear to have temperatures extremely close to absolute zero when not feeding.", "Their effective temperature, , due to Hawking radiation is given by:\nWhere is the speed of light in a vacuum, is the reduced Planck constant, is the black hole's mass, and is the gravitational constant, hence:\nWhich means a black hole of mass kg, about 1.67 times the mass of the moon, would have an effective temperature of ≈ 1 K. Black holes known to actually exist in nature have significantly larger masses (and lower effective temperatures) than this, being at least several solar masses.", "At a temperature of 1 K (and a pressure of 1 standard atmosphere) the overwhelming majority of substances are solids, including nitrogen and the even more volatile neon and hydrogen.", "An exception is helium whose most common isotope, helium-4, exists in an exotic liquid-like state known as a superfluid characterised by a total absence of viscosity, while the much rarer helium-3 isotope remains a \"normal\" liquid.", "At 1 K some common metals, including lead and mercury are superconductors, losing all electrical resistance.", "A black body at 1 K radiates energy at a rate of about 56.7 nW per square metre with a peak wavelength of about 2.9 mm, in the microwave spectrum.", "A heat pump attempting to extract heat from an refrigeration chamber at 1 K and vent it into an ambient environment at 20 °C, would require a minimum of 292.15 joules of mechanical work to draw out 1 joule of thermal energy.", "Before the 13th CGPM in 1967–1968, the unit kelvin was termed a \"degree\", the same as with the other temperature scales at the time.", "It was distinguished from the other scales with either the adjective suffix \"Kelvin\" (\"degree Kelvin\") or with \"absolute\" (\"degree absolute\") and its symbol was °K.", "The latter term (degree absolute), which was the unit's official name from 1948 until 1954, was ambiguous since it could also be interpreted as referring to the Rankine scale.", "Before the 13th CGPM, the plural form was \"degrees absolute\".", "The 13th CGPM changed the unit name to simply \"kelvin\" (symbol: K).", "The omission of \"degree\" indicates that it is not relative to an arbitrary reference point like the Celsius and Fahrenheit scales (although the Rankine scale continued to use \"degree Rankine\"), but rather an absolute unit of measure which can be manipulated algebraically (e.g., multiplied by two to indicate twice the amount of \"mean energy\" available among elementary degrees of freedom of the system).", "The preferred plural form of kelvin is not explicitly stated in the SI Brochure or in the for the kelvin.", "The 8th edition of the Brochure (written before the 2019 redefinition) refers to the kelvin in plural as \"kelvins\":\n\"A difference or interval of temperature may be expressed in kelvins or in degrees Celsius, the numerical value of the temperature difference being\nthe same.\"\nHowever in the 9th edition (written after the redefinition) this was changed to:\n\"A difference or interval of temperature may be expressed in kelvin or in degrees Celsius, the numerical value of the temperature difference being the same in either case.\"\nThe US based National Institute of Standards and Technology recommends the use of \"kelvins\":\n\"The kelvin unit is not expressed in degrees like Celsius or Fahrenheit are.", "It is used by itself to describe temperature.", "For example, 'mercury loses all electrical resistance at a temperature of 4.2 kelvins.", "The style guide for CERN, however, specifically says to always use \"kelvin\", even when plural.", "The US based Merriam-Webster dictionary recommends \"kelvins\"", "When writing the name of the unit out in full it is uncapitalised, except in contexts where most words would be capitalised (e.g. at the start of a sentence or as part of a title) however, when abbreviated to a symbol, K, it is \"always\" capitalised.", "In the SI an uncapitalised (and unitalicised) letter k would indicate the kilo- prefix:\n″The kelvin is the SI base unit of temperature.″\nAlex: ″What units do you want me to record this in?″", "Billie: ″Kelvins!″\n″The sample was chilled to 50 K.\"\n″Tay traveled 100 km from Poughkeepsie to Manhattan.″\nThis somewhat unintuitive convention is in fact in line with other SI units named after people, such as the newton, watt, and tesla, symbols N, W, and T respectively.", "When reference is made to the \"Kelvin \"scale\"\", the word \"kelvin\"—which is normally a noun—functions adjectivally to modify the noun \"scale\" and is capitalised.", "As with most other SI unit symbols (angle symbols, e.g., 45° 3′ 4″, are the exception) there is a space between the numeric value and the kelvin symbol (e.g., \"99.987 K\").", "The size of a degree Celsius (historically defined as of the temperature difference between the melting and boiling points of water, see history section for more details), was the template for the size of the kelvin and the convention that the Kelvin and Celsius scales have the same size increments remains in place today, meaning that a \"change\" in temperature or a \"difference\" in temperature necessarily has the same numerical value when expressed in kelvins as it does when expressed in degrees Celsius:\nHowever while the Kelvin scale takes absolute zero as its starting point, the modern iteration of the Celsius scale takes 273.15 K as its starting point, this being a close approximation of the melting point of water at standard atmospheric pressure, indeed, the 9th edition of the SI Brochure \"defines\" the temperature in Celsius such that:\nSo, for example, \"It is 10 °C colder outside the house than inside\" and \"It is 10 K colder outside the house than inside\" are exactly equivalent statements, while \"It is 10 °C outside\" and \"It is 10 K outside\" describe very different situations!", "This convention makes conversion between °C and K relatively straightforward, but has the downside that neither the melting nor boiling points of water have round values when expressed in kelvins, being approximately 273.15 K and 373.15 K respectively.", "As the melting and boiling points of water were historically 180 degrees apart on the Fahrenheit scale (32 °F and 212 °F, respectively) a temperature interval of 1 K (and of 1 °C) is equal to an interval of 1.8 °F.", "Absolute zero in °F is:\nHence:", "The kelvin is often used as a measure of the colour temperature of light sources.", "Colour temperature is based upon the principle that a black body radiator emits light with a frequency distribution characteristic of its temperature.", "Black bodies at temperatures below about appear reddish, whereas those above about appear bluish.", "Colour temperature is important in the fields of image projection and photography, where a colour temperature of approximately is required to match \"daylight\" film emulsions.", "In astronomy, the stellar classification of stars and their place on the Hertzsprung–Russell diagram are based, in part, upon their surface temperature, known as effective temperature.", "The photosphere of the Sun, for instance, has an effective temperature of .", "Digital cameras and photographic software often use colour temperature in K in edit and setup menus.", "The simple guide is that higher colour temperature produces an image with enhanced white and blue hues.", "The reduction in colour temperature produces an image more dominated by reddish, \"warmer\" colours.", "For electronics, the kelvin is used as an indicator of how noisy a circuit is in relation to an ultimate noise floor, i.e. the noise temperature.", "The so-called Johnson–Nyquist noise of discrete resistors and capacitors is a type of thermal noise derived from the Boltzmann constant and can be used to determine the noise temperature of a circuit using the Friis formulas for noise.", "The International System of Units (SI) is based on seven SI base units (the second, metre, kilogram, kelvin, ampere, mole, and candela) representing seven fundamental types of physical quantity, or \"dimensions\" (time, length, mass, temperature, electrical current, amount of substance, and luminous intensity respectively), with all other SI units defined using these seven basic building blocks.", "These SI derived units can either be given special names, e.g., tesla, volt, lux, etc., or left as bare descriptions, e.g. metre per second.", "The only SI unit with a special name derived from the kelvin is the degree Celsius, which is also the only SI unit derived from another by offsetting, rather than by multiplication or division.", "Some commonly used units derived from the kelvin without special names are:\nMany of these are of interest in the engineering of heating, ventilation, and air conditioning systems and of building insulation.", "Coefficient of thermal expansion is an important consideration in structural engineering.", "Like other SI units, the kelvin can modified by adding a prefix that multiplies it by a power of 10.", "A yoctokelvin (yK) is one septillionth of a kelvin () and the smallest unit of temperature defined in the International System of Units.", "It is a little more than the temperature increase that would result from adding 1 joule of thermal energy to the Indian Ocean, assuming properties similar to those of pure water.", "A zeptokelvin (zK) is one sextillionth of a kelvin ().", "It is somewhat less than the temperature increase that would result from adding 1 joule of thermal energy to the Baltic Sea, assuming properties similar to those of pure water.", "An attokelvin (aK) is one quintillionth of a kelvin ().", "It is the approximate effective temperature of an extremely massive 61.7 billion solar mass supermassive black hole, only a little less massive than the black hole Ton 618, and the approximate temperature increase that would result from adding 1 joule of thermal energy to Lake Toba, the largest lake in Indonesia.", "A femtokelvin (fK) is one quadrillionth of a kelvin ().", "It is the approximate effective temperature of a 61.7 million solar mass supermassive black hole.", "A picokelvin (pK) is one trillionth of a kelvin ().", "A nanokelvin (nK) is one billionth of a kelvin ().", "It is the approximate effective temperature of a fairly large 61.7 solar mass stellar-mass black hole.", "NASA's Cold Atom Laboratory can chill small numbers of atoms down to below 1 nanokelvin.", "A microkelvin (μK) is one millionth of a kelvin ().", "A millikelvin (mK) is one thousandth of a kelvin (0.001 K or ).", "A centikelvin (cK) is one hundredth of a kelvin (0.01 K or ).", "A decikelvin (dK) is one tenth of a kelvin (0.1 K or ).", "A decakelvin (daK) is ten kelvins (10 K or ).", "The main components of air, nitrogen and oxygen, boil at 77 K and 90 K respectively under 1 atmosphere of pressure.", "A hectokelvin (hK) is one hundred kelvins (100 K or ).", "Air temperatures recorded occurring naturally on Earth (excluding, e.g. wildfires, volcanoes, and meteorite impacts) range from 184 K at Vostok Station in Antarctica to 330 K at Furnace Creek in Death Valley.", "Yakutsk in Russia's Sakha Republic has a daily average low in January of 229 K. Ice melts at 273.15 K. Kuwait City has a daily average high in July and August of 320 K. Water boils at 373.15 K at 1 atmosphere.", "The average surface temperature on Venus in 737 K.", "A kilokelvin (kK) is one thousand kelvins (1000 K or ).", "Iron melts at 1811 K, or 1.8 kK. The temperature at the surface of the Sun is about 5800 K, or 5.8 kK.", "A megakelvin (MK) is one million kelvins ().", "The temperature at the centre of the Sun is about 15.7 MK.", "A gigakelvin (GK) is one billion kelvins ().", "A terakelvin (TK) is one trillion kelvins ().", "A petakelvin (PK) is one quadrillion kelvins ().", "An exakelvin (EK) is one quintillion kelvins ().", "A zettakelvin (ZK) is one sextillion kelvins ().", "A yottakelvin (YK) is one septillion kelvins () and the largest unit of temperature defined in the SI.", "It corresponds to a mean translational kinetic energy of joules, the same order of magnitude as the Oh-My-God particle.", "The Planck temperature is approximately 141,680,000 yottakelvins.", "The symbol is encoded in Unicode at code point .", "However, this is a compatibility character provided for compatibility with legacy encodings.", "The Unicode standard recommends using instead; that is, a normal capital K. \"Three letterlike symbols have been given canonical equivalence to regular letters: , , and .", "In all three instances, the regular letter should be used.\"" ]

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[ "Baron Kelvin (1824–1907).", "The Kelvin scale is an absolute thermodynamic temperature scale, meaning it uses absolute zero as its null point.", "Hence, one kelvin is equal to a change in the thermodynamic temperature T that results in a change of thermal energy T by J." ]

[ "During the 18th century multiple temperature scales were developed, most notably Fahrenheit and centigrade (later Celsius).", "These scales predated much of the modern science of thermodynamics, including the scientific consensus in favour of atomic theory and the kinetic theory of gases that underpin the concept of absolute zero.", "Instead, they chose defining points inside the range of human experience at the time that could be easily and reasonably accurately reproduced, but did not necessarily have any deep significance in thermal physics.", "In the case of the Celsius scale (and the long since defunct Newton scale and Réaumur scale) the melting point of water served as such a semi-arbitrary starting point, with Celsius being defined, from the 1740s up until the 1940s, by calibrating a thermometer such that:\n\nThis referring to pure water at a set pressure designed to approximate the natural air pressure at sea level.", "An implication of this was that an increment of 1 °C was equal to an increment of of the temperature difference between the melting and boiling points.", "This temperature interval would go on to become the template for the kelvin.", "In October 1848, William Thomson, a 24 year old professor of Natural Philosophy at the University of Glasgow, published a paper \"On an Absolute Thermometric Scale\".", "Using the soon-to-be-defunct caloric theory, he proposed an \"absolute\" scale based on the following parameters:\n\n\"The arbitrary points which coincide on the two scales are 0° and 100°\"\n\"The characteristic property of the scale which I now propose is, that all degrees have the same value; that is, that a unit of heat descending from a body \"A\" at the temperature \"T\"° of this scale, to a body \"B\" at the temperature (\"T\" − 1)°, would give out the same mechanical effect, whatever be the number \"T\".", "This may justly be termed an absolute scale, since its characteristic is quite independent of the physical properties of any specific substance.", "\"\nAs Carnot's theorem is understood in modern thermodynamics to simply describe the maximum efficiency with which thermal energy can be converted to mechanical energy and the predicted maximum efficiency is a function of the \"ratio\" between the absolute temperatures of the heat source and heat sink:\nIt follows that increments of equal numbers of degrees on this scale must always represent equal \"proportional\" increases in absolute temperature.", "The numerical value of an absolute temperature, , on the 1848 scale is related to the absolute temperature of the melting point of water, , and the absolute temperature of the boiling point of water, , by:\nOn this scale, an increase of 222 degrees always means an approximate doubling of absolute temperature regardless of the starting temperature.", "In a footnote Thomson calculated that \"infinite cold\" (absolute zero, which would have a numerical value of negative infinity on this scale) was equivalent to −273 °C using the air thermometers of the time.", "This value of \"−273\" was the negative reciprocal of 0.00366—the accepted expansion coefficient of gas per degree Celsius relative to the ice point, giving a remarkable consistency to the currently accepted value.", "Within a decade, Thomson had abandoned caloric theory and superseded the 1848 scale with a new one based on the 2 features that would characterise all future versions of the kelvin scale:\n\nIn 1892 Thomson was awarded the noble title 1st", "Baron Kelvin of Largs, or more succinctly Lord Kelvin.", "This name was a reference to the River Kelvin which flows through the grounds of Glasgow University.", "In the early decades of the 20th century, the Kelvin scale was often called the \"absolute Celsius\" scale, indicating Celsius degrees counted from absolute zero rather than the freezing point of water, and using the same symbol for regular Celsius degrees, °C.", "In 1873 William Thomson's older brother James coined the term \"triple point\" to describe the combination of temperature and pressure at which the solid, liquid, and gas phases of a substance were capable of coexisting in thermodynamic equilibrium.", "While any two phases could coexist along a range of temperature-pressure combinations (e.g. the boiling point of water can be affected quite dramatically by raising or lowering the pressure), the triple point condition for a given substance can occur only at 1 pressure and only at 1 temperature.", "By the 1940s, the triple point of water had been experimentally measured to be about 0.6% of standard atmospheric pressure and very close to 0.01 °C per the historical definition of Celsius then in use.", "In 1948, the Celsius scale was recalibrated by assigning the triple point temperature of water the value of 0.01 °C exactly and allowing the melting point at standard atmospheric pressure to have an empirically determined value (and the actual melting point at ambient pressure to have a fluctuating value) close to 0 °C.", "This was justified on the grounds that the triple point was judged to give a more accurately reproducible reference temperature than the melting point.", "In 1954, with absolute zero having been experimentally determined to be about −273.15 °C per the definition of °C then in use, Resolution 3 of the 10th General Conference on Weights and Measures (CGPM) introduced a new internationally standardised Kelvin scale which defined the triple point as exactly:\n273.15 + 0.01 = 273.16 \"degrees Kelvin\"\nIn 1967/1968, Resolution 3 of the 13th CGPM renamed the unit increment of thermodynamic temperature \"kelvin\", symbol K, replacing \"degree Kelvin\", symbol °K.", "Furthermore, feeling it useful to more explicitly define the magnitude of the unit increment, the 13th CGPM also held in Resolution 4 that \"The kelvin, unit of thermodynamic temperature, is equal to the fraction of the thermodynamic temperature of the triple point of water.", "\"\nAfter the 1983 redefinition of the metre, this left the kelvin, the second, and the kilogram as the only SI units not defined with reference to any other unit.", "Hydrogen has 2 stable isotopes (and one trace radioisotope) and oxygen has 3 stable isotopes.", "In 2005, noting that the triple point could be influenced by the isotopic ratio of the hydrogen and oxygen making up a water sample and that this was \"now one of the major sources of the observed variability between different realizations of the water triple point\", the International Committee for Weights and Measures (CIPM), a committee of the CGPM, affirmed that for the purposes of delineating the temperature of the triple point of water, the definition of the kelvin would refer to water having the isotopic composition specified for Vienna Standard Mean Ocean Water:", "In 2005 the CIPM began a programme to redefine the kelvin (along with the other SI units) using a more experimentally rigorous method.", "In particular, the committee proposed redefining the kelvin such that the Boltzmann constant takes the exact value .", "The committee had hoped that the program would be completed in time for its adoption by the CGPM at its 2011 meeting, but at the 2011 meeting the decision was postponed to the 2014 meeting when it would be considered as part of a larger program.", "The redefinition was further postponed in 2014, pending more accurate measurements of Boltzmann's constant in terms of the current definition,\nbut was finally adopted at the 26th CGPM in late 2018, with a value of  = \nFor scientific purposes, the main advantage is that this allows measurements at very low and very high temperatures to be made more accurately, as the techniques used depend on the Boltzmann constant.", "It also has the philosophical advantage of being independent of any particular substance.", "The unit J/K is equal to kg⋅m2⋅s−2⋅K−1, where the kilogram, metre and second are defined in terms of the Planck constant, the speed of light, and the duration of the caesium-133 ground-state hyperfine transition respectively.", "Thus, this definition depends only on universal constants, and not on any physical artifacts as practiced previously, such as the International Prototype of the Kilogram, whose mass diverged over time from the original value.", "The challenge was to avoid degrading the accuracy of measurements close to the triple point.", "For practical purposes, the redefinition was unnoticed; water still freezes at 273.15 K (0 °C), and the triple point of water continues to be a commonly used laboratory reference temperature.", "The difference is that, before the redefinition, the triple point of water was exact and the Boltzmann constant had a measured value of , with a relative standard uncertainty of .", "Afterward, the Boltzmann constant is exact and the uncertainty is transferred to the triple point of water, which is now .", "For legal metrology purposes, the new definition officially came into force on 20 May 2019, the 144th anniversary of the Metre Convention.", "The post-2019 definition is based on fixing the value of the Boltzmann constant , expressed in SI units, at joules per kelvin.", "This constant appears in (some formulations of) the ideal gas law, which links the pressure, , of an ideal gas, its volume, , its temperature, , and the number of gas particles making it up, , via the relationship:\nSubstituting in the defined value of gives:\nWhich can be rearranged to give:\nOr:\nWhere (K) is the numerical value of the temperature expressed in kelvins, and (J) is the numerical value of the product of the pressure and the average volume per gas particle expressed in joules.", "It is worth emphasising that in dimensional analysis terms the product of a pressure and a volume is an energy.", "This can be seen by considering that pressure, volume, and energy have the dimensions force/length2, length3 and force × length, respectively.", "Another context where this relationship becomes intuitive is in the case of a pump or a water turbine, where the minimum energy demand and maximum energy available, respectively, is given by the volume of fluid passing through the component multiplied by the pressure differential across it.", "The above temperature equation holds exactly for an ideal gas, a hypothetical substance composed of point particles affected only by elastic collisions with their container, but is closely approximated by a real gas that is well above its boiling or sublimation point and well below its critical pressure.", "Using the metric prefix system this can be given as:\nBecause the average kinetic energy per degree of freedom is and gas particles have 3 translational degrees of freedom, the temperature in kelvins is also related to the mean kinetic energy per degree of freedom by:\nAnd to the mean translational kinetic energy by:\nExpressed in terms of the SI defining constants 1 kelvin is:\nWhere is the Planck constant and is the caesium-133 hyperfine transition frequency.", "Because the term is equal to the photon energy of the caesium-133 hyperfine transition radiation, , and 1/ is equal to for an ideal gas:\nWhich can be rearranged to give:\nOr:\nExpressed in terms of mean kinetic energy, this becomes:\nAnd:", "Although the kelvin is an SI base unit, its only use in fundamental physics is the Boltzmann constant.", "This allows a natural unit definition that makes kelvins and joules different units for the same dimension, .", "Such a definition is already in use in some textbooks.", "However, such a definition is unlikely to have a practical use in an experiment due to the large orders of magnitude involved.", "Several physical constants are defined in terms of the Boltzmann constant and other SI defining constants, for example the universal gas constant, , is defined as the product of the Boltzmann constant, , and the Avogadro constant, A. Prior to 2019, its value in SI units could only be empirically estimated, with a small but inevitable degree of experimental uncertainty.", "After 2019, the kelvin was redefined by giving an exact value to the Boltzmann constant and the mole was redefined by assigning an exact value to the Avogadro constant, meaning the value of the universal gas constant in SI units could be calculated exactly as:\nSimilarly, the Stefan-Boltzmann constant, \"σ\", not to be confused with the Boltzmann constant, relates the temperature of a black body to the rate at which thermal energy is electromagnetically radiated from its surface and is equal to:\nWhere is the Planck constant, whose value now defines the kilogram, and is the speed of light, whose value now defines the metre (and had been implicit in the definition of the metre since 1983).", "The exact value of \"σ\" in SI units is therefore:\nThe second radiation constant in Planck's law, 2, is equal to:\nWhich means its exact value in SI units is:", "1 kelvin is the approximate temperature of the Boomerang Nebula, the coldest known natural environment in the universe.", "Because 1 K is colder than the effective temperature of the cosmic microwave background (about 2.7 K), it cannot be reached simply by moving a previously warm object far away from point sources of heat (e.g. stars) and requires additional cooling mechanisms, such as evaporative cooling, laser cooling, or adiabatic cooling to achieve in the current universe, though in the far future the ongoing expansion of the universe may cause the average temperature of the universe to drop below 1 K. Temperatures significantly colder than 1 K are not known to occur in nature, but have been produced in laboratories and, from the perspective of an external observer, black holes may appear to have temperatures extremely close to absolute zero when not feeding.", "Their effective temperature, , due to Hawking radiation is given by:\nWhere is the speed of light in a vacuum, is the reduced Planck constant, is the black hole's mass, and is the gravitational constant, hence:\nWhich means a black hole of mass kg, about 1.67 times the mass of the moon, would have an effective temperature of ≈ 1 K. Black holes known to actually exist in nature have significantly larger masses (and lower effective temperatures) than this, being at least several solar masses.", "At a temperature of 1 K (and a pressure of 1 standard atmosphere) the overwhelming majority of substances are solids, including nitrogen and the even more volatile neon and hydrogen.", "An exception is helium whose most common isotope, helium-4, exists in an exotic liquid-like state known as a superfluid characterised by a total absence of viscosity, while the much rarer helium-3 isotope remains a \"normal\" liquid.", "At 1 K some common metals, including lead and mercury are superconductors, losing all electrical resistance.", "A black body at 1 K radiates energy at a rate of about 56.7 nW per square metre with a peak wavelength of about 2.9 mm, in the microwave spectrum.", "A heat pump attempting to extract heat from an refrigeration chamber at 1 K and vent it into an ambient environment at 20 °C, would require a minimum of 292.15 joules of mechanical work to draw out 1 joule of thermal energy.", "Before the 13th CGPM in 1967–1968, the unit kelvin was termed a \"degree\", the same as with the other temperature scales at the time.", "It was distinguished from the other scales with either the adjective suffix \"Kelvin\" (\"degree Kelvin\") or with \"absolute\" (\"degree absolute\") and its symbol was °K.", "The latter term (degree absolute), which was the unit's official name from 1948 until 1954, was ambiguous since it could also be interpreted as referring to the Rankine scale.", "Before the 13th CGPM, the plural form was \"degrees absolute\".", "The 13th CGPM changed the unit name to simply \"kelvin\" (symbol: K).", "The omission of \"degree\" indicates that it is not relative to an arbitrary reference point like the Celsius and Fahrenheit scales (although the Rankine scale continued to use \"degree Rankine\"), but rather an absolute unit of measure which can be manipulated algebraically (e.g., multiplied by two to indicate twice the amount of \"mean energy\" available among elementary degrees of freedom of the system).", "The preferred plural form of kelvin is not explicitly stated in the SI Brochure or in the for the kelvin.", "The 8th edition of the Brochure (written before the 2019 redefinition) refers to the kelvin in plural as \"kelvins\":\n\"A difference or interval of temperature may be expressed in kelvins or in degrees Celsius, the numerical value of the temperature difference being\nthe same.\"\nHowever in the 9th edition (written after the redefinition) this was changed to:\n\"A difference or interval of temperature may be expressed in kelvin or in degrees Celsius, the numerical value of the temperature difference being the same in either case.\"\nThe US based National Institute of Standards and Technology recommends the use of \"kelvins\":\n\"The kelvin unit is not expressed in degrees like Celsius or Fahrenheit are.", "It is used by itself to describe temperature.", "For example, 'mercury loses all electrical resistance at a temperature of 4.2 kelvins.", "The style guide for CERN, however, specifically says to always use \"kelvin\", even when plural.", "The US based Merriam-Webster dictionary recommends \"kelvins\"", "When writing the name of the unit out in full it is uncapitalised, except in contexts where most words would be capitalised (e.g. at the start of a sentence or as part of a title) however, when abbreviated to a symbol, K, it is \"always\" capitalised.", "In the SI an uncapitalised (and unitalicised) letter k would indicate the kilo- prefix:\n″The kelvin is the SI base unit of temperature.″\nAlex: ″What units do you want me to record this in?″", "Billie: ″Kelvins!″\n″The sample was chilled to 50 K.\"\n″Tay traveled 100 km from Poughkeepsie to Manhattan.″\nThis somewhat unintuitive convention is in fact in line with other SI units named after people, such as the newton, watt, and tesla, symbols N, W, and T respectively.", "When reference is made to the \"Kelvin \"scale\"\", the word \"kelvin\"—which is normally a noun—functions adjectivally to modify the noun \"scale\" and is capitalised.", "As with most other SI unit symbols (angle symbols, e.g., 45° 3′ 4″, are the exception) there is a space between the numeric value and the kelvin symbol (e.g., \"99.987 K\").", "The size of a degree Celsius (historically defined as of the temperature difference between the melting and boiling points of water, see history section for more details), was the template for the size of the kelvin and the convention that the Kelvin and Celsius scales have the same size increments remains in place today, meaning that a \"change\" in temperature or a \"difference\" in temperature necessarily has the same numerical value when expressed in kelvins as it does when expressed in degrees Celsius:\nHowever while the Kelvin scale takes absolute zero as its starting point, the modern iteration of the Celsius scale takes 273.15 K as its starting point, this being a close approximation of the melting point of water at standard atmospheric pressure, indeed, the 9th edition of the SI Brochure \"defines\" the temperature in Celsius such that:\nSo, for example, \"It is 10 °C colder outside the house than inside\" and \"It is 10 K colder outside the house than inside\" are exactly equivalent statements, while \"It is 10 °C outside\" and \"It is 10 K outside\" describe very different situations!", "This convention makes conversion between °C and K relatively straightforward, but has the downside that neither the melting nor boiling points of water have round values when expressed in kelvins, being approximately 273.15 K and 373.15 K respectively.", "As the melting and boiling points of water were historically 180 degrees apart on the Fahrenheit scale (32 °F and 212 °F, respectively) a temperature interval of 1 K (and of 1 °C) is equal to an interval of 1.8 °F.", "Absolute zero in °F is:\nHence:", "The kelvin is often used as a measure of the colour temperature of light sources.", "Colour temperature is based upon the principle that a black body radiator emits light with a frequency distribution characteristic of its temperature.", "Black bodies at temperatures below about appear reddish, whereas those above about appear bluish.", "Colour temperature is important in the fields of image projection and photography, where a colour temperature of approximately is required to match \"daylight\" film emulsions.", "In astronomy, the stellar classification of stars and their place on the Hertzsprung–Russell diagram are based, in part, upon their surface temperature, known as effective temperature.", "The photosphere of the Sun, for instance, has an effective temperature of .", "Digital cameras and photographic software often use colour temperature in K in edit and setup menus.", "The simple guide is that higher colour temperature produces an image with enhanced white and blue hues.", "The reduction in colour temperature produces an image more dominated by reddish, \"warmer\" colours.", "For electronics, the kelvin is used as an indicator of how noisy a circuit is in relation to an ultimate noise floor, i.e. the noise temperature.", "The so-called Johnson–Nyquist noise of discrete resistors and capacitors is a type of thermal noise derived from the Boltzmann constant and can be used to determine the noise temperature of a circuit using the Friis formulas for noise.", "The International System of Units (SI) is based on seven SI base units (the second, metre, kilogram, kelvin, ampere, mole, and candela) representing seven fundamental types of physical quantity, or \"dimensions\" (time, length, mass, temperature, electrical current, amount of substance, and luminous intensity respectively), with all other SI units defined using these seven basic building blocks.", "These SI derived units can either be given special names, e.g., tesla, volt, lux, etc., or left as bare descriptions, e.g. metre per second.", "The only SI unit with a special name derived from the kelvin is the degree Celsius, which is also the only SI unit derived from another by offsetting, rather than by multiplication or division.", "Some commonly used units derived from the kelvin without special names are:\nMany of these are of interest in the engineering of heating, ventilation, and air conditioning systems and of building insulation.", "Coefficient of thermal expansion is an important consideration in structural engineering.", "Like other SI units, the kelvin can modified by adding a prefix that multiplies it by a power of 10.", "A yoctokelvin (yK) is one septillionth of a kelvin () and the smallest unit of temperature defined in the International System of Units.", "It is a little more than the temperature increase that would result from adding 1 joule of thermal energy to the Indian Ocean, assuming properties similar to those of pure water.", "A zeptokelvin (zK) is one sextillionth of a kelvin ().", "It is somewhat less than the temperature increase that would result from adding 1 joule of thermal energy to the Baltic Sea, assuming properties similar to those of pure water.", "An attokelvin (aK) is one quintillionth of a kelvin ().", "It is the approximate effective temperature of an extremely massive 61.7 billion solar mass supermassive black hole, only a little less massive than the black hole Ton 618, and the approximate temperature increase that would result from adding 1 joule of thermal energy to Lake Toba, the largest lake in Indonesia.", "A femtokelvin (fK) is one quadrillionth of a kelvin ().", "It is the approximate effective temperature of a 61.7 million solar mass supermassive black hole.", "A picokelvin (pK) is one trillionth of a kelvin ().", "A nanokelvin (nK) is one billionth of a kelvin ().", "It is the approximate effective temperature of a fairly large 61.7 solar mass stellar-mass black hole.", "NASA's Cold Atom Laboratory can chill small numbers of atoms down to below 1 nanokelvin.", "A microkelvin (μK) is one millionth of a kelvin ().", "A millikelvin (mK) is one thousandth of a kelvin (0.001 K or ).", "A centikelvin (cK) is one hundredth of a kelvin (0.01 K or ).", "A decikelvin (dK) is one tenth of a kelvin (0.1 K or ).", "A decakelvin (daK) is ten kelvins (10 K or ).", "The main components of air, nitrogen and oxygen, boil at 77 K and 90 K respectively under 1 atmosphere of pressure.", "A hectokelvin (hK) is one hundred kelvins (100 K or ).", "Air temperatures recorded occurring naturally on Earth (excluding, e.g. wildfires, volcanoes, and meteorite impacts) range from 184 K at Vostok Station in Antarctica to 330 K at Furnace Creek in Death Valley.", "Yakutsk in Russia's Sakha Republic has a daily average low in January of 229 K. Ice melts at 273.15 K. Kuwait City has a daily average high in July and August of 320 K. Water boils at 373.15 K at 1 atmosphere.", "The average surface temperature on Venus in 737 K.", "A kilokelvin (kK) is one thousand kelvins (1000 K or ).", "Iron melts at 1811 K, or 1.8 kK. The temperature at the surface of the Sun is about 5800 K, or 5.8 kK.", "A megakelvin (MK) is one million kelvins ().", "The temperature at the centre of the Sun is about 15.7 MK.", "A gigakelvin (GK) is one billion kelvins ().", "A terakelvin (TK) is one trillion kelvins ().", "A petakelvin (PK) is one quadrillion kelvins ().", "An exakelvin (EK) is one quintillion kelvins ().", "A zettakelvin (ZK) is one sextillion kelvins ().", "A yottakelvin (YK) is one septillion kelvins () and the largest unit of temperature defined in the SI.", "It corresponds to a mean translational kinetic energy of joules, the same order of magnitude as the Oh-My-God particle.", "The Planck temperature is approximately 141,680,000 yottakelvins.", "The symbol is encoded in Unicode at code point .", "However, this is a compatibility character provided for compatibility with legacy encodings.", "The Unicode standard recommends using instead; that is, a normal capital K. \"Three letterlike symbols have been given canonical equivalence to regular letters: , , and .", "In all three instances, the regular letter should be used.\"" ]

[ 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ]

[ "Baron Kelvin (1824–1907).", "The Kelvin scale is an absolute thermodynamic temperature scale, meaning it uses absolute zero as its null point.", "Hence, one kelvin is equal to a change in the thermodynamic temperature T that results in a change of thermal energy T by J." ]

[ "During the 18th century multiple temperature scales were developed, most notably Fahrenheit and centigrade (later Celsius).", "These scales predated much of the modern science of thermodynamics, including the scientific consensus in favour of atomic theory and the kinetic theory of gases that underpin the concept of absolute zero.", "Instead, they chose defining points inside the range of human experience at the time that could be easily and reasonably accurately reproduced, but did not necessarily have any deep significance in thermal physics.", "In the case of the Celsius scale (and the long since defunct Newton scale and Réaumur scale) the melting point of water served as such a semi-arbitrary starting point, with Celsius being defined, from the 1740s up until the 1940s, by calibrating a thermometer such that:\n\nThis referring to pure water at a set pressure designed to approximate the natural air pressure at sea level.", "An implication of this was that an increment of 1 °C was equal to an increment of of the temperature difference between the melting and boiling points.", "This temperature interval would go on to become the template for the kelvin.", "In October 1848, William Thomson, a 24 year old professor of Natural Philosophy at the University of Glasgow, published a paper \"On an Absolute Thermometric Scale\".", "Using the soon-to-be-defunct caloric theory, he proposed an \"absolute\" scale based on the following parameters:\n\n\"The arbitrary points which coincide on the two scales are 0° and 100°\"\n\"The characteristic property of the scale which I now propose is, that all degrees have the same value; that is, that a unit of heat descending from a body \"A\" at the temperature \"T\"° of this scale, to a body \"B\" at the temperature (\"T\" − 1)°, would give out the same mechanical effect, whatever be the number \"T\".", "This may justly be termed an absolute scale, since its characteristic is quite independent of the physical properties of any specific substance.", "\"\nAs Carnot's theorem is understood in modern thermodynamics to simply describe the maximum efficiency with which thermal energy can be converted to mechanical energy and the predicted maximum efficiency is a function of the \"ratio\" between the absolute temperatures of the heat source and heat sink:\nIt follows that increments of equal numbers of degrees on this scale must always represent equal \"proportional\" increases in absolute temperature.", "The numerical value of an absolute temperature, , on the 1848 scale is related to the absolute temperature of the melting point of water, , and the absolute temperature of the boiling point of water, , by:\nOn this scale, an increase of 222 degrees always means an approximate doubling of absolute temperature regardless of the starting temperature.", "In a footnote Thomson calculated that \"infinite cold\" (absolute zero, which would have a numerical value of negative infinity on this scale) was equivalent to −273 °C using the air thermometers of the time.", "This value of \"−273\" was the negative reciprocal of 0.00366—the accepted expansion coefficient of gas per degree Celsius relative to the ice point, giving a remarkable consistency to the currently accepted value.", "Within a decade, Thomson had abandoned caloric theory and superseded the 1848 scale with a new one based on the 2 features that would characterise all future versions of the kelvin scale:\n\nIn 1892 Thomson was awarded the noble title 1st", "Baron Kelvin of Largs, or more succinctly Lord Kelvin.", "This name was a reference to the River Kelvin which flows through the grounds of Glasgow University.", "In the early decades of the 20th century, the Kelvin scale was often called the \"absolute Celsius\" scale, indicating Celsius degrees counted from absolute zero rather than the freezing point of water, and using the same symbol for regular Celsius degrees, °C.", "In 1873 William Thomson's older brother James coined the term \"triple point\" to describe the combination of temperature and pressure at which the solid, liquid, and gas phases of a substance were capable of coexisting in thermodynamic equilibrium.", "While any two phases could coexist along a range of temperature-pressure combinations (e.g. the boiling point of water can be affected quite dramatically by raising or lowering the pressure), the triple point condition for a given substance can occur only at 1 pressure and only at 1 temperature.", "By the 1940s, the triple point of water had been experimentally measured to be about 0.6% of standard atmospheric pressure and very close to 0.01 °C per the historical definition of Celsius then in use.", "In 1948, the Celsius scale was recalibrated by assigning the triple point temperature of water the value of 0.01 °C exactly and allowing the melting point at standard atmospheric pressure to have an empirically determined value (and the actual melting point at ambient pressure to have a fluctuating value) close to 0 °C.", "This was justified on the grounds that the triple point was judged to give a more accurately reproducible reference temperature than the melting point.", "In 1954, with absolute zero having been experimentally determined to be about −273.15 °C per the definition of °C then in use, Resolution 3 of the 10th General Conference on Weights and Measures (CGPM) introduced a new internationally standardised Kelvin scale which defined the triple point as exactly:\n273.15 + 0.01 = 273.16 \"degrees Kelvin\"\nIn 1967/1968, Resolution 3 of the 13th CGPM renamed the unit increment of thermodynamic temperature \"kelvin\", symbol K, replacing \"degree Kelvin\", symbol °K.", "Furthermore, feeling it useful to more explicitly define the magnitude of the unit increment, the 13th CGPM also held in Resolution 4 that \"The kelvin, unit of thermodynamic temperature, is equal to the fraction of the thermodynamic temperature of the triple point of water.", "\"\nAfter the 1983 redefinition of the metre, this left the kelvin, the second, and the kilogram as the only SI units not defined with reference to any other unit.", "Hydrogen has 2 stable isotopes (and one trace radioisotope) and oxygen has 3 stable isotopes.", "In 2005, noting that the triple point could be influenced by the isotopic ratio of the hydrogen and oxygen making up a water sample and that this was \"now one of the major sources of the observed variability between different realizations of the water triple point\", the International Committee for Weights and Measures (CIPM), a committee of the CGPM, affirmed that for the purposes of delineating the temperature of the triple point of water, the definition of the kelvin would refer to water having the isotopic composition specified for Vienna Standard Mean Ocean Water:", "In 2005 the CIPM began a programme to redefine the kelvin (along with the other SI units) using a more experimentally rigorous method.", "In particular, the committee proposed redefining the kelvin such that the Boltzmann constant takes the exact value .", "The committee had hoped that the program would be completed in time for its adoption by the CGPM at its 2011 meeting, but at the 2011 meeting the decision was postponed to the 2014 meeting when it would be considered as part of a larger program.", "The redefinition was further postponed in 2014, pending more accurate measurements of Boltzmann's constant in terms of the current definition,\nbut was finally adopted at the 26th CGPM in late 2018, with a value of  = \nFor scientific purposes, the main advantage is that this allows measurements at very low and very high temperatures to be made more accurately, as the techniques used depend on the Boltzmann constant.", "It also has the philosophical advantage of being independent of any particular substance.", "The unit J/K is equal to kg⋅m2⋅s−2⋅K−1, where the kilogram, metre and second are defined in terms of the Planck constant, the speed of light, and the duration of the caesium-133 ground-state hyperfine transition respectively.", "Thus, this definition depends only on universal constants, and not on any physical artifacts as practiced previously, such as the International Prototype of the Kilogram, whose mass diverged over time from the original value.", "The challenge was to avoid degrading the accuracy of measurements close to the triple point.", "For practical purposes, the redefinition was unnoticed; water still freezes at 273.15 K (0 °C), and the triple point of water continues to be a commonly used laboratory reference temperature.", "The difference is that, before the redefinition, the triple point of water was exact and the Boltzmann constant had a measured value of , with a relative standard uncertainty of .", "Afterward, the Boltzmann constant is exact and the uncertainty is transferred to the triple point of water, which is now .", "For legal metrology purposes, the new definition officially came into force on 20 May 2019, the 144th anniversary of the Metre Convention.", "The post-2019 definition is based on fixing the value of the Boltzmann constant , expressed in SI units, at joules per kelvin.", "This constant appears in (some formulations of) the ideal gas law, which links the pressure, , of an ideal gas, its volume, , its temperature, , and the number of gas particles making it up, , via the relationship:\nSubstituting in the defined value of gives:\nWhich can be rearranged to give:\nOr:\nWhere (K) is the numerical value of the temperature expressed in kelvins, and (J) is the numerical value of the product of the pressure and the average volume per gas particle expressed in joules.", "It is worth emphasising that in dimensional analysis terms the product of a pressure and a volume is an energy.", "This can be seen by considering that pressure, volume, and energy have the dimensions force/length2, length3 and force × length, respectively.", "Another context where this relationship becomes intuitive is in the case of a pump or a water turbine, where the minimum energy demand and maximum energy available, respectively, is given by the volume of fluid passing through the component multiplied by the pressure differential across it.", "The above temperature equation holds exactly for an ideal gas, a hypothetical substance composed of point particles affected only by elastic collisions with their container, but is closely approximated by a real gas that is well above its boiling or sublimation point and well below its critical pressure.", "Using the metric prefix system this can be given as:\nBecause the average kinetic energy per degree of freedom is and gas particles have 3 translational degrees of freedom, the temperature in kelvins is also related to the mean kinetic energy per degree of freedom by:\nAnd to the mean translational kinetic energy by:\nExpressed in terms of the SI defining constants 1 kelvin is:\nWhere is the Planck constant and is the caesium-133 hyperfine transition frequency.", "Because the term is equal to the photon energy of the caesium-133 hyperfine transition radiation, , and 1/ is equal to for an ideal gas:\nWhich can be rearranged to give:\nOr:\nExpressed in terms of mean kinetic energy, this becomes:\nAnd:", "Although the kelvin is an SI base unit, its only use in fundamental physics is the Boltzmann constant.", "This allows a natural unit definition that makes kelvins and joules different units for the same dimension, .", "Such a definition is already in use in some textbooks.", "However, such a definition is unlikely to have a practical use in an experiment due to the large orders of magnitude involved.", "Several physical constants are defined in terms of the Boltzmann constant and other SI defining constants, for example the universal gas constant, , is defined as the product of the Boltzmann constant, , and the Avogadro constant, A. Prior to 2019, its value in SI units could only be empirically estimated, with a small but inevitable degree of experimental uncertainty.", "After 2019, the kelvin was redefined by giving an exact value to the Boltzmann constant and the mole was redefined by assigning an exact value to the Avogadro constant, meaning the value of the universal gas constant in SI units could be calculated exactly as:\nSimilarly, the Stefan-Boltzmann constant, \"σ\", not to be confused with the Boltzmann constant, relates the temperature of a black body to the rate at which thermal energy is electromagnetically radiated from its surface and is equal to:\nWhere is the Planck constant, whose value now defines the kilogram, and is the speed of light, whose value now defines the metre (and had been implicit in the definition of the metre since 1983).", "The exact value of \"σ\" in SI units is therefore:\nThe second radiation constant in Planck's law, 2, is equal to:\nWhich means its exact value in SI units is:", "1 kelvin is the approximate temperature of the Boomerang Nebula, the coldest known natural environment in the universe.", "Because 1 K is colder than the effective temperature of the cosmic microwave background (about 2.7 K), it cannot be reached simply by moving a previously warm object far away from point sources of heat (e.g. stars) and requires additional cooling mechanisms, such as evaporative cooling, laser cooling, or adiabatic cooling to achieve in the current universe, though in the far future the ongoing expansion of the universe may cause the average temperature of the universe to drop below 1 K. Temperatures significantly colder than 1 K are not known to occur in nature, but have been produced in laboratories and, from the perspective of an external observer, black holes may appear to have temperatures extremely close to absolute zero when not feeding.", "Their effective temperature, , due to Hawking radiation is given by:\nWhere is the speed of light in a vacuum, is the reduced Planck constant, is the black hole's mass, and is the gravitational constant, hence:\nWhich means a black hole of mass kg, about 1.67 times the mass of the moon, would have an effective temperature of ≈ 1 K. Black holes known to actually exist in nature have significantly larger masses (and lower effective temperatures) than this, being at least several solar masses.", "At a temperature of 1 K (and a pressure of 1 standard atmosphere) the overwhelming majority of substances are solids, including nitrogen and the even more volatile neon and hydrogen.", "An exception is helium whose most common isotope, helium-4, exists in an exotic liquid-like state known as a superfluid characterised by a total absence of viscosity, while the much rarer helium-3 isotope remains a \"normal\" liquid.", "At 1 K some common metals, including lead and mercury are superconductors, losing all electrical resistance.", "A black body at 1 K radiates energy at a rate of about 56.7 nW per square metre with a peak wavelength of about 2.9 mm, in the microwave spectrum.", "A heat pump attempting to extract heat from an refrigeration chamber at 1 K and vent it into an ambient environment at 20 °C, would require a minimum of 292.15 joules of mechanical work to draw out 1 joule of thermal energy.", "Before the 13th CGPM in 1967–1968, the unit kelvin was termed a \"degree\", the same as with the other temperature scales at the time.", "It was distinguished from the other scales with either the adjective suffix \"Kelvin\" (\"degree Kelvin\") or with \"absolute\" (\"degree absolute\") and its symbol was °K.", "The latter term (degree absolute), which was the unit's official name from 1948 until 1954, was ambiguous since it could also be interpreted as referring to the Rankine scale.", "Before the 13th CGPM, the plural form was \"degrees absolute\".", "The 13th CGPM changed the unit name to simply \"kelvin\" (symbol: K).", "The omission of \"degree\" indicates that it is not relative to an arbitrary reference point like the Celsius and Fahrenheit scales (although the Rankine scale continued to use \"degree Rankine\"), but rather an absolute unit of measure which can be manipulated algebraically (e.g., multiplied by two to indicate twice the amount of \"mean energy\" available among elementary degrees of freedom of the system).", "The preferred plural form of kelvin is not explicitly stated in the SI Brochure or in the for the kelvin.", "The 8th edition of the Brochure (written before the 2019 redefinition) refers to the kelvin in plural as \"kelvins\":\n\"A difference or interval of temperature may be expressed in kelvins or in degrees Celsius, the numerical value of the temperature difference being\nthe same.\"\nHowever in the 9th edition (written after the redefinition) this was changed to:\n\"A difference or interval of temperature may be expressed in kelvin or in degrees Celsius, the numerical value of the temperature difference being the same in either case.\"\nThe US based National Institute of Standards and Technology recommends the use of \"kelvins\":\n\"The kelvin unit is not expressed in degrees like Celsius or Fahrenheit are.", "It is used by itself to describe temperature.", "For example, 'mercury loses all electrical resistance at a temperature of 4.2 kelvins.", "The style guide for CERN, however, specifically says to always use \"kelvin\", even when plural.", "The US based Merriam-Webster dictionary recommends \"kelvins\"", "When writing the name of the unit out in full it is uncapitalised, except in contexts where most words would be capitalised (e.g. at the start of a sentence or as part of a title) however, when abbreviated to a symbol, K, it is \"always\" capitalised.", "In the SI an uncapitalised (and unitalicised) letter k would indicate the kilo- prefix:\n″The kelvin is the SI base unit of temperature.″\nAlex: ″What units do you want me to record this in?″", "Billie: ″Kelvins!″\n″The sample was chilled to 50 K.\"\n″Tay traveled 100 km from Poughkeepsie to Manhattan.″\nThis somewhat unintuitive convention is in fact in line with other SI units named after people, such as the newton, watt, and tesla, symbols N, W, and T respectively.", "When reference is made to the \"Kelvin \"scale\"\", the word \"kelvin\"—which is normally a noun—functions adjectivally to modify the noun \"scale\" and is capitalised.", "As with most other SI unit symbols (angle symbols, e.g., 45° 3′ 4″, are the exception) there is a space between the numeric value and the kelvin symbol (e.g., \"99.987 K\").", "The size of a degree Celsius (historically defined as of the temperature difference between the melting and boiling points of water, see history section for more details), was the template for the size of the kelvin and the convention that the Kelvin and Celsius scales have the same size increments remains in place today, meaning that a \"change\" in temperature or a \"difference\" in temperature necessarily has the same numerical value when expressed in kelvins as it does when expressed in degrees Celsius:\nHowever while the Kelvin scale takes absolute zero as its starting point, the modern iteration of the Celsius scale takes 273.15 K as its starting point, this being a close approximation of the melting point of water at standard atmospheric pressure, indeed, the 9th edition of the SI Brochure \"defines\" the temperature in Celsius such that:\nSo, for example, \"It is 10 °C colder outside the house than inside\" and \"It is 10 K colder outside the house than inside\" are exactly equivalent statements, while \"It is 10 °C outside\" and \"It is 10 K outside\" describe very different situations!", "This convention makes conversion between °C and K relatively straightforward, but has the downside that neither the melting nor boiling points of water have round values when expressed in kelvins, being approximately 273.15 K and 373.15 K respectively.", "As the melting and boiling points of water were historically 180 degrees apart on the Fahrenheit scale (32 °F and 212 °F, respectively) a temperature interval of 1 K (and of 1 °C) is equal to an interval of 1.8 °F.", "Absolute zero in °F is:\nHence:", "The kelvin is often used as a measure of the colour temperature of light sources.", "Colour temperature is based upon the principle that a black body radiator emits light with a frequency distribution characteristic of its temperature.", "Black bodies at temperatures below about appear reddish, whereas those above about appear bluish.", "Colour temperature is important in the fields of image projection and photography, where a colour temperature of approximately is required to match \"daylight\" film emulsions.", "In astronomy, the stellar classification of stars and their place on the Hertzsprung–Russell diagram are based, in part, upon their surface temperature, known as effective temperature.", "The photosphere of the Sun, for instance, has an effective temperature of .", "Digital cameras and photographic software often use colour temperature in K in edit and setup menus.", "The simple guide is that higher colour temperature produces an image with enhanced white and blue hues.", "The reduction in colour temperature produces an image more dominated by reddish, \"warmer\" colours.", "For electronics, the kelvin is used as an indicator of how noisy a circuit is in relation to an ultimate noise floor, i.e. the noise temperature.", "The so-called Johnson–Nyquist noise of discrete resistors and capacitors is a type of thermal noise derived from the Boltzmann constant and can be used to determine the noise temperature of a circuit using the Friis formulas for noise.", "The International System of Units (SI) is based on seven SI base units (the second, metre, kilogram, kelvin, ampere, mole, and candela) representing seven fundamental types of physical quantity, or \"dimensions\" (time, length, mass, temperature, electrical current, amount of substance, and luminous intensity respectively), with all other SI units defined using these seven basic building blocks.", "These SI derived units can either be given special names, e.g., tesla, volt, lux, etc., or left as bare descriptions, e.g. metre per second.", "The only SI unit with a special name derived from the kelvin is the degree Celsius, which is also the only SI unit derived from another by offsetting, rather than by multiplication or division.", "Some commonly used units derived from the kelvin without special names are:\nMany of these are of interest in the engineering of heating, ventilation, and air conditioning systems and of building insulation.", "Coefficient of thermal expansion is an important consideration in structural engineering.", "Like other SI units, the kelvin can modified by adding a prefix that multiplies it by a power of 10.", "A yoctokelvin (yK) is one septillionth of a kelvin () and the smallest unit of temperature defined in the International System of Units.", "It is a little more than the temperature increase that would result from adding 1 joule of thermal energy to the Indian Ocean, assuming properties similar to those of pure water.", "A zeptokelvin (zK) is one sextillionth of a kelvin ().", "It is somewhat less than the temperature increase that would result from adding 1 joule of thermal energy to the Baltic Sea, assuming properties similar to those of pure water.", "An attokelvin (aK) is one quintillionth of a kelvin ().", "It is the approximate effective temperature of an extremely massive 61.7 billion solar mass supermassive black hole, only a little less massive than the black hole Ton 618, and the approximate temperature increase that would result from adding 1 joule of thermal energy to Lake Toba, the largest lake in Indonesia.", "A femtokelvin (fK) is one quadrillionth of a kelvin ().", "It is the approximate effective temperature of a 61.7 million solar mass supermassive black hole.", "A picokelvin (pK) is one trillionth of a kelvin ().", "A nanokelvin (nK) is one billionth of a kelvin ().", "It is the approximate effective temperature of a fairly large 61.7 solar mass stellar-mass black hole.", "NASA's Cold Atom Laboratory can chill small numbers of atoms down to below 1 nanokelvin.", "A microkelvin (μK) is one millionth of a kelvin ().", "A millikelvin (mK) is one thousandth of a kelvin (0.001 K or ).", "A centikelvin (cK) is one hundredth of a kelvin (0.01 K or ).", "A decikelvin (dK) is one tenth of a kelvin (0.1 K or ).", "A decakelvin (daK) is ten kelvins (10 K or ).", "The main components of air, nitrogen and oxygen, boil at 77 K and 90 K respectively under 1 atmosphere of pressure.", "A hectokelvin (hK) is one hundred kelvins (100 K or ).", "Air temperatures recorded occurring naturally on Earth (excluding, e.g. wildfires, volcanoes, and meteorite impacts) range from 184 K at Vostok Station in Antarctica to 330 K at Furnace Creek in Death Valley.", "Yakutsk in Russia's Sakha Republic has a daily average low in January of 229 K. Ice melts at 273.15 K. Kuwait City has a daily average high in July and August of 320 K. Water boils at 373.15 K at 1 atmosphere.", "The average surface temperature on Venus in 737 K.", "A kilokelvin (kK) is one thousand kelvins (1000 K or ).", "Iron melts at 1811 K, or 1.8 kK. The temperature at the surface of the Sun is about 5800 K, or 5.8 kK.", "A megakelvin (MK) is one million kelvins ().", "The temperature at the centre of the Sun is about 15.7 MK.", "A gigakelvin (GK) is one billion kelvins ().", "A terakelvin (TK) is one trillion kelvins ().", "A petakelvin (PK) is one quadrillion kelvins ().", "An exakelvin (EK) is one quintillion kelvins ().", "A zettakelvin (ZK) is one sextillion kelvins ().", "A yottakelvin (YK) is one septillion kelvins () and the largest unit of temperature defined in the SI.", "It corresponds to a mean translational kinetic energy of joules, the same order of magnitude as the Oh-My-God particle.", "The Planck temperature is approximately 141,680,000 yottakelvins.", "The symbol is encoded in Unicode at code point .", "However, this is a compatibility character provided for compatibility with legacy encodings.", "The Unicode standard recommends using instead; that is, a normal capital K. \"Three letterlike symbols have been given canonical equivalence to regular letters: , , and .", "In all three instances, the regular letter should be used.\"" ]

[ 17, 18, 19, 20, 21, 22, 23, 24, 25, 26 ]

[ "The Kelvin scale is an absolute thermodynamic temperature scale, meaning it uses absolute zero as its null point." ]

[ "During the 18th century multiple temperature scales were developed, most notably Fahrenheit and centigrade (later Celsius).", "These scales predated much of the modern science of thermodynamics, including the scientific consensus in favour of atomic theory and the kinetic theory of gases that underpin the concept of absolute zero.", "Instead, they chose defining points inside the range of human experience at the time that could be easily and reasonably accurately reproduced, but did not necessarily have any deep significance in thermal physics.", "In the case of the Celsius scale (and the long since defunct Newton scale and Réaumur scale) the melting point of water served as such a semi-arbitrary starting point, with Celsius being defined, from the 1740s up until the 1940s, by calibrating a thermometer such that:\n\nThis referring to pure water at a set pressure designed to approximate the natural air pressure at sea level.", "An implication of this was that an increment of 1 °C was equal to an increment of of the temperature difference between the melting and boiling points.", "This temperature interval would go on to become the template for the kelvin.", "In October 1848, William Thomson, a 24 year old professor of Natural Philosophy at the University of Glasgow, published a paper \"On an Absolute Thermometric Scale\".", "Using the soon-to-be-defunct caloric theory, he proposed an \"absolute\" scale based on the following parameters:\n\n\"The arbitrary points which coincide on the two scales are 0° and 100°\"\n\"The characteristic property of the scale which I now propose is, that all degrees have the same value; that is, that a unit of heat descending from a body \"A\" at the temperature \"T\"° of this scale, to a body \"B\" at the temperature (\"T\" − 1)°, would give out the same mechanical effect, whatever be the number \"T\".", "This may justly be termed an absolute scale, since its characteristic is quite independent of the physical properties of any specific substance.", "\"\nAs Carnot's theorem is understood in modern thermodynamics to simply describe the maximum efficiency with which thermal energy can be converted to mechanical energy and the predicted maximum efficiency is a function of the \"ratio\" between the absolute temperatures of the heat source and heat sink:\nIt follows that increments of equal numbers of degrees on this scale must always represent equal \"proportional\" increases in absolute temperature.", "The numerical value of an absolute temperature, , on the 1848 scale is related to the absolute temperature of the melting point of water, , and the absolute temperature of the boiling point of water, , by:\nOn this scale, an increase of 222 degrees always means an approximate doubling of absolute temperature regardless of the starting temperature.", "In a footnote Thomson calculated that \"infinite cold\" (absolute zero, which would have a numerical value of negative infinity on this scale) was equivalent to −273 °C using the air thermometers of the time.", "This value of \"−273\" was the negative reciprocal of 0.00366—the accepted expansion coefficient of gas per degree Celsius relative to the ice point, giving a remarkable consistency to the currently accepted value.", "Within a decade, Thomson had abandoned caloric theory and superseded the 1848 scale with a new one based on the 2 features that would characterise all future versions of the kelvin scale:\n\nIn 1892 Thomson was awarded the noble title 1st", "Baron Kelvin of Largs, or more succinctly Lord Kelvin.", "This name was a reference to the River Kelvin which flows through the grounds of Glasgow University.", "In the early decades of the 20th century, the Kelvin scale was often called the \"absolute Celsius\" scale, indicating Celsius degrees counted from absolute zero rather than the freezing point of water, and using the same symbol for regular Celsius degrees, °C.", "In 1873 William Thomson's older brother James coined the term \"triple point\" to describe the combination of temperature and pressure at which the solid, liquid, and gas phases of a substance were capable of coexisting in thermodynamic equilibrium.", "While any two phases could coexist along a range of temperature-pressure combinations (e.g. the boiling point of water can be affected quite dramatically by raising or lowering the pressure), the triple point condition for a given substance can occur only at 1 pressure and only at 1 temperature.", "By the 1940s, the triple point of water had been experimentally measured to be about 0.6% of standard atmospheric pressure and very close to 0.01 °C per the historical definition of Celsius then in use.", "In 1948, the Celsius scale was recalibrated by assigning the triple point temperature of water the value of 0.01 °C exactly and allowing the melting point at standard atmospheric pressure to have an empirically determined value (and the actual melting point at ambient pressure to have a fluctuating value) close to 0 °C.", "This was justified on the grounds that the triple point was judged to give a more accurately reproducible reference temperature than the melting point.", "In 1954, with absolute zero having been experimentally determined to be about −273.15 °C per the definition of °C then in use, Resolution 3 of the 10th General Conference on Weights and Measures (CGPM) introduced a new internationally standardised Kelvin scale which defined the triple point as exactly:\n273.15 + 0.01 = 273.16 \"degrees Kelvin\"\nIn 1967/1968, Resolution 3 of the 13th CGPM renamed the unit increment of thermodynamic temperature \"kelvin\", symbol K, replacing \"degree Kelvin\", symbol °K.", "Furthermore, feeling it useful to more explicitly define the magnitude of the unit increment, the 13th CGPM also held in Resolution 4 that \"The kelvin, unit of thermodynamic temperature, is equal to the fraction of the thermodynamic temperature of the triple point of water.", "\"\nAfter the 1983 redefinition of the metre, this left the kelvin, the second, and the kilogram as the only SI units not defined with reference to any other unit.", "Hydrogen has 2 stable isotopes (and one trace radioisotope) and oxygen has 3 stable isotopes.", "In 2005, noting that the triple point could be influenced by the isotopic ratio of the hydrogen and oxygen making up a water sample and that this was \"now one of the major sources of the observed variability between different realizations of the water triple point\", the International Committee for Weights and Measures (CIPM), a committee of the CGPM, affirmed that for the purposes of delineating the temperature of the triple point of water, the definition of the kelvin would refer to water having the isotopic composition specified for Vienna Standard Mean Ocean Water:", "In 2005 the CIPM began a programme to redefine the kelvin (along with the other SI units) using a more experimentally rigorous method.", "In particular, the committee proposed redefining the kelvin such that the Boltzmann constant takes the exact value .", "The committee had hoped that the program would be completed in time for its adoption by the CGPM at its 2011 meeting, but at the 2011 meeting the decision was postponed to the 2014 meeting when it would be considered as part of a larger program.", "The redefinition was further postponed in 2014, pending more accurate measurements of Boltzmann's constant in terms of the current definition,\nbut was finally adopted at the 26th CGPM in late 2018, with a value of  = \nFor scientific purposes, the main advantage is that this allows measurements at very low and very high temperatures to be made more accurately, as the techniques used depend on the Boltzmann constant.", "It also has the philosophical advantage of being independent of any particular substance.", "The unit J/K is equal to kg⋅m2⋅s−2⋅K−1, where the kilogram, metre and second are defined in terms of the Planck constant, the speed of light, and the duration of the caesium-133 ground-state hyperfine transition respectively.", "Thus, this definition depends only on universal constants, and not on any physical artifacts as practiced previously, such as the International Prototype of the Kilogram, whose mass diverged over time from the original value.", "The challenge was to avoid degrading the accuracy of measurements close to the triple point.", "For practical purposes, the redefinition was unnoticed; water still freezes at 273.15 K (0 °C), and the triple point of water continues to be a commonly used laboratory reference temperature.", "The difference is that, before the redefinition, the triple point of water was exact and the Boltzmann constant had a measured value of , with a relative standard uncertainty of .", "Afterward, the Boltzmann constant is exact and the uncertainty is transferred to the triple point of water, which is now .", "For legal metrology purposes, the new definition officially came into force on 20 May 2019, the 144th anniversary of the Metre Convention.", "The post-2019 definition is based on fixing the value of the Boltzmann constant , expressed in SI units, at joules per kelvin.", "This constant appears in (some formulations of) the ideal gas law, which links the pressure, , of an ideal gas, its volume, , its temperature, , and the number of gas particles making it up, , via the relationship:\nSubstituting in the defined value of gives:\nWhich can be rearranged to give:\nOr:\nWhere (K) is the numerical value of the temperature expressed in kelvins, and (J) is the numerical value of the product of the pressure and the average volume per gas particle expressed in joules.", "It is worth emphasising that in dimensional analysis terms the product of a pressure and a volume is an energy.", "This can be seen by considering that pressure, volume, and energy have the dimensions force/length2, length3 and force × length, respectively.", "Another context where this relationship becomes intuitive is in the case of a pump or a water turbine, where the minimum energy demand and maximum energy available, respectively, is given by the volume of fluid passing through the component multiplied by the pressure differential across it.", "The above temperature equation holds exactly for an ideal gas, a hypothetical substance composed of point particles affected only by elastic collisions with their container, but is closely approximated by a real gas that is well above its boiling or sublimation point and well below its critical pressure.", "Using the metric prefix system this can be given as:\nBecause the average kinetic energy per degree of freedom is and gas particles have 3 translational degrees of freedom, the temperature in kelvins is also related to the mean kinetic energy per degree of freedom by:\nAnd to the mean translational kinetic energy by:\nExpressed in terms of the SI defining constants 1 kelvin is:\nWhere is the Planck constant and is the caesium-133 hyperfine transition frequency.", "Because the term is equal to the photon energy of the caesium-133 hyperfine transition radiation, , and 1/ is equal to for an ideal gas:\nWhich can be rearranged to give:\nOr:\nExpressed in terms of mean kinetic energy, this becomes:\nAnd:", "Although the kelvin is an SI base unit, its only use in fundamental physics is the Boltzmann constant.", "This allows a natural unit definition that makes kelvins and joules different units for the same dimension, .", "Such a definition is already in use in some textbooks.", "However, such a definition is unlikely to have a practical use in an experiment due to the large orders of magnitude involved.", "Several physical constants are defined in terms of the Boltzmann constant and other SI defining constants, for example the universal gas constant, , is defined as the product of the Boltzmann constant, , and the Avogadro constant, A. Prior to 2019, its value in SI units could only be empirically estimated, with a small but inevitable degree of experimental uncertainty.", "After 2019, the kelvin was redefined by giving an exact value to the Boltzmann constant and the mole was redefined by assigning an exact value to the Avogadro constant, meaning the value of the universal gas constant in SI units could be calculated exactly as:\nSimilarly, the Stefan-Boltzmann constant, \"σ\", not to be confused with the Boltzmann constant, relates the temperature of a black body to the rate at which thermal energy is electromagnetically radiated from its surface and is equal to:\nWhere is the Planck constant, whose value now defines the kilogram, and is the speed of light, whose value now defines the metre (and had been implicit in the definition of the metre since 1983).", "The exact value of \"σ\" in SI units is therefore:\nThe second radiation constant in Planck's law, 2, is equal to:\nWhich means its exact value in SI units is:", "1 kelvin is the approximate temperature of the Boomerang Nebula, the coldest known natural environment in the universe.", "Because 1 K is colder than the effective temperature of the cosmic microwave background (about 2.7 K), it cannot be reached simply by moving a previously warm object far away from point sources of heat (e.g. stars) and requires additional cooling mechanisms, such as evaporative cooling, laser cooling, or adiabatic cooling to achieve in the current universe, though in the far future the ongoing expansion of the universe may cause the average temperature of the universe to drop below 1 K. Temperatures significantly colder than 1 K are not known to occur in nature, but have been produced in laboratories and, from the perspective of an external observer, black holes may appear to have temperatures extremely close to absolute zero when not feeding.", "Their effective temperature, , due to Hawking radiation is given by:\nWhere is the speed of light in a vacuum, is the reduced Planck constant, is the black hole's mass, and is the gravitational constant, hence:\nWhich means a black hole of mass kg, about 1.67 times the mass of the moon, would have an effective temperature of ≈ 1 K. Black holes known to actually exist in nature have significantly larger masses (and lower effective temperatures) than this, being at least several solar masses.", "At a temperature of 1 K (and a pressure of 1 standard atmosphere) the overwhelming majority of substances are solids, including nitrogen and the even more volatile neon and hydrogen.", "An exception is helium whose most common isotope, helium-4, exists in an exotic liquid-like state known as a superfluid characterised by a total absence of viscosity, while the much rarer helium-3 isotope remains a \"normal\" liquid.", "At 1 K some common metals, including lead and mercury are superconductors, losing all electrical resistance.", "A black body at 1 K radiates energy at a rate of about 56.7 nW per square metre with a peak wavelength of about 2.9 mm, in the microwave spectrum.", "A heat pump attempting to extract heat from an refrigeration chamber at 1 K and vent it into an ambient environment at 20 °C, would require a minimum of 292.15 joules of mechanical work to draw out 1 joule of thermal energy.", "Before the 13th CGPM in 1967–1968, the unit kelvin was termed a \"degree\", the same as with the other temperature scales at the time.", "It was distinguished from the other scales with either the adjective suffix \"Kelvin\" (\"degree Kelvin\") or with \"absolute\" (\"degree absolute\") and its symbol was °K.", "The latter term (degree absolute), which was the unit's official name from 1948 until 1954, was ambiguous since it could also be interpreted as referring to the Rankine scale.", "Before the 13th CGPM, the plural form was \"degrees absolute\".", "The 13th CGPM changed the unit name to simply \"kelvin\" (symbol: K).", "The omission of \"degree\" indicates that it is not relative to an arbitrary reference point like the Celsius and Fahrenheit scales (although the Rankine scale continued to use \"degree Rankine\"), but rather an absolute unit of measure which can be manipulated algebraically (e.g., multiplied by two to indicate twice the amount of \"mean energy\" available among elementary degrees of freedom of the system).", "The preferred plural form of kelvin is not explicitly stated in the SI Brochure or in the for the kelvin.", "The 8th edition of the Brochure (written before the 2019 redefinition) refers to the kelvin in plural as \"kelvins\":\n\"A difference or interval of temperature may be expressed in kelvins or in degrees Celsius, the numerical value of the temperature difference being\nthe same.\"\nHowever in the 9th edition (written after the redefinition) this was changed to:\n\"A difference or interval of temperature may be expressed in kelvin or in degrees Celsius, the numerical value of the temperature difference being the same in either case.\"\nThe US based National Institute of Standards and Technology recommends the use of \"kelvins\":\n\"The kelvin unit is not expressed in degrees like Celsius or Fahrenheit are.", "It is used by itself to describe temperature.", "For example, 'mercury loses all electrical resistance at a temperature of 4.2 kelvins.", "The style guide for CERN, however, specifically says to always use \"kelvin\", even when plural.", "The US based Merriam-Webster dictionary recommends \"kelvins\"", "When writing the name of the unit out in full it is uncapitalised, except in contexts where most words would be capitalised (e.g. at the start of a sentence or as part of a title) however, when abbreviated to a symbol, K, it is \"always\" capitalised.", "In the SI an uncapitalised (and unitalicised) letter k would indicate the kilo- prefix:\n″The kelvin is the SI base unit of temperature.″\nAlex: ″What units do you want me to record this in?″", "Billie: ″Kelvins!″\n″The sample was chilled to 50 K.\"\n″Tay traveled 100 km from Poughkeepsie to Manhattan.″\nThis somewhat unintuitive convention is in fact in line with other SI units named after people, such as the newton, watt, and tesla, symbols N, W, and T respectively.", "When reference is made to the \"Kelvin \"scale\"\", the word \"kelvin\"—which is normally a noun—functions adjectivally to modify the noun \"scale\" and is capitalised.", "As with most other SI unit symbols (angle symbols, e.g., 45° 3′ 4″, are the exception) there is a space between the numeric value and the kelvin symbol (e.g., \"99.987 K\").", "The size of a degree Celsius (historically defined as of the temperature difference between the melting and boiling points of water, see history section for more details), was the template for the size of the kelvin and the convention that the Kelvin and Celsius scales have the same size increments remains in place today, meaning that a \"change\" in temperature or a \"difference\" in temperature necessarily has the same numerical value when expressed in kelvins as it does when expressed in degrees Celsius:\nHowever while the Kelvin scale takes absolute zero as its starting point, the modern iteration of the Celsius scale takes 273.15 K as its starting point, this being a close approximation of the melting point of water at standard atmospheric pressure, indeed, the 9th edition of the SI Brochure \"defines\" the temperature in Celsius such that:\nSo, for example, \"It is 10 °C colder outside the house than inside\" and \"It is 10 K colder outside the house than inside\" are exactly equivalent statements, while \"It is 10 °C outside\" and \"It is 10 K outside\" describe very different situations!", "This convention makes conversion between °C and K relatively straightforward, but has the downside that neither the melting nor boiling points of water have round values when expressed in kelvins, being approximately 273.15 K and 373.15 K respectively.", "As the melting and boiling points of water were historically 180 degrees apart on the Fahrenheit scale (32 °F and 212 °F, respectively) a temperature interval of 1 K (and of 1 °C) is equal to an interval of 1.8 °F.", "Absolute zero in °F is:\nHence:", "The kelvin is often used as a measure of the colour temperature of light sources.", "Colour temperature is based upon the principle that a black body radiator emits light with a frequency distribution characteristic of its temperature.", "Black bodies at temperatures below about appear reddish, whereas those above about appear bluish.", "Colour temperature is important in the fields of image projection and photography, where a colour temperature of approximately is required to match \"daylight\" film emulsions.", "In astronomy, the stellar classification of stars and their place on the Hertzsprung–Russell diagram are based, in part, upon their surface temperature, known as effective temperature.", "The photosphere of the Sun, for instance, has an effective temperature of .", "Digital cameras and photographic software often use colour temperature in K in edit and setup menus.", "The simple guide is that higher colour temperature produces an image with enhanced white and blue hues.", "The reduction in colour temperature produces an image more dominated by reddish, \"warmer\" colours.", "For electronics, the kelvin is used as an indicator of how noisy a circuit is in relation to an ultimate noise floor, i.e. the noise temperature.", "The so-called Johnson–Nyquist noise of discrete resistors and capacitors is a type of thermal noise derived from the Boltzmann constant and can be used to determine the noise temperature of a circuit using the Friis formulas for noise.", "The International System of Units (SI) is based on seven SI base units (the second, metre, kilogram, kelvin, ampere, mole, and candela) representing seven fundamental types of physical quantity, or \"dimensions\" (time, length, mass, temperature, electrical current, amount of substance, and luminous intensity respectively), with all other SI units defined using these seven basic building blocks.", "These SI derived units can either be given special names, e.g., tesla, volt, lux, etc., or left as bare descriptions, e.g. metre per second.", "The only SI unit with a special name derived from the kelvin is the degree Celsius, which is also the only SI unit derived from another by offsetting, rather than by multiplication or division.", "Some commonly used units derived from the kelvin without special names are:\nMany of these are of interest in the engineering of heating, ventilation, and air conditioning systems and of building insulation.", "Coefficient of thermal expansion is an important consideration in structural engineering.", "Like other SI units, the kelvin can modified by adding a prefix that multiplies it by a power of 10.", "A yoctokelvin (yK) is one septillionth of a kelvin () and the smallest unit of temperature defined in the International System of Units.", "It is a little more than the temperature increase that would result from adding 1 joule of thermal energy to the Indian Ocean, assuming properties similar to those of pure water.", "A zeptokelvin (zK) is one sextillionth of a kelvin ().", "It is somewhat less than the temperature increase that would result from adding 1 joule of thermal energy to the Baltic Sea, assuming properties similar to those of pure water.", "An attokelvin (aK) is one quintillionth of a kelvin ().", "It is the approximate effective temperature of an extremely massive 61.7 billion solar mass supermassive black hole, only a little less massive than the black hole Ton 618, and the approximate temperature increase that would result from adding 1 joule of thermal energy to Lake Toba, the largest lake in Indonesia.", "A femtokelvin (fK) is one quadrillionth of a kelvin ().", "It is the approximate effective temperature of a 61.7 million solar mass supermassive black hole.", "A picokelvin (pK) is one trillionth of a kelvin ().", "A nanokelvin (nK) is one billionth of a kelvin ().", "It is the approximate effective temperature of a fairly large 61.7 solar mass stellar-mass black hole.", "NASA's Cold Atom Laboratory can chill small numbers of atoms down to below 1 nanokelvin.", "A microkelvin (μK) is one millionth of a kelvin ().", "A millikelvin (mK) is one thousandth of a kelvin (0.001 K or ).", "A centikelvin (cK) is one hundredth of a kelvin (0.01 K or ).", "A decikelvin (dK) is one tenth of a kelvin (0.1 K or ).", "A decakelvin (daK) is ten kelvins (10 K or ).", "The main components of air, nitrogen and oxygen, boil at 77 K and 90 K respectively under 1 atmosphere of pressure.", "A hectokelvin (hK) is one hundred kelvins (100 K or ).", "Air temperatures recorded occurring naturally on Earth (excluding, e.g. wildfires, volcanoes, and meteorite impacts) range from 184 K at Vostok Station in Antarctica to 330 K at Furnace Creek in Death Valley.", "Yakutsk in Russia's Sakha Republic has a daily average low in January of 229 K. Ice melts at 273.15 K. Kuwait City has a daily average high in July and August of 320 K. Water boils at 373.15 K at 1 atmosphere.", "The average surface temperature on Venus in 737 K.", "A kilokelvin (kK) is one thousand kelvins (1000 K or ).", "Iron melts at 1811 K, or 1.8 kK. The temperature at the surface of the Sun is about 5800 K, or 5.8 kK.", "A megakelvin (MK) is one million kelvins ().", "The temperature at the centre of the Sun is about 15.7 MK.", "A gigakelvin (GK) is one billion kelvins ().", "A terakelvin (TK) is one trillion kelvins ().", "A petakelvin (PK) is one quadrillion kelvins ().", "An exakelvin (EK) is one quintillion kelvins ().", "A zettakelvin (ZK) is one sextillion kelvins ().", "A yottakelvin (YK) is one septillion kelvins () and the largest unit of temperature defined in the SI.", "It corresponds to a mean translational kinetic energy of joules, the same order of magnitude as the Oh-My-God particle.", "The Planck temperature is approximately 141,680,000 yottakelvins.", "The symbol is encoded in Unicode at code point .", "However, this is a compatibility character provided for compatibility with legacy encodings.", "The Unicode standard recommends using instead; that is, a normal capital K. \"Three letterlike symbols have been given canonical equivalence to regular letters: , , and .", "In all three instances, the regular letter should be used.\"" ]

[ 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78 ]

[ "Unlike the degree Fahrenheit and degree Celsius, the kelvin dates to the mid 19th century rather than the early to mid 18th and is never referred to nor written as a \"degree\", nor typically capitalised except when abbreviated to K, e.g. \"It's 50 degrees Fahrenheit outside\" vs \"It's 10 degrees Celsius outside\" vs \"It's 283 kelvins outside\"." ]

[ "During the 18th century multiple temperature scales were developed, most notably Fahrenheit and centigrade (later Celsius).", "These scales predated much of the modern science of thermodynamics, including the scientific consensus in favour of atomic theory and the kinetic theory of gases that underpin the concept of absolute zero.", "Instead, they chose defining points inside the range of human experience at the time that could be easily and reasonably accurately reproduced, but did not necessarily have any deep significance in thermal physics.", "In the case of the Celsius scale (and the long since defunct Newton scale and Réaumur scale) the melting point of water served as such a semi-arbitrary starting point, with Celsius being defined, from the 1740s up until the 1940s, by calibrating a thermometer such that:\n\nThis referring to pure water at a set pressure designed to approximate the natural air pressure at sea level.", "An implication of this was that an increment of 1 °C was equal to an increment of of the temperature difference between the melting and boiling points.", "This temperature interval would go on to become the template for the kelvin.", "In October 1848, William Thomson, a 24 year old professor of Natural Philosophy at the University of Glasgow, published a paper \"On an Absolute Thermometric Scale\".", "Using the soon-to-be-defunct caloric theory, he proposed an \"absolute\" scale based on the following parameters:\n\n\"The arbitrary points which coincide on the two scales are 0° and 100°\"\n\"The characteristic property of the scale which I now propose is, that all degrees have the same value; that is, that a unit of heat descending from a body \"A\" at the temperature \"T\"° of this scale, to a body \"B\" at the temperature (\"T\" − 1)°, would give out the same mechanical effect, whatever be the number \"T\".", "This may justly be termed an absolute scale, since its characteristic is quite independent of the physical properties of any specific substance.", "\"\nAs Carnot's theorem is understood in modern thermodynamics to simply describe the maximum efficiency with which thermal energy can be converted to mechanical energy and the predicted maximum efficiency is a function of the \"ratio\" between the absolute temperatures of the heat source and heat sink:\nIt follows that increments of equal numbers of degrees on this scale must always represent equal \"proportional\" increases in absolute temperature.", "The numerical value of an absolute temperature, , on the 1848 scale is related to the absolute temperature of the melting point of water, , and the absolute temperature of the boiling point of water, , by:\nOn this scale, an increase of 222 degrees always means an approximate doubling of absolute temperature regardless of the starting temperature.", "In a footnote Thomson calculated that \"infinite cold\" (absolute zero, which would have a numerical value of negative infinity on this scale) was equivalent to −273 °C using the air thermometers of the time.", "This value of \"−273\" was the negative reciprocal of 0.00366—the accepted expansion coefficient of gas per degree Celsius relative to the ice point, giving a remarkable consistency to the currently accepted value.", "Within a decade, Thomson had abandoned caloric theory and superseded the 1848 scale with a new one based on the 2 features that would characterise all future versions of the kelvin scale:\n\nIn 1892 Thomson was awarded the noble title 1st", "Baron Kelvin of Largs, or more succinctly Lord Kelvin.", "This name was a reference to the River Kelvin which flows through the grounds of Glasgow University.", "In the early decades of the 20th century, the Kelvin scale was often called the \"absolute Celsius\" scale, indicating Celsius degrees counted from absolute zero rather than the freezing point of water, and using the same symbol for regular Celsius degrees, °C.", "In 1873 William Thomson's older brother James coined the term \"triple point\" to describe the combination of temperature and pressure at which the solid, liquid, and gas phases of a substance were capable of coexisting in thermodynamic equilibrium.", "While any two phases could coexist along a range of temperature-pressure combinations (e.g. the boiling point of water can be affected quite dramatically by raising or lowering the pressure), the triple point condition for a given substance can occur only at 1 pressure and only at 1 temperature.", "By the 1940s, the triple point of water had been experimentally measured to be about 0.6% of standard atmospheric pressure and very close to 0.01 °C per the historical definition of Celsius then in use.", "In 1948, the Celsius scale was recalibrated by assigning the triple point temperature of water the value of 0.01 °C exactly and allowing the melting point at standard atmospheric pressure to have an empirically determined value (and the actual melting point at ambient pressure to have a fluctuating value) close to 0 °C.", "This was justified on the grounds that the triple point was judged to give a more accurately reproducible reference temperature than the melting point.", "In 1954, with absolute zero having been experimentally determined to be about −273.15 °C per the definition of °C then in use, Resolution 3 of the 10th General Conference on Weights and Measures (CGPM) introduced a new internationally standardised Kelvin scale which defined the triple point as exactly:\n273.15 + 0.01 = 273.16 \"degrees Kelvin\"\nIn 1967/1968, Resolution 3 of the 13th CGPM renamed the unit increment of thermodynamic temperature \"kelvin\", symbol K, replacing \"degree Kelvin\", symbol °K.", "Furthermore, feeling it useful to more explicitly define the magnitude of the unit increment, the 13th CGPM also held in Resolution 4 that \"The kelvin, unit of thermodynamic temperature, is equal to the fraction of the thermodynamic temperature of the triple point of water.", "\"\nAfter the 1983 redefinition of the metre, this left the kelvin, the second, and the kilogram as the only SI units not defined with reference to any other unit.", "Hydrogen has 2 stable isotopes (and one trace radioisotope) and oxygen has 3 stable isotopes.", "In 2005, noting that the triple point could be influenced by the isotopic ratio of the hydrogen and oxygen making up a water sample and that this was \"now one of the major sources of the observed variability between different realizations of the water triple point\", the International Committee for Weights and Measures (CIPM), a committee of the CGPM, affirmed that for the purposes of delineating the temperature of the triple point of water, the definition of the kelvin would refer to water having the isotopic composition specified for Vienna Standard Mean Ocean Water:", "In 2005 the CIPM began a programme to redefine the kelvin (along with the other SI units) using a more experimentally rigorous method.", "In particular, the committee proposed redefining the kelvin such that the Boltzmann constant takes the exact value .", "The committee had hoped that the program would be completed in time for its adoption by the CGPM at its 2011 meeting, but at the 2011 meeting the decision was postponed to the 2014 meeting when it would be considered as part of a larger program.", "The redefinition was further postponed in 2014, pending more accurate measurements of Boltzmann's constant in terms of the current definition,\nbut was finally adopted at the 26th CGPM in late 2018, with a value of  = \nFor scientific purposes, the main advantage is that this allows measurements at very low and very high temperatures to be made more accurately, as the techniques used depend on the Boltzmann constant.", "It also has the philosophical advantage of being independent of any particular substance.", "The unit J/K is equal to kg⋅m2⋅s−2⋅K−1, where the kilogram, metre and second are defined in terms of the Planck constant, the speed of light, and the duration of the caesium-133 ground-state hyperfine transition respectively.", "Thus, this definition depends only on universal constants, and not on any physical artifacts as practiced previously, such as the International Prototype of the Kilogram, whose mass diverged over time from the original value.", "The challenge was to avoid degrading the accuracy of measurements close to the triple point.", "For practical purposes, the redefinition was unnoticed; water still freezes at 273.15 K (0 °C), and the triple point of water continues to be a commonly used laboratory reference temperature.", "The difference is that, before the redefinition, the triple point of water was exact and the Boltzmann constant had a measured value of , with a relative standard uncertainty of .", "Afterward, the Boltzmann constant is exact and the uncertainty is transferred to the triple point of water, which is now .", "For legal metrology purposes, the new definition officially came into force on 20 May 2019, the 144th anniversary of the Metre Convention.", "The post-2019 definition is based on fixing the value of the Boltzmann constant , expressed in SI units, at joules per kelvin.", "This constant appears in (some formulations of) the ideal gas law, which links the pressure, , of an ideal gas, its volume, , its temperature, , and the number of gas particles making it up, , via the relationship:\nSubstituting in the defined value of gives:\nWhich can be rearranged to give:\nOr:\nWhere (K) is the numerical value of the temperature expressed in kelvins, and (J) is the numerical value of the product of the pressure and the average volume per gas particle expressed in joules.", "It is worth emphasising that in dimensional analysis terms the product of a pressure and a volume is an energy.", "This can be seen by considering that pressure, volume, and energy have the dimensions force/length2, length3 and force × length, respectively.", "Another context where this relationship becomes intuitive is in the case of a pump or a water turbine, where the minimum energy demand and maximum energy available, respectively, is given by the volume of fluid passing through the component multiplied by the pressure differential across it.", "The above temperature equation holds exactly for an ideal gas, a hypothetical substance composed of point particles affected only by elastic collisions with their container, but is closely approximated by a real gas that is well above its boiling or sublimation point and well below its critical pressure.", "Using the metric prefix system this can be given as:\nBecause the average kinetic energy per degree of freedom is and gas particles have 3 translational degrees of freedom, the temperature in kelvins is also related to the mean kinetic energy per degree of freedom by:\nAnd to the mean translational kinetic energy by:\nExpressed in terms of the SI defining constants 1 kelvin is:\nWhere is the Planck constant and is the caesium-133 hyperfine transition frequency.", "Because the term is equal to the photon energy of the caesium-133 hyperfine transition radiation, , and 1/ is equal to for an ideal gas:\nWhich can be rearranged to give:\nOr:\nExpressed in terms of mean kinetic energy, this becomes:\nAnd:", "Although the kelvin is an SI base unit, its only use in fundamental physics is the Boltzmann constant.", "This allows a natural unit definition that makes kelvins and joules different units for the same dimension, .", "Such a definition is already in use in some textbooks.", "However, such a definition is unlikely to have a practical use in an experiment due to the large orders of magnitude involved.", "Several physical constants are defined in terms of the Boltzmann constant and other SI defining constants, for example the universal gas constant, , is defined as the product of the Boltzmann constant, , and the Avogadro constant, A. Prior to 2019, its value in SI units could only be empirically estimated, with a small but inevitable degree of experimental uncertainty.", "After 2019, the kelvin was redefined by giving an exact value to the Boltzmann constant and the mole was redefined by assigning an exact value to the Avogadro constant, meaning the value of the universal gas constant in SI units could be calculated exactly as:\nSimilarly, the Stefan-Boltzmann constant, \"σ\", not to be confused with the Boltzmann constant, relates the temperature of a black body to the rate at which thermal energy is electromagnetically radiated from its surface and is equal to:\nWhere is the Planck constant, whose value now defines the kilogram, and is the speed of light, whose value now defines the metre (and had been implicit in the definition of the metre since 1983).", "The exact value of \"σ\" in SI units is therefore:\nThe second radiation constant in Planck's law, 2, is equal to:\nWhich means its exact value in SI units is:", "1 kelvin is the approximate temperature of the Boomerang Nebula, the coldest known natural environment in the universe.", "Because 1 K is colder than the effective temperature of the cosmic microwave background (about 2.7 K), it cannot be reached simply by moving a previously warm object far away from point sources of heat (e.g. stars) and requires additional cooling mechanisms, such as evaporative cooling, laser cooling, or adiabatic cooling to achieve in the current universe, though in the far future the ongoing expansion of the universe may cause the average temperature of the universe to drop below 1 K. Temperatures significantly colder than 1 K are not known to occur in nature, but have been produced in laboratories and, from the perspective of an external observer, black holes may appear to have temperatures extremely close to absolute zero when not feeding.", "Their effective temperature, , due to Hawking radiation is given by:\nWhere is the speed of light in a vacuum, is the reduced Planck constant, is the black hole's mass, and is the gravitational constant, hence:\nWhich means a black hole of mass kg, about 1.67 times the mass of the moon, would have an effective temperature of ≈ 1 K. Black holes known to actually exist in nature have significantly larger masses (and lower effective temperatures) than this, being at least several solar masses.", "At a temperature of 1 K (and a pressure of 1 standard atmosphere) the overwhelming majority of substances are solids, including nitrogen and the even more volatile neon and hydrogen.", "An exception is helium whose most common isotope, helium-4, exists in an exotic liquid-like state known as a superfluid characterised by a total absence of viscosity, while the much rarer helium-3 isotope remains a \"normal\" liquid.", "At 1 K some common metals, including lead and mercury are superconductors, losing all electrical resistance.", "A black body at 1 K radiates energy at a rate of about 56.7 nW per square metre with a peak wavelength of about 2.9 mm, in the microwave spectrum.", "A heat pump attempting to extract heat from an refrigeration chamber at 1 K and vent it into an ambient environment at 20 °C, would require a minimum of 292.15 joules of mechanical work to draw out 1 joule of thermal energy.", "Before the 13th CGPM in 1967–1968, the unit kelvin was termed a \"degree\", the same as with the other temperature scales at the time.", "It was distinguished from the other scales with either the adjective suffix \"Kelvin\" (\"degree Kelvin\") or with \"absolute\" (\"degree absolute\") and its symbol was °K.", "The latter term (degree absolute), which was the unit's official name from 1948 until 1954, was ambiguous since it could also be interpreted as referring to the Rankine scale.", "Before the 13th CGPM, the plural form was \"degrees absolute\".", "The 13th CGPM changed the unit name to simply \"kelvin\" (symbol: K).", "The omission of \"degree\" indicates that it is not relative to an arbitrary reference point like the Celsius and Fahrenheit scales (although the Rankine scale continued to use \"degree Rankine\"), but rather an absolute unit of measure which can be manipulated algebraically (e.g., multiplied by two to indicate twice the amount of \"mean energy\" available among elementary degrees of freedom of the system).", "The preferred plural form of kelvin is not explicitly stated in the SI Brochure or in the for the kelvin.", "The 8th edition of the Brochure (written before the 2019 redefinition) refers to the kelvin in plural as \"kelvins\":\n\"A difference or interval of temperature may be expressed in kelvins or in degrees Celsius, the numerical value of the temperature difference being\nthe same.\"\nHowever in the 9th edition (written after the redefinition) this was changed to:\n\"A difference or interval of temperature may be expressed in kelvin or in degrees Celsius, the numerical value of the temperature difference being the same in either case.\"\nThe US based National Institute of Standards and Technology recommends the use of \"kelvins\":\n\"The kelvin unit is not expressed in degrees like Celsius or Fahrenheit are.", "It is used by itself to describe temperature.", "For example, 'mercury loses all electrical resistance at a temperature of 4.2 kelvins.", "The style guide for CERN, however, specifically says to always use \"kelvin\", even when plural.", "The US based Merriam-Webster dictionary recommends \"kelvins\"", "When writing the name of the unit out in full it is uncapitalised, except in contexts where most words would be capitalised (e.g. at the start of a sentence or as part of a title) however, when abbreviated to a symbol, K, it is \"always\" capitalised.", "In the SI an uncapitalised (and unitalicised) letter k would indicate the kilo- prefix:\n″The kelvin is the SI base unit of temperature.″\nAlex: ″What units do you want me to record this in?″", "Billie: ″Kelvins!″\n″The sample was chilled to 50 K.\"\n″Tay traveled 100 km from Poughkeepsie to Manhattan.″\nThis somewhat unintuitive convention is in fact in line with other SI units named after people, such as the newton, watt, and tesla, symbols N, W, and T respectively.", "When reference is made to the \"Kelvin \"scale\"\", the word \"kelvin\"—which is normally a noun—functions adjectivally to modify the noun \"scale\" and is capitalised.", "As with most other SI unit symbols (angle symbols, e.g., 45° 3′ 4″, are the exception) there is a space between the numeric value and the kelvin symbol (e.g., \"99.987 K\").", "The size of a degree Celsius (historically defined as of the temperature difference between the melting and boiling points of water, see history section for more details), was the template for the size of the kelvin and the convention that the Kelvin and Celsius scales have the same size increments remains in place today, meaning that a \"change\" in temperature or a \"difference\" in temperature necessarily has the same numerical value when expressed in kelvins as it does when expressed in degrees Celsius:\nHowever while the Kelvin scale takes absolute zero as its starting point, the modern iteration of the Celsius scale takes 273.15 K as its starting point, this being a close approximation of the melting point of water at standard atmospheric pressure, indeed, the 9th edition of the SI Brochure \"defines\" the temperature in Celsius such that:\nSo, for example, \"It is 10 °C colder outside the house than inside\" and \"It is 10 K colder outside the house than inside\" are exactly equivalent statements, while \"It is 10 °C outside\" and \"It is 10 K outside\" describe very different situations!", "This convention makes conversion between °C and K relatively straightforward, but has the downside that neither the melting nor boiling points of water have round values when expressed in kelvins, being approximately 273.15 K and 373.15 K respectively.", "As the melting and boiling points of water were historically 180 degrees apart on the Fahrenheit scale (32 °F and 212 °F, respectively) a temperature interval of 1 K (and of 1 °C) is equal to an interval of 1.8 °F.", "Absolute zero in °F is:\nHence:", "The kelvin is often used as a measure of the colour temperature of light sources.", "Colour temperature is based upon the principle that a black body radiator emits light with a frequency distribution characteristic of its temperature.", "Black bodies at temperatures below about appear reddish, whereas those above about appear bluish.", "Colour temperature is important in the fields of image projection and photography, where a colour temperature of approximately is required to match \"daylight\" film emulsions.", "In astronomy, the stellar classification of stars and their place on the Hertzsprung–Russell diagram are based, in part, upon their surface temperature, known as effective temperature.", "The photosphere of the Sun, for instance, has an effective temperature of .", "Digital cameras and photographic software often use colour temperature in K in edit and setup menus.", "The simple guide is that higher colour temperature produces an image with enhanced white and blue hues.", "The reduction in colour temperature produces an image more dominated by reddish, \"warmer\" colours.", "For electronics, the kelvin is used as an indicator of how noisy a circuit is in relation to an ultimate noise floor, i.e. the noise temperature.", "The so-called Johnson–Nyquist noise of discrete resistors and capacitors is a type of thermal noise derived from the Boltzmann constant and can be used to determine the noise temperature of a circuit using the Friis formulas for noise.", "The International System of Units (SI) is based on seven SI base units (the second, metre, kilogram, kelvin, ampere, mole, and candela) representing seven fundamental types of physical quantity, or \"dimensions\" (time, length, mass, temperature, electrical current, amount of substance, and luminous intensity respectively), with all other SI units defined using these seven basic building blocks.", "These SI derived units can either be given special names, e.g., tesla, volt, lux, etc., or left as bare descriptions, e.g. metre per second.", "The only SI unit with a special name derived from the kelvin is the degree Celsius, which is also the only SI unit derived from another by offsetting, rather than by multiplication or division.", "Some commonly used units derived from the kelvin without special names are:\nMany of these are of interest in the engineering of heating, ventilation, and air conditioning systems and of building insulation.", "Coefficient of thermal expansion is an important consideration in structural engineering.", "Like other SI units, the kelvin can modified by adding a prefix that multiplies it by a power of 10.", "A yoctokelvin (yK) is one septillionth of a kelvin () and the smallest unit of temperature defined in the International System of Units.", "It is a little more than the temperature increase that would result from adding 1 joule of thermal energy to the Indian Ocean, assuming properties similar to those of pure water.", "A zeptokelvin (zK) is one sextillionth of a kelvin ().", "It is somewhat less than the temperature increase that would result from adding 1 joule of thermal energy to the Baltic Sea, assuming properties similar to those of pure water.", "An attokelvin (aK) is one quintillionth of a kelvin ().", "It is the approximate effective temperature of an extremely massive 61.7 billion solar mass supermassive black hole, only a little less massive than the black hole Ton 618, and the approximate temperature increase that would result from adding 1 joule of thermal energy to Lake Toba, the largest lake in Indonesia.", "A femtokelvin (fK) is one quadrillionth of a kelvin ().", "It is the approximate effective temperature of a 61.7 million solar mass supermassive black hole.", "A picokelvin (pK) is one trillionth of a kelvin ().", "A nanokelvin (nK) is one billionth of a kelvin ().", "It is the approximate effective temperature of a fairly large 61.7 solar mass stellar-mass black hole.", "NASA's Cold Atom Laboratory can chill small numbers of atoms down to below 1 nanokelvin.", "A microkelvin (μK) is one millionth of a kelvin ().", "A millikelvin (mK) is one thousandth of a kelvin (0.001 K or ).", "A centikelvin (cK) is one hundredth of a kelvin (0.01 K or ).", "A decikelvin (dK) is one tenth of a kelvin (0.1 K or ).", "A decakelvin (daK) is ten kelvins (10 K or ).", "The main components of air, nitrogen and oxygen, boil at 77 K and 90 K respectively under 1 atmosphere of pressure.", "A hectokelvin (hK) is one hundred kelvins (100 K or ).", "Air temperatures recorded occurring naturally on Earth (excluding, e.g. wildfires, volcanoes, and meteorite impacts) range from 184 K at Vostok Station in Antarctica to 330 K at Furnace Creek in Death Valley.", "Yakutsk in Russia's Sakha Republic has a daily average low in January of 229 K. Ice melts at 273.15 K. Kuwait City has a daily average high in July and August of 320 K. Water boils at 373.15 K at 1 atmosphere.", "The average surface temperature on Venus in 737 K.", "A kilokelvin (kK) is one thousand kelvins (1000 K or ).", "Iron melts at 1811 K, or 1.8 kK. The temperature at the surface of the Sun is about 5800 K, or 5.8 kK.", "A megakelvin (MK) is one million kelvins ().", "The temperature at the centre of the Sun is about 15.7 MK.", "A gigakelvin (GK) is one billion kelvins ().", "A terakelvin (TK) is one trillion kelvins ().", "A petakelvin (PK) is one quadrillion kelvins ().", "An exakelvin (EK) is one quintillion kelvins ().", "A zettakelvin (ZK) is one sextillion kelvins ().", "A yottakelvin (YK) is one septillion kelvins () and the largest unit of temperature defined in the SI.", "It corresponds to a mean translational kinetic energy of joules, the same order of magnitude as the Oh-My-God particle.", "The Planck temperature is approximately 141,680,000 yottakelvins.", "The symbol is encoded in Unicode at code point .", "However, this is a compatibility character provided for compatibility with legacy encodings.", "The Unicode standard recommends using instead; that is, a normal capital K. \"Three letterlike symbols have been given canonical equivalence to regular letters: , , and .", "In all three instances, the regular letter should be used.\"" ]

[ 79, 80, 81, 82 ]

[ "It was developed by shifting the starting point of the much older Celsius scale down from the melting point of water to absolute zero and its increments still closely approximate the historic definition of a degree Celsius, but as of 2019 the scale is defined by fixing the numerical value of the Boltzmann constant to .", "The temperature in Celsius is now defined as the temperature in kelvins minus 273.15, meaning that a \"change\" or \"difference\" in temperature has exactly the same value when expressed in kelvins as in Celsius, that absolute zero is exactly 0 K and −273.15 °C, and that pure water freezes very close to 273.15 K and boils close to 373.15 K at standard atmospheric pressure." ]

[ "Governmental functions\nMinister of Industry : 1967–1968.", "Minister of Planning and Land Management : 1968–1969.", "Minister of National Education : 1969–1972.", "Minister of Equipment, Housing and Tourism : 1972–1974.", "Minister of State, minister of Land Management, Equipment and Transports : March–May 1974.", "Minister of State, Keeper of the Seals : 1976–1977.", "Electoral mandates\nNational Assembly of France\nMember of the National Assembly of France for Loire-Atlantique : Elected in 1967, but he became minister / Reelected in 1968, but he stays minister / Reelected in 1973, but he stays minister / 1974–1976 (Became minister) / 1978–1997.", "Elected in 1967, reelected in 1968, 1973, 1978, 1981, 1986, 1988, 1993.", "Regional Council\nPresident of the Regional Council of Pays de la Loire : 1974–1998.", "Elected in 1986, reelected in 1992.", "Regional councillor of Pays de la Loire : 1974–1998.", "Elected in 1986, reelected in 1992.", "General Council\nGeneral councillor of Loire-Atlantique : 1970–1982.", "Reelected in 1976.", "Municipal Council\nMayor of Néac : 1962–1971.", "Reelected in 1965.", "Municipal councillor of Néac : 1962–1971.", "Reelected in 1965.", "Mayor of La Baule-Escoublac : 1971–1995.", "Reelected in 1977, 1983, 1989.", "Municipal councillor of La Baule-Escoublac : 1971–1995.", "Reelected in 1977, 1983, 1989." ]

[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 ]

[ "He has been a member of parliament and several time minister.", "From 1969 until 1972, he was Minister of National Education.", "Between 1972 and 1974, he was Minister of Public Works.", "And between 1976 and 1977, he was Minister of Justice." ]

[ "The Iranian Constitutional Revolution took place between 1905 and 1911.", "The early cores of consciousness of women's rights (or rather lack of rights) which led to establishment of societies and magazines started shortly after.", "The low status of women and secret operation of many of their organizations and societies, have somewhat limited the amount of data on the subject.", "Women's writing in that era, mainly through newspapers and periodicals are one of the most valuable sources of information on the movement.", "Most important of these periodicals are listed below.", "Additionally, Iranian women were aware of women's conditions and educational opportunities elsewhere and were inspired by them.", "Women activists determined that education was central to their cause.", "The argument they put forward was that providing women with education was overall good for Iran, in terms of mothers raising better children for their country.", "At the beginning of the century, foreign missionaries founded the first school for girls, which was attended mostly by religious minorities.", "Haji-Mirza Hassan Roshdieh and Bibi Khanoom Astarabadi later also founded schools for girls, but both were quickly closed.", "Eventually, in 1918, after years of private and unregulated schools, the government provided funds to establish ten primary schools for girls and a teacher training college.", "From 1914 to 1925, the women's publications expanded beyond discussions of education onto subjects such as child marriage, economic non social empowerment, and the rights and legal status of women.", "In 1906, despite the parliament refusing their request, women established several organizations, including the \"Society for Women's Freedom\", which met in secret until it was discovered and attacked.", "The Jam'iat e nesvan e vatan-khah (Patriotic Women’s League) was founded approximately around 1918; it published Nosvan Vatankhah.\nIn 1922, Mohtaram Eskandari created the \"Patriotic Women's Organization\".", "She was arrested and her house was burned.", "Zandokht Shirazi, another women activist, organized the \"Women's Revolutionary Association.\"", "During this early phase of the women's movement, women who became involved were in general daughters, sisters and wives of well-known constitutionalists.", "Generally, they were from educated middle-class families.", "The low status of women and secret operation of many of their organizations and societies have somewhat limited the amount of data on the subject.", "Women's writing in that era, mainly through newspapers and periodicals are one of the most valuable sources of information on the movement.", "Some of the most important periodicals of that era are listed below (the year of publication of the first issue is mentioned in brackets, sometimes with the city of publication):", "Women’s first strides were in education: in 1928, they were provided with financial support to study abroad; in 1935 they were admitted to Tehran University, and in 1944 education became compulsory.", "In 1932, the Second Congress of Women of the East was organized in Tehran, and Iranian women activists met with activists from Lebanon, Egypt, India and Iraq.", "Dowlatabadi was the secretary.", "In 1936, Reza Shah Pahlavi set the mandatory unveiling of women known as Kashf-e hijab —a highly controversial policy which caused many conservative women to simply stay inside the house rather than go out in a veil and be subjected to harassment from the police, but also caused desegregation in some sectors of society.", "The reform was supported by many of the leading women's rights activists, who campaigned for it via the women's organisation Kanoun-e-Banovan.", "The 1940s saw a heightened consciousness of the role of women in society; and the 1950s the birth of numerous women’s rights organizations, among which \"Rah-e Now\" (New Path) founded by Mehrangiz Dowlatshahi in 1955, and \"Women’s League of Supporters of the Declaration of Human Rights\" founded by Safieh Firouz in 1956.", "In 1959 fifteen of those organizations formed a federation called the \"High Council of Women’s Organizations in Iran\".", "The High Council decided to concentrate its efforts on women’s suffrage.", "Despite much opposition by clerics, the suffrage was gained in 1963 when a national referendum reflected general support for the 6-point reform program known as the White Revolution which included women’s right to vote and to stand for public office.", "Six women were elected to Parliament (\"Majlis\").", "In the late 1960s, women entered the diplomatic corps, the judiciary and police force, and the revolutionary service corps (education, health and development): in 1968, Farrokhroo Parsa became Minister of Education - she was the first woman to hold a cabinet position; in 1969 the judiciary was opened to women and five female judges were appointed, including future Nobel prize winner Shirin Ebadi.", "Women were elected to town, city and county councils.", "Looking for a way to achieve a more viable organization structure for women’s activities, a coalition of women’s groups forms the Women’s Organization of Iran in 1966.", "Though the WOI was patroned by Princess Ashraf (the Shah's twin sister), Iranian women and the WOI had to fight for every improvement in their lives.", "The Women’s Organization of Iran was a non-profit grassroots organization working mainly through volunteers.", "Its goals were to encourage women’s education for change, to work towards securing economic independence for women, and at the same time to remain within the spirit of Islam and the cultural traditions of the nation.", "It worked through local branches and Women’s Centers, which provided useful services for women – literacy classes, vocational training, counseling, sports and cultural activities and childcare.", "One of the major victories of the WOI was the Family Protection Law of 1975.", "It granted women equal rights in marriage and divorce, enhanced women’s rights in child custody, increased the minimum age of marriage to 18 for women and 20 for men, and practically eliminated polygamy.", "Abortion was also made legal without arousing much public attention, by removing the penalty for performing the operation embodied in a law dealing with medical malpractice.", "All labor laws and regulations were revised to eliminate sex discrimination and incorporate equal pay for equal work.", "Women were encouraged to run for political office.", "By 1978 nearly 40% of girls 6 and above were literate; over 12,000 literacy corps women were teaching in villages; 33% of university students were women, and more women than men took the entrance exam for the school of medicine.", "333 women were elected to local councils, 22 women were elected to parliament, and 2 served in the Senate.", "There were one cabinet minister (for women’s affairs), 3 sub-cabinet under-secretaries, one governor, an ambassador, and five women mayors.", "Iran has also established itself as playing a leading role for women’s rights among developing countries, introducing ideas and funds for the UN Regional Center for Research and Development for Asia and the Pacific, and the International Center for Research on Women.", "After the Iranian Revolution in February 1979, the status of women changed substantially.", "The massive participation of women in the 1978–79 revolution was in part a result of the mobilization efforts of women’s organization in the preceding decades, including the WOI’s activities in the late 1960s and 70s during which women had gained consciousness of their own collective political power, and understood the need for women to assert themselves.", "Women marched in support of a freer, more egalitarian government.", "With passage of time, some of the rights that women had gained under Shah, were systematically removed, through legislation, such as the forced wearing of the hijab, particularly the chador.", "Soon after the revolution, there were rumors of plans for forced hijab, and abolition of some women's rights protected by \"Family protection act\" conceived to be \"against Islam\".", "The rumors were denied by some state officials and many women refused to accept it.", "Not long after, however, the rumors were realized.", "A new family law was annulled, and veiling became obligatory.", "Farrokhrou Parsa, the first woman to serve in the Iranian cabinet, was executed.", "The veiling law was met with protests comprising heterogeneous groups of women.", "The demonstrations did not aim to expand women's rights in Iran, but simply to keep what they had already earned.", "There were three major collective attempts to voice concerns:\n#A five-day demonstration starting on March 8, 1979\n#The Conference of Unity of Women in December 1979\n#Demonstrations after the Ayatollah Khomeini's decree on eliminating any symbol or practice reminiscent of the Shah's rule.", "A consequence of that decree was forced hijab.", "These collective attempts, as well as the smaller ones, not only faced opposition from the Islamic conservatives, but were sometimes damaged by the leftist political groups, exemplified by the organization of a demonstration scheduled by the Fedai for the same day as that of the Conference of Unity of Women in December 1979 — despite the pleas mentioned above.", "In fact, most leftist groups did not have a well-established vision or plan for pursuing women's rights.", "The status of women, it was presumed, would be improved automatically by the establishment of an ideal socialist/communist society.", "Aspects of Islamic law pertaining to women can be seen in Articles 20 and 21 of the 1979 constitution, and two manifestations of Islamic law are now infamous among women's rights activists: stoning and polygamy, to name two.", "At the beginning of the Islamic revolution, some of the leaders of the women’s rights, were discredited.", "For the first time since the revolution, several women succeeded in 1997 in getting into a stadium to watch a soccer match.", "Female legal consultants have been introduced in special family courts.", "One Million Signatures for the Repeal of Discriminatory Laws notable campaign was launched in 2006 to collect one million signatures in support of changing discriminatory laws against women in Iran and reforming of family laws, to ask Parliament for the revision and reform of current laws which discriminate against women.", "Another campaign was 'Stop Stoning Forever'.", "By all accounts, the degree of mobilization and consciousness among women in Iran is remarkable.", "The women’s rights movement is vibrant and well-organized.", "The movement has also been credited with very smart use of information and communication technologies.", "However, the active participation of many women in the revolution helped awaken many women about their political potential, and many middle-class women acted increasingly to support women’s rights.", "Increasing vocal opposition to policies which sanctioned polygamy, temporary marriage, free divorce for men, and child custody to fathers also took hold.", "A growing trend of women began to interpret Islam in more gender-egalitarian ways with the entry of more women in the public sphere and limitation of discourse to Islamic parameters.", "Growing activism and publicity brought some legal remedies to the women’s struggle for example limits on a husband’s right to prevent his wife from taking a job, and a new marriage contract which gave women the right to divorce.", "Judges became more sympathetic to women’s issues because of the hardship, and when some reforms did not make it through the legislative process, the government tried to ameliorate some of the injustices and gave instructions to the courts on how to do so.", "As more Iranian girls were being educated in the 1980s, and the government opened higher religious education to women, some mastered technical forms of Islamic argumentation which helped in the fight for the liberalization of women’s rights.", "Furthermore, many women became successful entrepreneurs, and worked in other highly visible professions including parliament.", "As stated in an interview in 1996, prominent secular lawyer Mehrangiz Kar stated “The revolution gave women confidence in themselves.", "With all the sacrifices they made, Iranian women know how much their current and future rulers owe to them.", "This demand is no longer that of a group of women; it is a nationwide one.", "The Islamic government cannot escape it without risking a brutal separation of the state and religion.”", "Women's Cultural Centre is an organization founded in the 1990s by Noushin Ahmadi Khorasani and Parvin Ardalan and has been a center for forming opinions, analyzing and documenting women's issues in Iran.", "Since 2005, the organization has published Iran's first online magazine on women's rights, Zanestan, with Ardalan as its editor.", "In its constant struggle against censorship – the magazine comes back with a new name all the time – the newspaper has dealt with marriage, prostitution, education, AIDS, and violence against women.", "\"Zanan\" magazine is a monthly women's magazine published in Iran, founded in 1992.", "It is the only Persian women's magazine in the country.", "The magazine ceased publication in 2008, but was relaunched on 29 May 2014.", "In September 2014, its founder and editor Shahla Sherkat was charged in Iran's Press Court (part of the Islamic Revolutionary Court) for promoting un-Islamic and \"obsolete\" views and in April 2015, publication of the magazine was again suspended.", "\"Zanan\" focused on the concerns of Iranian women with an Islamic point of view and had intentions of protecting and promoting their rights.", "However, the monthly magazine tested the political waters with its coverage of reform politics, domestic abuse, and sex.", "Article topics covered controversial issues from domestic abuse to plastic surgery.", "It argued that gender equality was Islamic and that religious literature had been misread and misappropriated by misogynists.", "Mehangiz Kar, Shahla Lahiji, and Shahla Sherkat, the editors of \"Zanan\", led the debate on women's rights and demanded reforms.", "The leadership did not respond but, for the first time since the revolution, did not silence the movement.", "One Million Signatures for the Repeal of Discriminatory Laws, also known as Change for Equality, is a campaign by women in Iran to collect one million signatures in support of changing discriminatory laws against women in their country.", "The campaign seeks to secure equal rights in marriage and inheritance, an end to polygamy, and stricter punishments for honour killings and other forms of violence.", "It was founded in late August 2006 on Tehran by Noushin Ahmadi Khorasani and Parvin Ardalan who were imprisoned in sentenced to three years in prison for \"threatening the national security.", "\"\nActivists of the movement have been attacked and jailed by the government, and the campaign has had to extend its two-year target to collect the full number of signatures.", "My Stealthy Freedom is an online movement that was commenced in 2014 by Masih Alinejad, an Iranian-born journalist and activist based in the United Kingdom and the United States.", "This movement started from a Facebook page \"My Stealthy Freedom\" where women from Iran post their photos without scarfs, and by the end of 2016 page has surpassed 1 million Facebook likes.", "Initiative has received wide international and national coverage, Hopes were high that the re-election of Iranian President Hassan Rouhani would see the abolishment of the compulsory hijab law, which has never happened.", "To this end, Alinejad launched \"White Wednesdays,\" where women protest the law by wearing white veils on Wednesdays (men, in solidarity, tie white ribbons around their wrists).", "Iranian feminists generally fall into two camps when it comes to the women's rights movement in Iran, post 1979.", "Some believe that Islamization has resulted in the \"marginalizing\" of women.", "Others believe that through the dynamic nature of Islamic law, known as Sharia, a unique consciousness of feminism has been formed in Iran.", "Both these views have been challenged.", "Among the women's rights activists in Iran, \"feminism\" means different things.", "A major contrast is seen between secular feminists and those who are dubbed Islamic feminists, on the nature of feminism.", "Islamic feminists, or more accurately Muslim feminists, are women rights advocates who seek to improve the status of women through more favorable interpretations of Islamic law, supporting what is called \"Dynamic Interpretation\" (\"Feqh-e pouya\" in Persian).", "Some Muslim feminists prefer the term \"indigenous feminists\" (\"feminist-e boomi\").", "Despite the disagreements among different factions, when it comes to the improvement of women's conditions, feminist groups have shown that they can cooperate with an emphasis on common ground.", "The chief editor of \"Zanan\" magazine, Shahla Sherkat, for example, a woman with definite religious beliefs, invited prominent Muslim women rights activist Shirin Ebadi, and prominent secular women rights activist Mehrangiz Kar, to write on women's issues in her magazine.", "These activists have also taken advantage of new technologies in their efforts for women's rights; Mehrangiz Kar, for example, has taught classes and written manuals on women's rights defense for Tavaana: E-Learning Institute for Iranian Civil Society.", "Through the efforts of women's rights advocates in Iran, in 2001 Allameh Tabatabaii University, Tarbiat Modares University, and Alzahra University initiated women's studies programs at the Master of Arts level, and shortly thereafter Tehran University began a similar university course for a degree.", "There are three sub-specialties: women and family, the history of women, and women's rights in Islam.", "These programs are needed, it is stated, to try and remedy some of the damage caused by centuries of the dominance of negative views on women, sociologically and humanistically, and other hardships suffered by women in Iran.", "It is hoped that graduates of women's studies programs will be able to present gender-neutral points of view.", "Some of the most notable activists are:" ]

[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ]

[ "This movement first emerged after the Iranian Constitutional Revolution in 1910, the year in which the first Women Journal was published by women.", "The movement lasted until 1933 in which the last women’s association was dissolved by the Reza Shah Pahlavi’s government." ]

[ "The Iranian Constitutional Revolution took place between 1905 and 1911.", "The early cores of consciousness of women's rights (or rather lack of rights) which led to establishment of societies and magazines started shortly after.", "The low status of women and secret operation of many of their organizations and societies, have somewhat limited the amount of data on the subject.", "Women's writing in that era, mainly through newspapers and periodicals are one of the most valuable sources of information on the movement.", "Most important of these periodicals are listed below.", "Additionally, Iranian women were aware of women's conditions and educational opportunities elsewhere and were inspired by them.", "Women activists determined that education was central to their cause.", "The argument they put forward was that providing women with education was overall good for Iran, in terms of mothers raising better children for their country.", "At the beginning of the century, foreign missionaries founded the first school for girls, which was attended mostly by religious minorities.", "Haji-Mirza Hassan Roshdieh and Bibi Khanoom Astarabadi later also founded schools for girls, but both were quickly closed.", "Eventually, in 1918, after years of private and unregulated schools, the government provided funds to establish ten primary schools for girls and a teacher training college.", "From 1914 to 1925, the women's publications expanded beyond discussions of education onto subjects such as child marriage, economic non social empowerment, and the rights and legal status of women.", "In 1906, despite the parliament refusing their request, women established several organizations, including the \"Society for Women's Freedom\", which met in secret until it was discovered and attacked.", "The Jam'iat e nesvan e vatan-khah (Patriotic Women’s League) was founded approximately around 1918; it published Nosvan Vatankhah.\nIn 1922, Mohtaram Eskandari created the \"Patriotic Women's Organization\".", "She was arrested and her house was burned.", "Zandokht Shirazi, another women activist, organized the \"Women's Revolutionary Association.\"", "During this early phase of the women's movement, women who became involved were in general daughters, sisters and wives of well-known constitutionalists.", "Generally, they were from educated middle-class families.", "The low status of women and secret operation of many of their organizations and societies have somewhat limited the amount of data on the subject.", "Women's writing in that era, mainly through newspapers and periodicals are one of the most valuable sources of information on the movement.", "Some of the most important periodicals of that era are listed below (the year of publication of the first issue is mentioned in brackets, sometimes with the city of publication):", "Women’s first strides were in education: in 1928, they were provided with financial support to study abroad; in 1935 they were admitted to Tehran University, and in 1944 education became compulsory.", "In 1932, the Second Congress of Women of the East was organized in Tehran, and Iranian women activists met with activists from Lebanon, Egypt, India and Iraq.", "Dowlatabadi was the secretary.", "In 1936, Reza Shah Pahlavi set the mandatory unveiling of women known as Kashf-e hijab —a highly controversial policy which caused many conservative women to simply stay inside the house rather than go out in a veil and be subjected to harassment from the police, but also caused desegregation in some sectors of society.", "The reform was supported by many of the leading women's rights activists, who campaigned for it via the women's organisation Kanoun-e-Banovan.", "The 1940s saw a heightened consciousness of the role of women in society; and the 1950s the birth of numerous women’s rights organizations, among which \"Rah-e Now\" (New Path) founded by Mehrangiz Dowlatshahi in 1955, and \"Women’s League of Supporters of the Declaration of Human Rights\" founded by Safieh Firouz in 1956.", "In 1959 fifteen of those organizations formed a federation called the \"High Council of Women’s Organizations in Iran\".", "The High Council decided to concentrate its efforts on women’s suffrage.", "Despite much opposition by clerics, the suffrage was gained in 1963 when a national referendum reflected general support for the 6-point reform program known as the White Revolution which included women’s right to vote and to stand for public office.", "Six women were elected to Parliament (\"Majlis\").", "In the late 1960s, women entered the diplomatic corps, the judiciary and police force, and the revolutionary service corps (education, health and development): in 1968, Farrokhroo Parsa became Minister of Education - she was the first woman to hold a cabinet position; in 1969 the judiciary was opened to women and five female judges were appointed, including future Nobel prize winner Shirin Ebadi.", "Women were elected to town, city and county councils.", "Looking for a way to achieve a more viable organization structure for women’s activities, a coalition of women’s groups forms the Women’s Organization of Iran in 1966.", "Though the WOI was patroned by Princess Ashraf (the Shah's twin sister), Iranian women and the WOI had to fight for every improvement in their lives.", "The Women’s Organization of Iran was a non-profit grassroots organization working mainly through volunteers.", "Its goals were to encourage women’s education for change, to work towards securing economic independence for women, and at the same time to remain within the spirit of Islam and the cultural traditions of the nation.", "It worked through local branches and Women’s Centers, which provided useful services for women – literacy classes, vocational training, counseling, sports and cultural activities and childcare.", "One of the major victories of the WOI was the Family Protection Law of 1975.", "It granted women equal rights in marriage and divorce, enhanced women’s rights in child custody, increased the minimum age of marriage to 18 for women and 20 for men, and practically eliminated polygamy.", "Abortion was also made legal without arousing much public attention, by removing the penalty for performing the operation embodied in a law dealing with medical malpractice.", "All labor laws and regulations were revised to eliminate sex discrimination and incorporate equal pay for equal work.", "Women were encouraged to run for political office.", "By 1978 nearly 40% of girls 6 and above were literate; over 12,000 literacy corps women were teaching in villages; 33% of university students were women, and more women than men took the entrance exam for the school of medicine.", "333 women were elected to local councils, 22 women were elected to parliament, and 2 served in the Senate.", "There were one cabinet minister (for women’s affairs), 3 sub-cabinet under-secretaries, one governor, an ambassador, and five women mayors.", "Iran has also established itself as playing a leading role for women’s rights among developing countries, introducing ideas and funds for the UN Regional Center for Research and Development for Asia and the Pacific, and the International Center for Research on Women.", "After the Iranian Revolution in February 1979, the status of women changed substantially.", "The massive participation of women in the 1978–79 revolution was in part a result of the mobilization efforts of women’s organization in the preceding decades, including the WOI’s activities in the late 1960s and 70s during which women had gained consciousness of their own collective political power, and understood the need for women to assert themselves.", "Women marched in support of a freer, more egalitarian government.", "With passage of time, some of the rights that women had gained under Shah, were systematically removed, through legislation, such as the forced wearing of the hijab, particularly the chador.", "Soon after the revolution, there were rumors of plans for forced hijab, and abolition of some women's rights protected by \"Family protection act\" conceived to be \"against Islam\".", "The rumors were denied by some state officials and many women refused to accept it.", "Not long after, however, the rumors were realized.", "A new family law was annulled, and veiling became obligatory.", "Farrokhrou Parsa, the first woman to serve in the Iranian cabinet, was executed.", "The veiling law was met with protests comprising heterogeneous groups of women.", "The demonstrations did not aim to expand women's rights in Iran, but simply to keep what they had already earned.", "There were three major collective attempts to voice concerns:\n#A five-day demonstration starting on March 8, 1979\n#The Conference of Unity of Women in December 1979\n#Demonstrations after the Ayatollah Khomeini's decree on eliminating any symbol or practice reminiscent of the Shah's rule.", "A consequence of that decree was forced hijab.", "These collective attempts, as well as the smaller ones, not only faced opposition from the Islamic conservatives, but were sometimes damaged by the leftist political groups, exemplified by the organization of a demonstration scheduled by the Fedai for the same day as that of the Conference of Unity of Women in December 1979 — despite the pleas mentioned above.", "In fact, most leftist groups did not have a well-established vision or plan for pursuing women's rights.", "The status of women, it was presumed, would be improved automatically by the establishment of an ideal socialist/communist society.", "Aspects of Islamic law pertaining to women can be seen in Articles 20 and 21 of the 1979 constitution, and two manifestations of Islamic law are now infamous among women's rights activists: stoning and polygamy, to name two.", "At the beginning of the Islamic revolution, some of the leaders of the women’s rights, were discredited.", "For the first time since the revolution, several women succeeded in 1997 in getting into a stadium to watch a soccer match.", "Female legal consultants have been introduced in special family courts.", "One Million Signatures for the Repeal of Discriminatory Laws notable campaign was launched in 2006 to collect one million signatures in support of changing discriminatory laws against women in Iran and reforming of family laws, to ask Parliament for the revision and reform of current laws which discriminate against women.", "Another campaign was 'Stop Stoning Forever'.", "By all accounts, the degree of mobilization and consciousness among women in Iran is remarkable.", "The women’s rights movement is vibrant and well-organized.", "The movement has also been credited with very smart use of information and communication technologies.", "However, the active participation of many women in the revolution helped awaken many women about their political potential, and many middle-class women acted increasingly to support women’s rights.", "Increasing vocal opposition to policies which sanctioned polygamy, temporary marriage, free divorce for men, and child custody to fathers also took hold.", "A growing trend of women began to interpret Islam in more gender-egalitarian ways with the entry of more women in the public sphere and limitation of discourse to Islamic parameters.", "Growing activism and publicity brought some legal remedies to the women’s struggle for example limits on a husband’s right to prevent his wife from taking a job, and a new marriage contract which gave women the right to divorce.", "Judges became more sympathetic to women’s issues because of the hardship, and when some reforms did not make it through the legislative process, the government tried to ameliorate some of the injustices and gave instructions to the courts on how to do so.", "As more Iranian girls were being educated in the 1980s, and the government opened higher religious education to women, some mastered technical forms of Islamic argumentation which helped in the fight for the liberalization of women’s rights.", "Furthermore, many women became successful entrepreneurs, and worked in other highly visible professions including parliament.", "As stated in an interview in 1996, prominent secular lawyer Mehrangiz Kar stated “The revolution gave women confidence in themselves.", "With all the sacrifices they made, Iranian women know how much their current and future rulers owe to them.", "This demand is no longer that of a group of women; it is a nationwide one.", "The Islamic government cannot escape it without risking a brutal separation of the state and religion.”", "Women's Cultural Centre is an organization founded in the 1990s by Noushin Ahmadi Khorasani and Parvin Ardalan and has been a center for forming opinions, analyzing and documenting women's issues in Iran.", "Since 2005, the organization has published Iran's first online magazine on women's rights, Zanestan, with Ardalan as its editor.", "In its constant struggle against censorship – the magazine comes back with a new name all the time – the newspaper has dealt with marriage, prostitution, education, AIDS, and violence against women.", "\"Zanan\" magazine is a monthly women's magazine published in Iran, founded in 1992.", "It is the only Persian women's magazine in the country.", "The magazine ceased publication in 2008, but was relaunched on 29 May 2014.", "In September 2014, its founder and editor Shahla Sherkat was charged in Iran's Press Court (part of the Islamic Revolutionary Court) for promoting un-Islamic and \"obsolete\" views and in April 2015, publication of the magazine was again suspended.", "\"Zanan\" focused on the concerns of Iranian women with an Islamic point of view and had intentions of protecting and promoting their rights.", "However, the monthly magazine tested the political waters with its coverage of reform politics, domestic abuse, and sex.", "Article topics covered controversial issues from domestic abuse to plastic surgery.", "It argued that gender equality was Islamic and that religious literature had been misread and misappropriated by misogynists.", "Mehangiz Kar, Shahla Lahiji, and Shahla Sherkat, the editors of \"Zanan\", led the debate on women's rights and demanded reforms.", "The leadership did not respond but, for the first time since the revolution, did not silence the movement.", "One Million Signatures for the Repeal of Discriminatory Laws, also known as Change for Equality, is a campaign by women in Iran to collect one million signatures in support of changing discriminatory laws against women in their country.", "The campaign seeks to secure equal rights in marriage and inheritance, an end to polygamy, and stricter punishments for honour killings and other forms of violence.", "It was founded in late August 2006 on Tehran by Noushin Ahmadi Khorasani and Parvin Ardalan who were imprisoned in sentenced to three years in prison for \"threatening the national security.", "\"\nActivists of the movement have been attacked and jailed by the government, and the campaign has had to extend its two-year target to collect the full number of signatures.", "My Stealthy Freedom is an online movement that was commenced in 2014 by Masih Alinejad, an Iranian-born journalist and activist based in the United Kingdom and the United States.", "This movement started from a Facebook page \"My Stealthy Freedom\" where women from Iran post their photos without scarfs, and by the end of 2016 page has surpassed 1 million Facebook likes.", "Initiative has received wide international and national coverage, Hopes were high that the re-election of Iranian President Hassan Rouhani would see the abolishment of the compulsory hijab law, which has never happened.", "To this end, Alinejad launched \"White Wednesdays,\" where women protest the law by wearing white veils on Wednesdays (men, in solidarity, tie white ribbons around their wrists).", "Iranian feminists generally fall into two camps when it comes to the women's rights movement in Iran, post 1979.", "Some believe that Islamization has resulted in the \"marginalizing\" of women.", "Others believe that through the dynamic nature of Islamic law, known as Sharia, a unique consciousness of feminism has been formed in Iran.", "Both these views have been challenged.", "Among the women's rights activists in Iran, \"feminism\" means different things.", "A major contrast is seen between secular feminists and those who are dubbed Islamic feminists, on the nature of feminism.", "Islamic feminists, or more accurately Muslim feminists, are women rights advocates who seek to improve the status of women through more favorable interpretations of Islamic law, supporting what is called \"Dynamic Interpretation\" (\"Feqh-e pouya\" in Persian).", "Some Muslim feminists prefer the term \"indigenous feminists\" (\"feminist-e boomi\").", "Despite the disagreements among different factions, when it comes to the improvement of women's conditions, feminist groups have shown that they can cooperate with an emphasis on common ground.", "The chief editor of \"Zanan\" magazine, Shahla Sherkat, for example, a woman with definite religious beliefs, invited prominent Muslim women rights activist Shirin Ebadi, and prominent secular women rights activist Mehrangiz Kar, to write on women's issues in her magazine.", "These activists have also taken advantage of new technologies in their efforts for women's rights; Mehrangiz Kar, for example, has taught classes and written manuals on women's rights defense for Tavaana: E-Learning Institute for Iranian Civil Society.", "Through the efforts of women's rights advocates in Iran, in 2001 Allameh Tabatabaii University, Tarbiat Modares University, and Alzahra University initiated women's studies programs at the Master of Arts level, and shortly thereafter Tehran University began a similar university course for a degree.", "There are three sub-specialties: women and family, the history of women, and women's rights in Islam.", "These programs are needed, it is stated, to try and remedy some of the damage caused by centuries of the dominance of negative views on women, sociologically and humanistically, and other hardships suffered by women in Iran.", "It is hoped that graduates of women's studies programs will be able to present gender-neutral points of view.", "Some of the most notable activists are:" ]

[ 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46 ]

[ "The Iranian Women's Rights Movement (Persian: جنبش زنان ایران), is the social movement for women's rights of the women in Iran.", "Between 1962 and 1978, the Iranian Women's Movement gained victories such as the right for women to vote (in 1963, part of Mohammad Reza Shah's White Revolution).", "They were also allowed to take part in public office, and in 1975 the Family Protection Law provided new rights for women, including expanded divorce and custody rights and reduced polygamy." ]

[ "The Iranian Constitutional Revolution took place between 1905 and 1911.", "The early cores of consciousness of women's rights (or rather lack of rights) which led to establishment of societies and magazines started shortly after.", "The low status of women and secret operation of many of their organizations and societies, have somewhat limited the amount of data on the subject.", "Women's writing in that era, mainly through newspapers and periodicals are one of the most valuable sources of information on the movement.", "Most important of these periodicals are listed below.", "Additionally, Iranian women were aware of women's conditions and educational opportunities elsewhere and were inspired by them.", "Women activists determined that education was central to their cause.", "The argument they put forward was that providing women with education was overall good for Iran, in terms of mothers raising better children for their country.", "At the beginning of the century, foreign missionaries founded the first school for girls, which was attended mostly by religious minorities.", "Haji-Mirza Hassan Roshdieh and Bibi Khanoom Astarabadi later also founded schools for girls, but both were quickly closed.", "Eventually, in 1918, after years of private and unregulated schools, the government provided funds to establish ten primary schools for girls and a teacher training college.", "From 1914 to 1925, the women's publications expanded beyond discussions of education onto subjects such as child marriage, economic non social empowerment, and the rights and legal status of women.", "In 1906, despite the parliament refusing their request, women established several organizations, including the \"Society for Women's Freedom\", which met in secret until it was discovered and attacked.", "The Jam'iat e nesvan e vatan-khah (Patriotic Women’s League) was founded approximately around 1918; it published Nosvan Vatankhah.\nIn 1922, Mohtaram Eskandari created the \"Patriotic Women's Organization\".", "She was arrested and her house was burned.", "Zandokht Shirazi, another women activist, organized the \"Women's Revolutionary Association.\"", "During this early phase of the women's movement, women who became involved were in general daughters, sisters and wives of well-known constitutionalists.", "Generally, they were from educated middle-class families.", "The low status of women and secret operation of many of their organizations and societies have somewhat limited the amount of data on the subject.", "Women's writing in that era, mainly through newspapers and periodicals are one of the most valuable sources of information on the movement.", "Some of the most important periodicals of that era are listed below (the year of publication of the first issue is mentioned in brackets, sometimes with the city of publication):", "Women’s first strides were in education: in 1928, they were provided with financial support to study abroad; in 1935 they were admitted to Tehran University, and in 1944 education became compulsory.", "In 1932, the Second Congress of Women of the East was organized in Tehran, and Iranian women activists met with activists from Lebanon, Egypt, India and Iraq.", "Dowlatabadi was the secretary.", "In 1936, Reza Shah Pahlavi set the mandatory unveiling of women known as Kashf-e hijab —a highly controversial policy which caused many conservative women to simply stay inside the house rather than go out in a veil and be subjected to harassment from the police, but also caused desegregation in some sectors of society.", "The reform was supported by many of the leading women's rights activists, who campaigned for it via the women's organisation Kanoun-e-Banovan.", "The 1940s saw a heightened consciousness of the role of women in society; and the 1950s the birth of numerous women’s rights organizations, among which \"Rah-e Now\" (New Path) founded by Mehrangiz Dowlatshahi in 1955, and \"Women’s League of Supporters of the Declaration of Human Rights\" founded by Safieh Firouz in 1956.", "In 1959 fifteen of those organizations formed a federation called the \"High Council of Women’s Organizations in Iran\".", "The High Council decided to concentrate its efforts on women’s suffrage.", "Despite much opposition by clerics, the suffrage was gained in 1963 when a national referendum reflected general support for the 6-point reform program known as the White Revolution which included women’s right to vote and to stand for public office.", "Six women were elected to Parliament (\"Majlis\").", "In the late 1960s, women entered the diplomatic corps, the judiciary and police force, and the revolutionary service corps (education, health and development): in 1968, Farrokhroo Parsa became Minister of Education - she was the first woman to hold a cabinet position; in 1969 the judiciary was opened to women and five female judges were appointed, including future Nobel prize winner Shirin Ebadi.", "Women were elected to town, city and county councils.", "Looking for a way to achieve a more viable organization structure for women’s activities, a coalition of women’s groups forms the Women’s Organization of Iran in 1966.", "Though the WOI was patroned by Princess Ashraf (the Shah's twin sister), Iranian women and the WOI had to fight for every improvement in their lives.", "The Women’s Organization of Iran was a non-profit grassroots organization working mainly through volunteers.", "Its goals were to encourage women’s education for change, to work towards securing economic independence for women, and at the same time to remain within the spirit of Islam and the cultural traditions of the nation.", "It worked through local branches and Women’s Centers, which provided useful services for women – literacy classes, vocational training, counseling, sports and cultural activities and childcare.", "One of the major victories of the WOI was the Family Protection Law of 1975.", "It granted women equal rights in marriage and divorce, enhanced women’s rights in child custody, increased the minimum age of marriage to 18 for women and 20 for men, and practically eliminated polygamy.", "Abortion was also made legal without arousing much public attention, by removing the penalty for performing the operation embodied in a law dealing with medical malpractice.", "All labor laws and regulations were revised to eliminate sex discrimination and incorporate equal pay for equal work.", "Women were encouraged to run for political office.", "By 1978 nearly 40% of girls 6 and above were literate; over 12,000 literacy corps women were teaching in villages; 33% of university students were women, and more women than men took the entrance exam for the school of medicine.", "333 women were elected to local councils, 22 women were elected to parliament, and 2 served in the Senate.", "There were one cabinet minister (for women’s affairs), 3 sub-cabinet under-secretaries, one governor, an ambassador, and five women mayors.", "Iran has also established itself as playing a leading role for women’s rights among developing countries, introducing ideas and funds for the UN Regional Center for Research and Development for Asia and the Pacific, and the International Center for Research on Women.", "After the Iranian Revolution in February 1979, the status of women changed substantially.", "The massive participation of women in the 1978–79 revolution was in part a result of the mobilization efforts of women’s organization in the preceding decades, including the WOI’s activities in the late 1960s and 70s during which women had gained consciousness of their own collective political power, and understood the need for women to assert themselves.", "Women marched in support of a freer, more egalitarian government.", "With passage of time, some of the rights that women had gained under Shah, were systematically removed, through legislation, such as the forced wearing of the hijab, particularly the chador.", "Soon after the revolution, there were rumors of plans for forced hijab, and abolition of some women's rights protected by \"Family protection act\" conceived to be \"against Islam\".", "The rumors were denied by some state officials and many women refused to accept it.", "Not long after, however, the rumors were realized.", "A new family law was annulled, and veiling became obligatory.", "Farrokhrou Parsa, the first woman to serve in the Iranian cabinet, was executed.", "The veiling law was met with protests comprising heterogeneous groups of women.", "The demonstrations did not aim to expand women's rights in Iran, but simply to keep what they had already earned.", "There were three major collective attempts to voice concerns:\n#A five-day demonstration starting on March 8, 1979\n#The Conference of Unity of Women in December 1979\n#Demonstrations after the Ayatollah Khomeini's decree on eliminating any symbol or practice reminiscent of the Shah's rule.", "A consequence of that decree was forced hijab.", "These collective attempts, as well as the smaller ones, not only faced opposition from the Islamic conservatives, but were sometimes damaged by the leftist political groups, exemplified by the organization of a demonstration scheduled by the Fedai for the same day as that of the Conference of Unity of Women in December 1979 — despite the pleas mentioned above.", "In fact, most leftist groups did not have a well-established vision or plan for pursuing women's rights.", "The status of women, it was presumed, would be improved automatically by the establishment of an ideal socialist/communist society.", "Aspects of Islamic law pertaining to women can be seen in Articles 20 and 21 of the 1979 constitution, and two manifestations of Islamic law are now infamous among women's rights activists: stoning and polygamy, to name two.", "At the beginning of the Islamic revolution, some of the leaders of the women’s rights, were discredited.", "For the first time since the revolution, several women succeeded in 1997 in getting into a stadium to watch a soccer match.", "Female legal consultants have been introduced in special family courts.", "One Million Signatures for the Repeal of Discriminatory Laws notable campaign was launched in 2006 to collect one million signatures in support of changing discriminatory laws against women in Iran and reforming of family laws, to ask Parliament for the revision and reform of current laws which discriminate against women.", "Another campaign was 'Stop Stoning Forever'.", "By all accounts, the degree of mobilization and consciousness among women in Iran is remarkable.", "The women’s rights movement is vibrant and well-organized.", "The movement has also been credited with very smart use of information and communication technologies.", "However, the active participation of many women in the revolution helped awaken many women about their political potential, and many middle-class women acted increasingly to support women’s rights.", "Increasing vocal opposition to policies which sanctioned polygamy, temporary marriage, free divorce for men, and child custody to fathers also took hold.", "A growing trend of women began to interpret Islam in more gender-egalitarian ways with the entry of more women in the public sphere and limitation of discourse to Islamic parameters.", "Growing activism and publicity brought some legal remedies to the women’s struggle for example limits on a husband’s right to prevent his wife from taking a job, and a new marriage contract which gave women the right to divorce.", "Judges became more sympathetic to women’s issues because of the hardship, and when some reforms did not make it through the legislative process, the government tried to ameliorate some of the injustices and gave instructions to the courts on how to do so.", "As more Iranian girls were being educated in the 1980s, and the government opened higher religious education to women, some mastered technical forms of Islamic argumentation which helped in the fight for the liberalization of women’s rights.", "Furthermore, many women became successful entrepreneurs, and worked in other highly visible professions including parliament.", "As stated in an interview in 1996, prominent secular lawyer Mehrangiz Kar stated “The revolution gave women confidence in themselves.", "With all the sacrifices they made, Iranian women know how much their current and future rulers owe to them.", "This demand is no longer that of a group of women; it is a nationwide one.", "The Islamic government cannot escape it without risking a brutal separation of the state and religion.”", "Women's Cultural Centre is an organization founded in the 1990s by Noushin Ahmadi Khorasani and Parvin Ardalan and has been a center for forming opinions, analyzing and documenting women's issues in Iran.", "Since 2005, the organization has published Iran's first online magazine on women's rights, Zanestan, with Ardalan as its editor.", "In its constant struggle against censorship – the magazine comes back with a new name all the time – the newspaper has dealt with marriage, prostitution, education, AIDS, and violence against women.", "\"Zanan\" magazine is a monthly women's magazine published in Iran, founded in 1992.", "It is the only Persian women's magazine in the country.", "The magazine ceased publication in 2008, but was relaunched on 29 May 2014.", "In September 2014, its founder and editor Shahla Sherkat was charged in Iran's Press Court (part of the Islamic Revolutionary Court) for promoting un-Islamic and \"obsolete\" views and in April 2015, publication of the magazine was again suspended.", "\"Zanan\" focused on the concerns of Iranian women with an Islamic point of view and had intentions of protecting and promoting their rights.", "However, the monthly magazine tested the political waters with its coverage of reform politics, domestic abuse, and sex.", "Article topics covered controversial issues from domestic abuse to plastic surgery.", "It argued that gender equality was Islamic and that religious literature had been misread and misappropriated by misogynists.", "Mehangiz Kar, Shahla Lahiji, and Shahla Sherkat, the editors of \"Zanan\", led the debate on women's rights and demanded reforms.", "The leadership did not respond but, for the first time since the revolution, did not silence the movement.", "One Million Signatures for the Repeal of Discriminatory Laws, also known as Change for Equality, is a campaign by women in Iran to collect one million signatures in support of changing discriminatory laws against women in their country.", "The campaign seeks to secure equal rights in marriage and inheritance, an end to polygamy, and stricter punishments for honour killings and other forms of violence.", "It was founded in late August 2006 on Tehran by Noushin Ahmadi Khorasani and Parvin Ardalan who were imprisoned in sentenced to three years in prison for \"threatening the national security.", "\"\nActivists of the movement have been attacked and jailed by the government, and the campaign has had to extend its two-year target to collect the full number of signatures.", "My Stealthy Freedom is an online movement that was commenced in 2014 by Masih Alinejad, an Iranian-born journalist and activist based in the United Kingdom and the United States.", "This movement started from a Facebook page \"My Stealthy Freedom\" where women from Iran post their photos without scarfs, and by the end of 2016 page has surpassed 1 million Facebook likes.", "Initiative has received wide international and national coverage, Hopes were high that the re-election of Iranian President Hassan Rouhani would see the abolishment of the compulsory hijab law, which has never happened.", "To this end, Alinejad launched \"White Wednesdays,\" where women protest the law by wearing white veils on Wednesdays (men, in solidarity, tie white ribbons around their wrists).", "Iranian feminists generally fall into two camps when it comes to the women's rights movement in Iran, post 1979.", "Some believe that Islamization has resulted in the \"marginalizing\" of women.", "Others believe that through the dynamic nature of Islamic law, known as Sharia, a unique consciousness of feminism has been formed in Iran.", "Both these views have been challenged.", "Among the women's rights activists in Iran, \"feminism\" means different things.", "A major contrast is seen between secular feminists and those who are dubbed Islamic feminists, on the nature of feminism.", "Islamic feminists, or more accurately Muslim feminists, are women rights advocates who seek to improve the status of women through more favorable interpretations of Islamic law, supporting what is called \"Dynamic Interpretation\" (\"Feqh-e pouya\" in Persian).", "Some Muslim feminists prefer the term \"indigenous feminists\" (\"feminist-e boomi\").", "Despite the disagreements among different factions, when it comes to the improvement of women's conditions, feminist groups have shown that they can cooperate with an emphasis on common ground.", "The chief editor of \"Zanan\" magazine, Shahla Sherkat, for example, a woman with definite religious beliefs, invited prominent Muslim women rights activist Shirin Ebadi, and prominent secular women rights activist Mehrangiz Kar, to write on women's issues in her magazine.", "These activists have also taken advantage of new technologies in their efforts for women's rights; Mehrangiz Kar, for example, has taught classes and written manuals on women's rights defense for Tavaana: E-Learning Institute for Iranian Civil Society.", "Through the efforts of women's rights advocates in Iran, in 2001 Allameh Tabatabaii University, Tarbiat Modares University, and Alzahra University initiated women's studies programs at the Master of Arts level, and shortly thereafter Tehran University began a similar university course for a degree.", "There are three sub-specialties: women and family, the history of women, and women's rights in Islam.", "These programs are needed, it is stated, to try and remedy some of the damage caused by centuries of the dominance of negative views on women, sociologically and humanistically, and other hardships suffered by women in Iran.", "It is hoped that graduates of women's studies programs will be able to present gender-neutral points of view.", "Some of the most notable activists are:" ]

[ 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46 ]

[ "They were also allowed to take part in public office, and in 1975 the Family Protection Law provided new rights for women, including expanded divorce and custody rights and reduced polygamy." ]

[ "The Iranian Constitutional Revolution took place between 1905 and 1911.", "The early cores of consciousness of women's rights (or rather lack of rights) which led to establishment of societies and magazines started shortly after.", "The low status of women and secret operation of many of their organizations and societies, have somewhat limited the amount of data on the subject.", "Women's writing in that era, mainly through newspapers and periodicals are one of the most valuable sources of information on the movement.", "Most important of these periodicals are listed below.", "Additionally, Iranian women were aware of women's conditions and educational opportunities elsewhere and were inspired by them.", "Women activists determined that education was central to their cause.", "The argument they put forward was that providing women with education was overall good for Iran, in terms of mothers raising better children for their country.", "At the beginning of the century, foreign missionaries founded the first school for girls, which was attended mostly by religious minorities.", "Haji-Mirza Hassan Roshdieh and Bibi Khanoom Astarabadi later also founded schools for girls, but both were quickly closed.", "Eventually, in 1918, after years of private and unregulated schools, the government provided funds to establish ten primary schools for girls and a teacher training college.", "From 1914 to 1925, the women's publications expanded beyond discussions of education onto subjects such as child marriage, economic non social empowerment, and the rights and legal status of women.", "In 1906, despite the parliament refusing their request, women established several organizations, including the \"Society for Women's Freedom\", which met in secret until it was discovered and attacked.", "The Jam'iat e nesvan e vatan-khah (Patriotic Women’s League) was founded approximately around 1918; it published Nosvan Vatankhah.\nIn 1922, Mohtaram Eskandari created the \"Patriotic Women's Organization\".", "She was arrested and her house was burned.", "Zandokht Shirazi, another women activist, organized the \"Women's Revolutionary Association.\"", "During this early phase of the women's movement, women who became involved were in general daughters, sisters and wives of well-known constitutionalists.", "Generally, they were from educated middle-class families.", "The low status of women and secret operation of many of their organizations and societies have somewhat limited the amount of data on the subject.", "Women's writing in that era, mainly through newspapers and periodicals are one of the most valuable sources of information on the movement.", "Some of the most important periodicals of that era are listed below (the year of publication of the first issue is mentioned in brackets, sometimes with the city of publication):", "Women’s first strides were in education: in 1928, they were provided with financial support to study abroad; in 1935 they were admitted to Tehran University, and in 1944 education became compulsory.", "In 1932, the Second Congress of Women of the East was organized in Tehran, and Iranian women activists met with activists from Lebanon, Egypt, India and Iraq.", "Dowlatabadi was the secretary.", "In 1936, Reza Shah Pahlavi set the mandatory unveiling of women known as Kashf-e hijab —a highly controversial policy which caused many conservative women to simply stay inside the house rather than go out in a veil and be subjected to harassment from the police, but also caused desegregation in some sectors of society.", "The reform was supported by many of the leading women's rights activists, who campaigned for it via the women's organisation Kanoun-e-Banovan.", "The 1940s saw a heightened consciousness of the role of women in society; and the 1950s the birth of numerous women’s rights organizations, among which \"Rah-e Now\" (New Path) founded by Mehrangiz Dowlatshahi in 1955, and \"Women’s League of Supporters of the Declaration of Human Rights\" founded by Safieh Firouz in 1956.", "In 1959 fifteen of those organizations formed a federation called the \"High Council of Women’s Organizations in Iran\".", "The High Council decided to concentrate its efforts on women’s suffrage.", "Despite much opposition by clerics, the suffrage was gained in 1963 when a national referendum reflected general support for the 6-point reform program known as the White Revolution which included women’s right to vote and to stand for public office.", "Six women were elected to Parliament (\"Majlis\").", "In the late 1960s, women entered the diplomatic corps, the judiciary and police force, and the revolutionary service corps (education, health and development): in 1968, Farrokhroo Parsa became Minister of Education - she was the first woman to hold a cabinet position; in 1969 the judiciary was opened to women and five female judges were appointed, including future Nobel prize winner Shirin Ebadi.", "Women were elected to town, city and county councils.", "Looking for a way to achieve a more viable organization structure for women’s activities, a coalition of women’s groups forms the Women’s Organization of Iran in 1966.", "Though the WOI was patroned by Princess Ashraf (the Shah's twin sister), Iranian women and the WOI had to fight for every improvement in their lives.", "The Women’s Organization of Iran was a non-profit grassroots organization working mainly through volunteers.", "Its goals were to encourage women’s education for change, to work towards securing economic independence for women, and at the same time to remain within the spirit of Islam and the cultural traditions of the nation.", "It worked through local branches and Women’s Centers, which provided useful services for women – literacy classes, vocational training, counseling, sports and cultural activities and childcare.", "One of the major victories of the WOI was the Family Protection Law of 1975.", "It granted women equal rights in marriage and divorce, enhanced women’s rights in child custody, increased the minimum age of marriage to 18 for women and 20 for men, and practically eliminated polygamy.", "Abortion was also made legal without arousing much public attention, by removing the penalty for performing the operation embodied in a law dealing with medical malpractice.", "All labor laws and regulations were revised to eliminate sex discrimination and incorporate equal pay for equal work.", "Women were encouraged to run for political office.", "By 1978 nearly 40% of girls 6 and above were literate; over 12,000 literacy corps women were teaching in villages; 33% of university students were women, and more women than men took the entrance exam for the school of medicine.", "333 women were elected to local councils, 22 women were elected to parliament, and 2 served in the Senate.", "There were one cabinet minister (for women’s affairs), 3 sub-cabinet under-secretaries, one governor, an ambassador, and five women mayors.", "Iran has also established itself as playing a leading role for women’s rights among developing countries, introducing ideas and funds for the UN Regional Center for Research and Development for Asia and the Pacific, and the International Center for Research on Women.", "After the Iranian Revolution in February 1979, the status of women changed substantially.", "The massive participation of women in the 1978–79 revolution was in part a result of the mobilization efforts of women’s organization in the preceding decades, including the WOI’s activities in the late 1960s and 70s during which women had gained consciousness of their own collective political power, and understood the need for women to assert themselves.", "Women marched in support of a freer, more egalitarian government.", "With passage of time, some of the rights that women had gained under Shah, were systematically removed, through legislation, such as the forced wearing of the hijab, particularly the chador.", "Soon after the revolution, there were rumors of plans for forced hijab, and abolition of some women's rights protected by \"Family protection act\" conceived to be \"against Islam\".", "The rumors were denied by some state officials and many women refused to accept it.", "Not long after, however, the rumors were realized.", "A new family law was annulled, and veiling became obligatory.", "Farrokhrou Parsa, the first woman to serve in the Iranian cabinet, was executed.", "The veiling law was met with protests comprising heterogeneous groups of women.", "The demonstrations did not aim to expand women's rights in Iran, but simply to keep what they had already earned.", "There were three major collective attempts to voice concerns:\n#A five-day demonstration starting on March 8, 1979\n#The Conference of Unity of Women in December 1979\n#Demonstrations after the Ayatollah Khomeini's decree on eliminating any symbol or practice reminiscent of the Shah's rule.", "A consequence of that decree was forced hijab.", "These collective attempts, as well as the smaller ones, not only faced opposition from the Islamic conservatives, but were sometimes damaged by the leftist political groups, exemplified by the organization of a demonstration scheduled by the Fedai for the same day as that of the Conference of Unity of Women in December 1979 — despite the pleas mentioned above.", "In fact, most leftist groups did not have a well-established vision or plan for pursuing women's rights.", "The status of women, it was presumed, would be improved automatically by the establishment of an ideal socialist/communist society.", "Aspects of Islamic law pertaining to women can be seen in Articles 20 and 21 of the 1979 constitution, and two manifestations of Islamic law are now infamous among women's rights activists: stoning and polygamy, to name two.", "At the beginning of the Islamic revolution, some of the leaders of the women’s rights, were discredited.", "For the first time since the revolution, several women succeeded in 1997 in getting into a stadium to watch a soccer match.", "Female legal consultants have been introduced in special family courts.", "One Million Signatures for the Repeal of Discriminatory Laws notable campaign was launched in 2006 to collect one million signatures in support of changing discriminatory laws against women in Iran and reforming of family laws, to ask Parliament for the revision and reform of current laws which discriminate against women.", "Another campaign was 'Stop Stoning Forever'.", "By all accounts, the degree of mobilization and consciousness among women in Iran is remarkable.", "The women’s rights movement is vibrant and well-organized.", "The movement has also been credited with very smart use of information and communication technologies.", "However, the active participation of many women in the revolution helped awaken many women about their political potential, and many middle-class women acted increasingly to support women’s rights.", "Increasing vocal opposition to policies which sanctioned polygamy, temporary marriage, free divorce for men, and child custody to fathers also took hold.", "A growing trend of women began to interpret Islam in more gender-egalitarian ways with the entry of more women in the public sphere and limitation of discourse to Islamic parameters.", "Growing activism and publicity brought some legal remedies to the women’s struggle for example limits on a husband’s right to prevent his wife from taking a job, and a new marriage contract which gave women the right to divorce.", "Judges became more sympathetic to women’s issues because of the hardship, and when some reforms did not make it through the legislative process, the government tried to ameliorate some of the injustices and gave instructions to the courts on how to do so.", "As more Iranian girls were being educated in the 1980s, and the government opened higher religious education to women, some mastered technical forms of Islamic argumentation which helped in the fight for the liberalization of women’s rights.", "Furthermore, many women became successful entrepreneurs, and worked in other highly visible professions including parliament.", "As stated in an interview in 1996, prominent secular lawyer Mehrangiz Kar stated “The revolution gave women confidence in themselves.", "With all the sacrifices they made, Iranian women know how much their current and future rulers owe to them.", "This demand is no longer that of a group of women; it is a nationwide one.", "The Islamic government cannot escape it without risking a brutal separation of the state and religion.”", "Women's Cultural Centre is an organization founded in the 1990s by Noushin Ahmadi Khorasani and Parvin Ardalan and has been a center for forming opinions, analyzing and documenting women's issues in Iran.", "Since 2005, the organization has published Iran's first online magazine on women's rights, Zanestan, with Ardalan as its editor.", "In its constant struggle against censorship – the magazine comes back with a new name all the time – the newspaper has dealt with marriage, prostitution, education, AIDS, and violence against women.", "\"Zanan\" magazine is a monthly women's magazine published in Iran, founded in 1992.", "It is the only Persian women's magazine in the country.", "The magazine ceased publication in 2008, but was relaunched on 29 May 2014.", "In September 2014, its founder and editor Shahla Sherkat was charged in Iran's Press Court (part of the Islamic Revolutionary Court) for promoting un-Islamic and \"obsolete\" views and in April 2015, publication of the magazine was again suspended.", "\"Zanan\" focused on the concerns of Iranian women with an Islamic point of view and had intentions of protecting and promoting their rights.", "However, the monthly magazine tested the political waters with its coverage of reform politics, domestic abuse, and sex.", "Article topics covered controversial issues from domestic abuse to plastic surgery.", "It argued that gender equality was Islamic and that religious literature had been misread and misappropriated by misogynists.", "Mehangiz Kar, Shahla Lahiji, and Shahla Sherkat, the editors of \"Zanan\", led the debate on women's rights and demanded reforms.", "The leadership did not respond but, for the first time since the revolution, did not silence the movement.", "One Million Signatures for the Repeal of Discriminatory Laws, also known as Change for Equality, is a campaign by women in Iran to collect one million signatures in support of changing discriminatory laws against women in their country.", "The campaign seeks to secure equal rights in marriage and inheritance, an end to polygamy, and stricter punishments for honour killings and other forms of violence.", "It was founded in late August 2006 on Tehran by Noushin Ahmadi Khorasani and Parvin Ardalan who were imprisoned in sentenced to three years in prison for \"threatening the national security.", "\"\nActivists of the movement have been attacked and jailed by the government, and the campaign has had to extend its two-year target to collect the full number of signatures.", "My Stealthy Freedom is an online movement that was commenced in 2014 by Masih Alinejad, an Iranian-born journalist and activist based in the United Kingdom and the United States.", "This movement started from a Facebook page \"My Stealthy Freedom\" where women from Iran post their photos without scarfs, and by the end of 2016 page has surpassed 1 million Facebook likes.", "Initiative has received wide international and national coverage, Hopes were high that the re-election of Iranian President Hassan Rouhani would see the abolishment of the compulsory hijab law, which has never happened.", "To this end, Alinejad launched \"White Wednesdays,\" where women protest the law by wearing white veils on Wednesdays (men, in solidarity, tie white ribbons around their wrists).", "Iranian feminists generally fall into two camps when it comes to the women's rights movement in Iran, post 1979.", "Some believe that Islamization has resulted in the \"marginalizing\" of women.", "Others believe that through the dynamic nature of Islamic law, known as Sharia, a unique consciousness of feminism has been formed in Iran.", "Both these views have been challenged.", "Among the women's rights activists in Iran, \"feminism\" means different things.", "A major contrast is seen between secular feminists and those who are dubbed Islamic feminists, on the nature of feminism.", "Islamic feminists, or more accurately Muslim feminists, are women rights advocates who seek to improve the status of women through more favorable interpretations of Islamic law, supporting what is called \"Dynamic Interpretation\" (\"Feqh-e pouya\" in Persian).", "Some Muslim feminists prefer the term \"indigenous feminists\" (\"feminist-e boomi\").", "Despite the disagreements among different factions, when it comes to the improvement of women's conditions, feminist groups have shown that they can cooperate with an emphasis on common ground.", "The chief editor of \"Zanan\" magazine, Shahla Sherkat, for example, a woman with definite religious beliefs, invited prominent Muslim women rights activist Shirin Ebadi, and prominent secular women rights activist Mehrangiz Kar, to write on women's issues in her magazine.", "These activists have also taken advantage of new technologies in their efforts for women's rights; Mehrangiz Kar, for example, has taught classes and written manuals on women's rights defense for Tavaana: E-Learning Institute for Iranian Civil Society.", "Through the efforts of women's rights advocates in Iran, in 2001 Allameh Tabatabaii University, Tarbiat Modares University, and Alzahra University initiated women's studies programs at the Master of Arts level, and shortly thereafter Tehran University began a similar university course for a degree.", "There are three sub-specialties: women and family, the history of women, and women's rights in Islam.", "These programs are needed, it is stated, to try and remedy some of the damage caused by centuries of the dominance of negative views on women, sociologically and humanistically, and other hardships suffered by women in Iran.", "It is hoped that graduates of women's studies programs will be able to present gender-neutral points of view.", "Some of the most notable activists are:" ]

[ 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103 ]

[ "It heightened again after the Iranian Revolution (1979).", "Women's rights have been restricted since the Islamic Revolution.", "The Women's Rights Movement in Iran continues to attempt influencing reforms, particularly with the One Million Signatures Campaign to End Discrimination Against Women." ]

[ "The Iranian Constitutional Revolution took place between 1905 and 1911.", "The early cores of consciousness of women's rights (or rather lack of rights) which led to establishment of societies and magazines started shortly after.", "The low status of women and secret operation of many of their organizations and societies, have somewhat limited the amount of data on the subject.", "Women's writing in that era, mainly through newspapers and periodicals are one of the most valuable sources of information on the movement.", "Most important of these periodicals are listed below.", "Additionally, Iranian women were aware of women's conditions and educational opportunities elsewhere and were inspired by them.", "Women activists determined that education was central to their cause.", "The argument they put forward was that providing women with education was overall good for Iran, in terms of mothers raising better children for their country.", "At the beginning of the century, foreign missionaries founded the first school for girls, which was attended mostly by religious minorities.", "Haji-Mirza Hassan Roshdieh and Bibi Khanoom Astarabadi later also founded schools for girls, but both were quickly closed.", "Eventually, in 1918, after years of private and unregulated schools, the government provided funds to establish ten primary schools for girls and a teacher training college.", "From 1914 to 1925, the women's publications expanded beyond discussions of education onto subjects such as child marriage, economic non social empowerment, and the rights and legal status of women.", "In 1906, despite the parliament refusing their request, women established several organizations, including the \"Society for Women's Freedom\", which met in secret until it was discovered and attacked.", "The Jam'iat e nesvan e vatan-khah (Patriotic Women’s League) was founded approximately around 1918; it published Nosvan Vatankhah.\nIn 1922, Mohtaram Eskandari created the \"Patriotic Women's Organization\".", "She was arrested and her house was burned.", "Zandokht Shirazi, another women activist, organized the \"Women's Revolutionary Association.\"", "During this early phase of the women's movement, women who became involved were in general daughters, sisters and wives of well-known constitutionalists.", "Generally, they were from educated middle-class families.", "The low status of women and secret operation of many of their organizations and societies have somewhat limited the amount of data on the subject.", "Women's writing in that era, mainly through newspapers and periodicals are one of the most valuable sources of information on the movement.", "Some of the most important periodicals of that era are listed below (the year of publication of the first issue is mentioned in brackets, sometimes with the city of publication):", "Women’s first strides were in education: in 1928, they were provided with financial support to study abroad; in 1935 they were admitted to Tehran University, and in 1944 education became compulsory.", "In 1932, the Second Congress of Women of the East was organized in Tehran, and Iranian women activists met with activists from Lebanon, Egypt, India and Iraq.", "Dowlatabadi was the secretary.", "In 1936, Reza Shah Pahlavi set the mandatory unveiling of women known as Kashf-e hijab —a highly controversial policy which caused many conservative women to simply stay inside the house rather than go out in a veil and be subjected to harassment from the police, but also caused desegregation in some sectors of society.", "The reform was supported by many of the leading women's rights activists, who campaigned for it via the women's organisation Kanoun-e-Banovan.", "The 1940s saw a heightened consciousness of the role of women in society; and the 1950s the birth of numerous women’s rights organizations, among which \"Rah-e Now\" (New Path) founded by Mehrangiz Dowlatshahi in 1955, and \"Women’s League of Supporters of the Declaration of Human Rights\" founded by Safieh Firouz in 1956.", "In 1959 fifteen of those organizations formed a federation called the \"High Council of Women’s Organizations in Iran\".", "The High Council decided to concentrate its efforts on women’s suffrage.", "Despite much opposition by clerics, the suffrage was gained in 1963 when a national referendum reflected general support for the 6-point reform program known as the White Revolution which included women’s right to vote and to stand for public office.", "Six women were elected to Parliament (\"Majlis\").", "In the late 1960s, women entered the diplomatic corps, the judiciary and police force, and the revolutionary service corps (education, health and development): in 1968, Farrokhroo Parsa became Minister of Education - she was the first woman to hold a cabinet position; in 1969 the judiciary was opened to women and five female judges were appointed, including future Nobel prize winner Shirin Ebadi.", "Women were elected to town, city and county councils.", "Looking for a way to achieve a more viable organization structure for women’s activities, a coalition of women’s groups forms the Women’s Organization of Iran in 1966.", "Though the WOI was patroned by Princess Ashraf (the Shah's twin sister), Iranian women and the WOI had to fight for every improvement in their lives.", "The Women’s Organization of Iran was a non-profit grassroots organization working mainly through volunteers.", "Its goals were to encourage women’s education for change, to work towards securing economic independence for women, and at the same time to remain within the spirit of Islam and the cultural traditions of the nation.", "It worked through local branches and Women’s Centers, which provided useful services for women – literacy classes, vocational training, counseling, sports and cultural activities and childcare.", "One of the major victories of the WOI was the Family Protection Law of 1975.", "It granted women equal rights in marriage and divorce, enhanced women’s rights in child custody, increased the minimum age of marriage to 18 for women and 20 for men, and practically eliminated polygamy.", "Abortion was also made legal without arousing much public attention, by removing the penalty for performing the operation embodied in a law dealing with medical malpractice.", "All labor laws and regulations were revised to eliminate sex discrimination and incorporate equal pay for equal work.", "Women were encouraged to run for political office.", "By 1978 nearly 40% of girls 6 and above were literate; over 12,000 literacy corps women were teaching in villages; 33% of university students were women, and more women than men took the entrance exam for the school of medicine.", "333 women were elected to local councils, 22 women were elected to parliament, and 2 served in the Senate.", "There were one cabinet minister (for women’s affairs), 3 sub-cabinet under-secretaries, one governor, an ambassador, and five women mayors.", "Iran has also established itself as playing a leading role for women’s rights among developing countries, introducing ideas and funds for the UN Regional Center for Research and Development for Asia and the Pacific, and the International Center for Research on Women.", "After the Iranian Revolution in February 1979, the status of women changed substantially.", "The massive participation of women in the 1978–79 revolution was in part a result of the mobilization efforts of women’s organization in the preceding decades, including the WOI’s activities in the late 1960s and 70s during which women had gained consciousness of their own collective political power, and understood the need for women to assert themselves.", "Women marched in support of a freer, more egalitarian government.", "With passage of time, some of the rights that women had gained under Shah, were systematically removed, through legislation, such as the forced wearing of the hijab, particularly the chador.", "Soon after the revolution, there were rumors of plans for forced hijab, and abolition of some women's rights protected by \"Family protection act\" conceived to be \"against Islam\".", "The rumors were denied by some state officials and many women refused to accept it.", "Not long after, however, the rumors were realized.", "A new family law was annulled, and veiling became obligatory.", "Farrokhrou Parsa, the first woman to serve in the Iranian cabinet, was executed.", "The veiling law was met with protests comprising heterogeneous groups of women.", "The demonstrations did not aim to expand women's rights in Iran, but simply to keep what they had already earned.", "There were three major collective attempts to voice concerns:\n#A five-day demonstration starting on March 8, 1979\n#The Conference of Unity of Women in December 1979\n#Demonstrations after the Ayatollah Khomeini's decree on eliminating any symbol or practice reminiscent of the Shah's rule.", "A consequence of that decree was forced hijab.", "These collective attempts, as well as the smaller ones, not only faced opposition from the Islamic conservatives, but were sometimes damaged by the leftist political groups, exemplified by the organization of a demonstration scheduled by the Fedai for the same day as that of the Conference of Unity of Women in December 1979 — despite the pleas mentioned above.", "In fact, most leftist groups did not have a well-established vision or plan for pursuing women's rights.", "The status of women, it was presumed, would be improved automatically by the establishment of an ideal socialist/communist society.", "Aspects of Islamic law pertaining to women can be seen in Articles 20 and 21 of the 1979 constitution, and two manifestations of Islamic law are now infamous among women's rights activists: stoning and polygamy, to name two.", "At the beginning of the Islamic revolution, some of the leaders of the women’s rights, were discredited.", "For the first time since the revolution, several women succeeded in 1997 in getting into a stadium to watch a soccer match.", "Female legal consultants have been introduced in special family courts.", "One Million Signatures for the Repeal of Discriminatory Laws notable campaign was launched in 2006 to collect one million signatures in support of changing discriminatory laws against women in Iran and reforming of family laws, to ask Parliament for the revision and reform of current laws which discriminate against women.", "Another campaign was 'Stop Stoning Forever'.", "By all accounts, the degree of mobilization and consciousness among women in Iran is remarkable.", "The women’s rights movement is vibrant and well-organized.", "The movement has also been credited with very smart use of information and communication technologies.", "However, the active participation of many women in the revolution helped awaken many women about their political potential, and many middle-class women acted increasingly to support women’s rights.", "Increasing vocal opposition to policies which sanctioned polygamy, temporary marriage, free divorce for men, and child custody to fathers also took hold.", "A growing trend of women began to interpret Islam in more gender-egalitarian ways with the entry of more women in the public sphere and limitation of discourse to Islamic parameters.", "Growing activism and publicity brought some legal remedies to the women’s struggle for example limits on a husband’s right to prevent his wife from taking a job, and a new marriage contract which gave women the right to divorce.", "Judges became more sympathetic to women’s issues because of the hardship, and when some reforms did not make it through the legislative process, the government tried to ameliorate some of the injustices and gave instructions to the courts on how to do so.", "As more Iranian girls were being educated in the 1980s, and the government opened higher religious education to women, some mastered technical forms of Islamic argumentation which helped in the fight for the liberalization of women’s rights.", "Furthermore, many women became successful entrepreneurs, and worked in other highly visible professions including parliament.", "As stated in an interview in 1996, prominent secular lawyer Mehrangiz Kar stated “The revolution gave women confidence in themselves.", "With all the sacrifices they made, Iranian women know how much their current and future rulers owe to them.", "This demand is no longer that of a group of women; it is a nationwide one.", "The Islamic government cannot escape it without risking a brutal separation of the state and religion.”", "Women's Cultural Centre is an organization founded in the 1990s by Noushin Ahmadi Khorasani and Parvin Ardalan and has been a center for forming opinions, analyzing and documenting women's issues in Iran.", "Since 2005, the organization has published Iran's first online magazine on women's rights, Zanestan, with Ardalan as its editor.", "In its constant struggle against censorship – the magazine comes back with a new name all the time – the newspaper has dealt with marriage, prostitution, education, AIDS, and violence against women.", "\"Zanan\" magazine is a monthly women's magazine published in Iran, founded in 1992.", "It is the only Persian women's magazine in the country.", "The magazine ceased publication in 2008, but was relaunched on 29 May 2014.", "In September 2014, its founder and editor Shahla Sherkat was charged in Iran's Press Court (part of the Islamic Revolutionary Court) for promoting un-Islamic and \"obsolete\" views and in April 2015, publication of the magazine was again suspended.", "\"Zanan\" focused on the concerns of Iranian women with an Islamic point of view and had intentions of protecting and promoting their rights.", "However, the monthly magazine tested the political waters with its coverage of reform politics, domestic abuse, and sex.", "Article topics covered controversial issues from domestic abuse to plastic surgery.", "It argued that gender equality was Islamic and that religious literature had been misread and misappropriated by misogynists.", "Mehangiz Kar, Shahla Lahiji, and Shahla Sherkat, the editors of \"Zanan\", led the debate on women's rights and demanded reforms.", "The leadership did not respond but, for the first time since the revolution, did not silence the movement.", "One Million Signatures for the Repeal of Discriminatory Laws, also known as Change for Equality, is a campaign by women in Iran to collect one million signatures in support of changing discriminatory laws against women in their country.", "The campaign seeks to secure equal rights in marriage and inheritance, an end to polygamy, and stricter punishments for honour killings and other forms of violence.", "It was founded in late August 2006 on Tehran by Noushin Ahmadi Khorasani and Parvin Ardalan who were imprisoned in sentenced to three years in prison for \"threatening the national security.", "\"\nActivists of the movement have been attacked and jailed by the government, and the campaign has had to extend its two-year target to collect the full number of signatures.", "My Stealthy Freedom is an online movement that was commenced in 2014 by Masih Alinejad, an Iranian-born journalist and activist based in the United Kingdom and the United States.", "This movement started from a Facebook page \"My Stealthy Freedom\" where women from Iran post their photos without scarfs, and by the end of 2016 page has surpassed 1 million Facebook likes.", "Initiative has received wide international and national coverage, Hopes were high that the re-election of Iranian President Hassan Rouhani would see the abolishment of the compulsory hijab law, which has never happened.", "To this end, Alinejad launched \"White Wednesdays,\" where women protest the law by wearing white veils on Wednesdays (men, in solidarity, tie white ribbons around their wrists).", "Iranian feminists generally fall into two camps when it comes to the women's rights movement in Iran, post 1979.", "Some believe that Islamization has resulted in the \"marginalizing\" of women.", "Others believe that through the dynamic nature of Islamic law, known as Sharia, a unique consciousness of feminism has been formed in Iran.", "Both these views have been challenged.", "Among the women's rights activists in Iran, \"feminism\" means different things.", "A major contrast is seen between secular feminists and those who are dubbed Islamic feminists, on the nature of feminism.", "Islamic feminists, or more accurately Muslim feminists, are women rights advocates who seek to improve the status of women through more favorable interpretations of Islamic law, supporting what is called \"Dynamic Interpretation\" (\"Feqh-e pouya\" in Persian).", "Some Muslim feminists prefer the term \"indigenous feminists\" (\"feminist-e boomi\").", "Despite the disagreements among different factions, when it comes to the improvement of women's conditions, feminist groups have shown that they can cooperate with an emphasis on common ground.", "The chief editor of \"Zanan\" magazine, Shahla Sherkat, for example, a woman with definite religious beliefs, invited prominent Muslim women rights activist Shirin Ebadi, and prominent secular women rights activist Mehrangiz Kar, to write on women's issues in her magazine.", "These activists have also taken advantage of new technologies in their efforts for women's rights; Mehrangiz Kar, for example, has taught classes and written manuals on women's rights defense for Tavaana: E-Learning Institute for Iranian Civil Society.", "Through the efforts of women's rights advocates in Iran, in 2001 Allameh Tabatabaii University, Tarbiat Modares University, and Alzahra University initiated women's studies programs at the Master of Arts level, and shortly thereafter Tehran University began a similar university course for a degree.", "There are three sub-specialties: women and family, the history of women, and women's rights in Islam.", "These programs are needed, it is stated, to try and remedy some of the damage caused by centuries of the dominance of negative views on women, sociologically and humanistically, and other hardships suffered by women in Iran.", "It is hoped that graduates of women's studies programs will be able to present gender-neutral points of view.", "Some of the most notable activists are:" ]

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[ "The Women's Rights Movement in Iran continues to attempt influencing reforms, particularly with the One Million Signatures Campaign to End Discrimination Against Women." ]

[ "Babu is a young man who works as a rickshaw puller and he has fallen in love with Kammo.", "His only true friend is Shambu Nath.", "One day he helps Shankerlal and his family and in return, Shankerlal invites him to his house.", "Instantly the whole family including Shankerlal's wife and Pinky both begin to shower love on Babu.", "Babu having led a tough childhood feels very ecstatic and feels grateful to Shankerlal on having provided him food, clothes and more importantly respect given to him.", "Meanwhile, a goon in the village rapes Kammo and Babu kills him and thereby lands in jail.", "After his release he finds Pinky begging in the streets and then he gets shocked as to how a rich girl has been forced to beg.", "realizes that now Pinky's mother is a widow.", "His sole aim now becomes to help this widow and her child.", "He gives up his personal life, drives a hand-drawn rickshaw, saves some money, so that he can buy provisions for them, as well as send the child, Pinky, to a decent school.", "Pinky then grows up and later starts disliking Babu.", "The rest of the story is how Pinky realizes her folly later on, how Pinky's mother feels indebted to Babu for having helped them in return for one night's shower of affection on Babu by Shankerlal." ]

[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ]

[ "Babu (transl." ]

[ "The mechanisms of energy transfer that define heat include conduction, through direct contact of immobile bodies, or through a wall or barrier that is impermeable to matter; or radiation between separated bodies; or friction due to isochoric mechanical or electrical or magnetic or gravitational work done by the surroundings on the system of interest, such as Joule heating due to an electric current driven through the system of interest by an external system, or through a magnetic stirrer.", "When there is a suitable path between two systems with different temperatures, heat transfer occurs necessarily, immediately, and spontaneously from the hotter to the colder system.", "Thermal conduction occurs by the stochastic (random) motion of microscopic particles (such as atoms or molecules).", "In contrast, thermodynamic work is defined by mechanisms that act macroscopically and directly on the system's whole-body state variables; for example, change of the system's volume through a piston's motion with externally measurable force; or change of the system's internal electric polarization through an externally measurable change in electric field.", "The definition of heat transfer does not require that the process be in any sense smooth.", "For example, a bolt of lightning may transfer heat to a body.", "Convective circulation allows one body to heat another, through an intermediate circulating fluid that carries energy from a boundary of one to a boundary of the other; the actual heat transfer is by conduction and radiation between the fluid and the respective bodies.", "Convective circulation, though spontaneous, does not necessarily and immediately occur simply because of some slight temperature difference; for it to occur in a given arrangement of systems, there is a threshold that must be crossed.", "Although heat flows spontaneously from a hotter body to a cooler one, it is possible to construct a heat pump which expends work to transfer energy from a colder body to a hotter body.", "In contrast, a heat engine reduces an existing temperature difference to supply work to another system.", "Another thermodynamic type of heat transfer device is an active heat spreader, which expends work to speed up transfer of energy to colder surroundings from a hotter body, for example a computer component.", "As a form of energy, heat has the unit joule (J) in the International System of Units (SI).", "However, in many applied fields in engineering the British thermal unit (BTU) and the calorie are often used.", "The standard unit for the rate of heat transferred is the watt (W), defined as one joule per second.", "The symbol for the total amount of energy transferred as heat was used by Rudolf Clausius in 1850:\n\"Let the amount of heat which must be imparted during the transition of the gas in a definite manner from any given state to another, in which its volume is \"v\" and its temperature \"t\", be called \"Q\"\"\nHeat released by a system into its surroundings is by convention a negative quantity (); when a system absorbs heat from its surroundings, it is positive ().", "Heat transfer rate, or heat flow per unit time, is denoted by formula_1.", "This should not be confused with a time derivative of a function of state (which can also be written with the dot notation) since heat is not a function of state.", "Heat flux is defined as rate of heat transfer per unit cross-sectional area (units watts per square metre).", "In 1856, Rudolf Clausius, referring to closed systems, in which transfers of matter do not occur, defined the \"second fundamental theorem\" (the second law of thermodynamics) in the mechanical theory of heat (thermodynamics): \"if two transformations which, without necessitating any other permanent change, can mutually replace one another, be called equivalent, then the generations of the quantity of heat \"Q\" from work at the temperature \"T\", has the \"equivalence-value\":\"\nformula_2\nIn 1865, he came to define the entropy symbolized by \"S\", such that, due to the supply of the amount of heat \"Q\" at temperature \"T\" the entropy of the system is increased by\nIn a transfer of energy as heat without work being done, there are changes of entropy in both the surroundings which lose heat and the system which gains it.", "The increase, , of entropy in the system may be considered to consist of two parts, an increment, that matches, or 'compensates', the change, , of entropy in the surroundings, and a further increment, that may be considered to be 'generated' or 'produced' in the system, and is said therefore to be 'uncompensated'.", "Thus\nformula_3\nThis may also be written\nformula_4\nThe total change of entropy in the system and surroundings is thus\nformula_5\nThis may also be written\nformula_6\nIt is then said that an amount of entropy has been transferred from the surroundings to the system.", "Because entropy is not a conserved quantity, this is an exception to the general way of speaking, in which an amount transferred is of a conserved quantity.", "From the second law of thermodynamics follows that in a spontaneous transfer of heat, in which the temperature of the system is different from that of the surroundings:\nformula_7\nFor purposes of mathematical analysis of transfers, one thinks of fictive processes that are called \"reversible\", with the temperature of the system being hardly less than that of the surroundings, and the transfer taking place at an imperceptibly slow rate.", "Following the definition above in formula (), for such a fictive reversible process, a quantity of transferred heat (an inexact differential) is analyzed as a quantity , with (an exact differential):\nformula_8\nThis equality is only valid for a fictive transfer in which there is no production of entropy, that is to say, in which there is no uncompensated entropy.", "If, in contrast, the process is natural, and can really occur, with irreversibility, then there is entropy production, with .", "The quantity was termed by Clausius the \"uncompensated heat\", though that does not accord with present-day terminology.", "Then one has\nformula_9\nThis leads to the statement\nformula_10\nwhich is the second law of thermodynamics for closed systems.", "In non-equilibrium thermodynamics that makes the approximation of assuming the hypothesis of local thermodynamic equilibrium, there is a special notation for this.", "The transfer of energy as heat is assumed to take place across an infinitesimal temperature difference, so that the system element and its surroundings have near enough the same temperature .", "Then one writes\nformula_11\nwhere by definition\nformula_12\nThe second law for a natural process asserts that\nformula_13", "For a closed system (a system from which no matter can enter or exit), one version of the first law of thermodynamics states that the change in internal energy of the system is equal to the amount of heat supplied to the system minus the amount of thermodynamic work done by system on its surroundings.", "The foregoing sign convention for work is used in the present article, but an alternate sign convention, followed by IUPAC, for work, is to consider the work performed on the system by its surroundings as positive.", "This is the convention adopted by many modern textbooks of physical chemistry, such as those by Peter Atkins and Ira Levine, but many textbooks on physics define work as work done by the system.", "formula_14\nThis formula can be re-written so as to express a definition of quantity of energy transferred as heat, based purely on the concept of adiabatic work, if it is supposed that is defined and measured solely by processes of adiabatic work:\nformula_15\nThe thermodynamic work done by the system is through mechanisms defined by its thermodynamic state variables, for example, its volume , not through variables that necessarily involve mechanisms in the surroundings.", "The latter are such as shaft work, and include isochoric work.", "The internal energy, , is a state function.", "In cyclical processes, such as the operation of a heat engine, state functions of the working substance return to their initial values upon completion of a cycle.", "The differential, or infinitesimal increment, for the internal energy in an infinitesimal process is an exact differential .", "The symbol for exact differentials is the lowercase letter .", "In contrast, neither of the infinitesimal increments nor in an infinitesimal process represents the change in a state function of the system.", "Thus, infinitesimal increments of heat and work are inexact differentials.", "The lowercase Greek letter delta, , is the symbol for inexact differentials.", "The integral of any inexact differential in a process where the system leaves and then returns to the same thermodynamic state does not necessarily equal zero.", "As recounted above, in the section headed \"heat and entropy\", the second law of thermodynamics observes that if heat is supplied to a system in a reversible process, the increment of heat and the temperature form the exact differential\nformula_16\nand that , the entropy of the working body, is a state function.", "Likewise, with a well-defined pressure, , behind a slowly moving (quasistatic) boundary, the work differential, , and the pressure, , combine to form the exact differential\nformula_17\nwith the volume of the system, which is a state variable.", "In general, for systems of uniform pressure and temperature without composition change,\nformula_18\nAssociated with this differential equation is the concept that the internal energy may be considered to be a function of its natural variables and .", "The internal energy representation of the fundamental thermodynamic relation is written as\nformula_19\nIf is constant\nformula_20\nand if is constant\nformula_21\nwith the enthalpy defined by\nformula_22\nThe enthalpy may be considered to be a function of its natural variables and .", "The enthalpy representation of the fundamental thermodynamic relation is written\nformula_23\nThe internal energy representation and the enthalpy representation are partial Legendre transforms of one another.", "They contain the same physical information, written in different ways.", "Like the internal energy, the enthalpy stated as a function of its natural variables is a thermodynamic potential and contains all thermodynamic information about a body.", "If a quantity of heat is added to a body while it does only expansion work on its surroundings, one has\nformula_24\nIf this is constrained to happen at constant pressure, i.e. with , the expansion work done by the body is given by ; recalling the first law of thermodynamics, one has\nformula_25\nConsequently, by substitution one has\nformula_26\nIn this scenario, the increase in enthalpy is equal to the quantity of heat added to the system.", "This is the basis of the determination of enthalpy changes in chemical reactions by calorimetry.", "Since many processes do take place at constant atmospheric pressure, the enthalpy is sometimes given the misleading name of 'heat content' or heat function, while it actually depends strongly on the energies of covalent bonds and intermolecular forces.", "In terms of the natural variables of the state function , this process of change of state from state 1 to state 2 can be expressed as\nformula_27\nIt is known that the temperature is identically stated by\nformula_28\nConsequently,\nformula_29\nIn this case, the integral specifies a quantity of heat transferred at constant pressure.", "As a common noun, English \"heat\" or \"warmth\" (just as French \"chaleur\", German \"Wärme\", Latin \"calor\", Greek θάλπος, etc.) refers to (the human perception of) either thermal energy or temperature.", "Speculation on thermal energy or \"heat\" as a separate form of matter has a long history, see caloric theory, phlogiston and fire (classical element).", "The modern understanding of thermal energy originates with Thompson's 1798 mechanical theory of heat (\"An Experimental Enquiry Concerning the Source of the Heat which is Excited by Friction\"), postulating a mechanical equivalent of heat.", "A collaboration between Nicolas Clément and Sadi Carnot (\"Reflections on the Motive Power of Fire\") in the 1820s had some related thinking along similar lines.", "In 1845, Joule published a paper entitled \"The Mechanical Equivalent of Heat\", in which he specified a numerical value for the amount of mechanical work required to \"produce a unit of heat\".", "The theory of classical thermodynamics matured in the 1850s to 1860s.", "John Tyndall's \"Heat Considered as Mode of Motion\" (1863) was instrumental in popularizing the idea of heat as motion to the English-speaking public.", "The theory was developed in academic publications in French, English and German.", "From an early time, the French technical term \"chaleur\" used by Carnot was taken as equivalent to the English \"heat\" and German \"Wärme\" (lit.", "\"warmth\", while the equivalent of \"heat\" would be German \"Hitze\").", "The process function was introduced by Rudolf Clausius in 1850.", "Clausius described it with the German compound \"Wärmemenge\", translated as \"amount of heat\".", "James Clerk Maxwell in his 1871 \"Theory of Heat\" outlines four stipulations for the definition of heat:\n\n\nThe process function is referred to as \"Wärmemenge\" by Clausius, or as \"amount of heat\" in translation.", "Use of \"heat\" as an abbreviated form of the specific concept of \"quantity of energy transferred as heat\" led to some terminological confusion by the early 20th century.", "The generic meaning of \"heat\", even in classical thermodynamics, is just \"thermal energy\".", "Since the 1920s, it has been recommended practice to use enthalpy to refer to the \"heat content at constant volume\", and to thermal energy when \"heat\" in the general sense is intended, while \"heat\" is reserved for the very specific context of the transfer of thermal energy between two systems.", "Leonard Benedict Loeb in his \"Kinetic Theory of Gases\" (1927) makes a point of using \"quantity of heat\"\nor \"heat–quantity\" when referring to :", "After the perfection of thermometry [...] the next great advance made in the field of heat was the definition of a term which is called the quantity of heat.", "[... after the abandonment of caloric theory,] It still remains to interpret this very definite concept, the quantity of heat, in terms of a theory ascribing all heat to the kinetics of gas molecules.", "A frequent definition of heat is based on the work of Carathéodory (1909), referring to processes in a closed system.", "The internal energy of a body in an arbitrary state can be determined by amounts of work adiabatically performed by the body on its surroundings when it starts from a reference state .", "Such work is assessed through quantities defined in the surroundings of the body.", "It is supposed that such work can be assessed accurately, without error due to friction in the surroundings; friction in the body is not excluded by this definition.", "The adiabatic performance of work is defined in terms of adiabatic walls, which allow transfer of energy as work, but no other transfer, of energy or matter.", "In particular they do not allow the passage of energy as heat.", "According to this definition, work performed adiabatically is in general accompanied by friction within the thermodynamic system or body.", "On the other hand, according to Carathéodory (1909), there also exist non-adiabatic, \"diathermal\" walls, which are postulated to be permeable only to heat.", "For the definition of quantity of energy transferred as heat, it is customarily envisaged that an arbitrary state of interest is reached from state by a process with two components, one adiabatic and the other not adiabatic.", "For convenience one may say that the adiabatic component was the sum of work done by the body through volume change through movement of the walls while the non-adiabatic wall was temporarily rendered adiabatic, and of isochoric adiabatic work.", "Then the non-adiabatic component is a process of energy transfer through the wall that passes only heat, newly made accessible for the purpose of this transfer, from the surroundings to the body.", "The change in internal energy to reach the state from the state is the difference of the two amounts of energy transferred.", "Although Carathéodory himself did not state such a definition, following his work it is customary in theoretical studies to define heat, , to the body from its surroundings, in the combined process of change to state from the state , as the change in internal energy, , minus the amount of work, , done by the body on its surrounds by the adiabatic process, so that .", "In this definition, for the sake of conceptual rigour, the quantity of energy transferred as heat is not specified directly in terms of the non-adiabatic process.", "It is defined through knowledge of precisely two variables, the change of internal energy and the amount of adiabatic work done, for the combined process of change from the reference state to the arbitrary state .", "It is important that this does not explicitly involve the amount of energy transferred in the non-adiabatic component of the combined process.", "It is assumed here that the amount of energy required to pass from state to state , the change of internal energy, is known, independently of the combined process, by a determination through a purely adiabatic process, like that for the determination of the internal energy of state above.", "The rigour that is prized in this definition is that there is one and only one kind of energy transfer admitted as fundamental: energy transferred as work.", "Energy transfer as heat is considered as a derived quantity.", "The uniqueness of work in this scheme is considered to guarantee rigor and purity of conception.", "The conceptual purity of this definition, based on the concept of energy transferred as work as an ideal notion, relies on the idea that some frictionless and otherwise non-dissipative processes of energy transfer can be realized in physical actuality.", "The second law of thermodynamics, on the other hand, assures us that such processes are not found in nature.", "Before the rigorous mathematical definition of heat based on Carathéodory's 1909 paper,\nhistorically, heat, temperature, and thermal equilibrium were presented in thermodynamics textbooks as jointly primitive notions.", "Carathéodory introduced his 1909 paper thus: \"The proposition that the discipline of thermodynamics can be justified without recourse to any hypothesis that cannot be verified experimentally must be regarded as one of the most noteworthy results of the research in thermodynamics that was accomplished during the last century.\"", "Referring to the \"point of view adopted by most authors who were active in the last fifty years\", Carathéodory wrote: \"There exists a physical quantity called heat that is not identical with the mechanical quantities (mass, force, pressure, etc.) and whose variations can be determined by calorimetric measurements.\"", "James Serrin introduces an account of the theory of thermodynamics thus: \"In the following section, we shall use the classical notions of \"heat\", \"work\", and \"hotness\" as primitive elements, ...", "That heat is an appropriate and natural primitive for thermodynamics was already accepted by Carnot.", "Its continued validity as a primitive element of thermodynamical structure is due to the fact that it synthesizes an essential physical concept, as well as to its successful use in recent work to unify different constitutive theories.\"", "This traditional kind of presentation of the basis of thermodynamics includes ideas that may be summarized by the statement that heat transfer is purely due to spatial non-uniformity of temperature, and is by conduction and radiation, from hotter to colder bodies.", "It is sometimes proposed that this traditional kind of presentation necessarily rests on \"circular reasoning\"; against this proposal, there stands the rigorously logical mathematical development of the theory presented by Truesdell and Bharatha (1977).", "This alternative approach to the definition of quantity of energy transferred as heat differs in logical structure from that of Carathéodory, recounted just above.", "This alternative approach admits calorimetry as a primary or direct way to measure quantity of energy transferred as heat.", "It relies on temperature as one of its primitive concepts, and used in calorimetry.", "It is presupposed that enough processes exist physically to allow measurement of differences in internal energies.", "Such processes are not restricted to adiabatic transfers of energy as work.", "They include calorimetry, which is the commonest practical way of finding internal energy differences.", "The needed temperature can be either empirical or absolute thermodynamic.", "In contrast, the Carathéodory way recounted just above does not use calorimetry or temperature in its primary definition of quantity of energy transferred as heat.", "The Carathéodory way regards calorimetry only as a secondary or indirect way of measuring quantity of energy transferred as heat.", "As recounted in more detail just above, the Carathéodory way regards quantity of energy transferred as heat in a process as primarily or directly defined as a residual quantity.", "It is calculated from the difference of the internal energies of the initial and final states of the system, and from the actual work done by the system during the process.", "That internal energy difference is supposed to have been measured in advance through processes of purely adiabatic transfer of energy as work, processes that take the system between the initial and final states.", "By the Carathéodory way it is presupposed as known from experiment that there actually physically exist enough such adiabatic processes, so that there need be no recourse to calorimetry for measurement of quantity of energy transferred as heat.", "This presupposition is essential but is explicitly labeled neither as a law of thermodynamics nor as an axiom of the Carathéodory way.", "In fact, the actual physical existence of such adiabatic processes is indeed mostly supposition, and those supposed processes have in most cases not been actually verified empirically to exist.", "Referring to conduction, Partington writes: \"If a hot body is brought in conducting contact with a cold body, the temperature of the hot body falls and that of the cold body rises, and it is said that a \"quantity of heat\" has passed from the hot body to the cold body.", "\"\nReferring to radiation, Maxwell writes: \"In Radiation, the hotter body loses heat, and the colder body receives heat by means of a process occurring in some intervening medium which does not itself thereby become hot.\"\nMaxwell writes that convection as such \"is not a purely thermal phenomenon\".", "In thermodynamics, convection in general is regarded as transport of internal energy.", "If, however, the convection is enclosed and circulatory, then it may be regarded as an intermediary that transfers energy as heat between source and destination bodies, because it transfers only energy and not matter from the source to the destination body.", "In accordance with the first law for closed systems, energy transferred solely as heat leaves one body and enters another, changing the internal energies of each.", "Transfer, between bodies, of energy as work is a complementary way of changing internal energies.", "Though it is not logically rigorous from the viewpoint of strict physical concepts, a common form of words that expresses this is to say that heat and work are interconvertible.", "Cyclically operating engines that use only heat and work transfers have two thermal reservoirs, a hot and a cold one.", "They may be classified by the range of operating temperatures of the working body, relative to those reservoirs.", "In a heat engine, the working body is at all times colder than the hot reservoir and hotter than the cold reservoir.", "In a sense, it uses heat transfer to produce work.", "In a heat pump, the working body, at stages of the cycle, goes both hotter than the hot reservoir, and colder than the cold reservoir.", "In a sense, it uses work to produce heat transfer.", "In classical thermodynamics, a commonly considered model is the heat engine.", "It consists of four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir.", "A cyclic process leaves the working body in an unchanged state, and is envisaged as being repeated indefinitely often.", "Work transfers between the working body and the work reservoir are envisaged as reversible, and thus only one work reservoir is needed.", "But two thermal reservoirs are needed, because transfer of energy as heat is irreversible.", "A single cycle sees energy taken by the working body from the hot reservoir and sent to the two other reservoirs, the work reservoir and the cold reservoir.", "The hot reservoir always and only supplies energy and the cold reservoir always and only receives energy.", "The second law of thermodynamics requires that no cycle can occur in which no energy is received by the cold reservoir.", "Heat engines achieve higher efficiency when the ratio of the initial and final temperature is greater.", "Another commonly considered model is the heat pump or refrigerator.", "Again there are four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir.", "A single cycle starts with the working body colder than the cold reservoir, and then energy is taken in as heat by the working body from the cold reservoir.", "Then the work reservoir does work on the working body, adding more to its internal energy, making it hotter than the hot reservoir.", "The hot working body passes heat to the hot reservoir, but still remains hotter than the cold reservoir.", "Then, by allowing it to expand without passing heat to another body, the working body is made colder than the cold reservoir.", "It can now accept heat transfer from the cold reservoir to start another cycle.", "The device has transported energy from a colder to a hotter reservoir, but this is not regarded as by an inanimate agency; rather, it is regarded as by the harnessing of work .", "This is because work is supplied from the work reservoir, not just by a simple thermodynamic process, but by a cycle of thermodynamic operations and processes, which may be regarded as directed by an animate or harnessing agency.", "Accordingly, the cycle is still in accord with the second law of thermodynamics.", "The 'efficiency' of a heat pump (which exceeds unity) is best when the temperature difference between the hot and cold reservoirs is least.", "Functionally, such engines are used in two ways, distinguishing a target reservoir and a resource or surrounding reservoir.", "A heat pump transfers heat to the hot reservoir as the target from the resource or surrounding reservoir.", "A refrigerator transfers heat, from the cold reservoir as the target, to the resource or surrounding reservoir.", "The target reservoir may be regarded as leaking: when the target leaks heat to the surroundings, heat pumping is used; when the target leaks coldness to the surroundings, refrigeration is used.", "The engines harness work to overcome the leaks.", "According to Planck, there are three main conceptual approaches to heat.", "One is the microscopic or kinetic theory approach.", "The other two are macroscopic approaches.", "One is the approach through the law of conservation of energy taken as prior to thermodynamics, with a mechanical analysis of processes, for example in the work of Helmholtz.", "This mechanical view is taken in this article as currently customary for thermodynamic theory.", "The other macroscopic approach is the thermodynamic one, which admits heat as a primitive concept, which contributes, by scientific induction to knowledge of the law of conservation of energy.", "This view is widely taken as the practical one, quantity of heat being measured by calorimetry.", "Bailyn also distinguishes the two macroscopic approaches as the mechanical and the thermodynamic.", "The thermodynamic view was taken by the founders of thermodynamics in the nineteenth century.", "It regards quantity of energy transferred as heat as a primitive concept coherent with a primitive concept of temperature, measured primarily by calorimetry.", "A calorimeter is a body in the surroundings of the system, with its own temperature and internal energy; when it is connected to the system by a path for heat transfer, changes in it measure heat transfer.", "The mechanical view was pioneered by Helmholtz and developed and used in the twentieth century, largely through the influence of Max Born.", "It regards quantity of heat transferred as heat as a derived concept, defined for closed systems as quantity of heat transferred by mechanisms other than work transfer, the latter being regarded as primitive for thermodynamics, defined by macroscopic mechanics.", "According to Born, the transfer of internal energy between open systems that accompanies transfer of matter \"cannot be reduced to mechanics\".", "It follows that there is no well-founded definition of quantities of energy transferred as heat or as work associated with transfer of matter.", "Nevertheless, for the thermodynamical description of non-equilibrium processes, it is desired to consider the effect of a temperature gradient established by the surroundings across the system of interest when there is no physical barrier or wall between system and surroundings, that is to say, when they are open with respect to one another.", "The impossibility of a mechanical definition in terms of work for this circumstance does not alter the physical fact that a temperature gradient causes a diffusive flux of internal energy, a process that, in the thermodynamic view, might be proposed as a candidate concept for transfer of energy as heat.", "In this circumstance, it may be expected that there may also be active other drivers of diffusive flux of internal energy, such as gradient of chemical potential which drives transfer of matter, and gradient of electric potential which drives electric current and iontophoresis; such effects usually interact with diffusive flux of internal energy driven by temperature gradient, and such interactions are known as cross-effects.", "If cross-effects that result in diffusive transfer of internal energy were also labeled as heat transfers, they would sometimes violate the rule that pure heat transfer occurs only down a temperature gradient, never up one.", "They would also contradict the principle that all heat transfer is of one and the same kind, a principle founded on the idea of heat conduction between closed systems.", "One might to try to think narrowly of heat flux driven purely by temperature gradient as a conceptual component of diffusive internal energy flux, in the thermodynamic view, the concept resting specifically on careful calculations based on detailed knowledge of the processes and being indirectly assessed.", "In these circumstances, if perchance it happens that no transfer of matter is actualized, and there are no cross-effects, then the thermodynamic concept and the mechanical concept coincide, as if one were dealing with closed systems.", "But when there is transfer of matter, the exact laws by which temperature gradient drives diffusive flux of internal energy, rather than being exactly knowable, mostly need to be assumed, and in many cases are practically unverifiable.", "Consequently, when there is transfer of matter, the calculation of the pure 'heat flux' component of the diffusive flux of internal energy rests on practically unverifiable assumptions.", "This is a reason to think of heat as a specialized concept that relates primarily and precisely to closed systems, and applicable only in a very restricted way to open systems.", "In many writings in this context, the term \"heat flux\" is used when what is meant is therefore more accurately called diffusive flux of internal energy; such usage of the term \"heat flux\" is a residue of older and now obsolete language usage that allowed that a body may have a \"heat content\".", "In the kinetic theory, heat is explained in terms of the microscopic motions and interactions of constituent particles, such as electrons, atoms, and molecules.", "The immediate meaning of the kinetic energy of the constituent particles is not as heat.", "It is as a component of internal energy.", "In microscopic terms, heat is a transfer quantity, and is described by a transport theory, not as steadily localized kinetic energy of particles.", "Heat transfer arises from temperature gradients or differences, through the diffuse exchange of microscopic kinetic and potential particle energy, by particle collisions and other interactions.", "An early and vague expression of this was made by Francis Bacon.", "Precise and detailed versions of it were developed in the nineteenth century.", "In statistical mechanics, for a closed system (no transfer of matter), heat is the energy transfer associated with a disordered, microscopic action on the system, associated with jumps in occupation numbers of the energy levels of the system, without change in the values of the energy levels themselves.", "It is possible for macroscopic thermodynamic work to alter the occupation numbers without change in the values of the system energy levels themselves, but what distinguishes transfer as heat is that the transfer is entirely due to disordered, microscopic action, including radiative transfer.", "A mathematical definition can be formulated for small increments of quasi-static adiabatic work in terms of the statistical distribution of an ensemble of microstates.", "Quantity of heat transferred can be measured by calorimetry, or determined through calculations based on other quantities.", "Calorimetry is the empirical basis of the idea of quantity of heat transferred in a process.", "The transferred heat is measured by changes in a body of known properties, for example, temperature rise, change in volume or length, or phase change, such as melting of ice.", "A calculation of quantity of heat transferred can rely on a hypothetical quantity of energy transferred as adiabatic work and on the first law of thermodynamics.", "Such calculation is the primary approach of many theoretical studies of quantity of heat transferred.", "The discipline of heat transfer, typically considered an aspect of mechanical engineering and chemical engineering, deals with specific applied methods by which thermal energy in a system is generated, or converted, or transferred to another system.", "Although the definition of heat implicitly means the transfer of energy, the term \"heat transfer\" encompasses this traditional usage in many engineering disciplines and laymen language.", "\"Heat transfer\" is generally described as including the mechanisms of heat conduction, heat convection, thermal radiation, but may include mass transfer and heat in processes of phase changes.", "Convection may be described as the combined effects of conduction and fluid flow.", "From the thermodynamic point of view, heat flows into a fluid by diffusion to increase its energy, the fluid then transfers (advects) this increased internal energy (not heat) from one location to another, and this is then followed by a second thermal interaction which transfers heat to a second body or system, again by diffusion.", "This entire process is often regarded as an additional mechanism of heat transfer, although technically, \"heat transfer\" and thus heating and cooling occurs only on either end of such a conductive flow, but not as a result of flow.", "Thus, conduction can be said to \"transfer\" heat only as a net result of the process, but may not do so at every time within the complicated convective process.", "In an 1847 lecture entitled \"On Matter, Living Force, and Heat\", James Prescott Joule characterized the terms latent heat and sensible heat as components of heat each affecting distinct physical phenomena, namely the potential and kinetic energy of particles, respectively.", "He described latent energy as the energy possessed via a distancing of particles where attraction was over a greater distance, i.e. a form of potential energy, and the sensible heat as an energy involving the motion of particles, i.e. kinetic energy.", "Latent heat is the heat released or absorbed by a chemical substance or a thermodynamic system during a change of state that occurs without a change in temperature.", "Such a process may be a phase transition, such as the melting of ice or the boiling of water.", "Heat capacity is a measurable physical quantity equal to the ratio of the heat added to an object to the resulting temperature change.", "The \"molar heat capacity\" is the heat capacity per unit amount (SI unit: mole) of a pure substance, and the \"specific heat capacity\", often called simply \"specific heat\", is the heat capacity per unit mass of a material.", "Heat capacity is a physical property of a substance, which means that it depends on the state and properties of the substance under consideration.", "The specific heats of monatomic gases, such as helium, are nearly constant with temperature.", "Diatomic gases such as hydrogen display some temperature dependence, and triatomic gases (e.g., carbon dioxide) still more.", "Before the development of the laws of thermodynamics, heat was measured by changes in the states of the participating bodies.", "Some general rules, with important exceptions, can be stated as follows.", "In general, most bodies expand on heating.", "In this circumstance, heating a body at a constant volume increases the pressure it exerts on its constraining walls, while heating at a constant pressure increases its volume.", "Beyond this, most substances have three ordinarily recognized states of matter, solid, liquid, and gas.", "Some can also exist in a plasma.", "Many have further, more finely differentiated, states of matter, such as glass and liquid crystal.", "In many cases, at fixed temperature and pressure, a substance can exist in several distinct states of matter in what might be viewed as the same 'body'.", "For example, ice may float in a glass of water.", "Then the ice and the water are said to constitute two phases within the 'body'.", "Definite rules are known, telling how distinct phases may coexist in a 'body'.", "Mostly, at a fixed pressure, there is a definite temperature at which heating causes a solid to melt or evaporate, and a definite temperature at which heating causes a liquid to evaporate.", "In such cases, cooling has the reverse effects.", "All of these, the commonest cases, fit with a rule that heating can be measured by changes of state of a body.", "Such cases supply what are called \"thermometric bodies\", that allow the definition of empirical temperatures.", "Before 1848, all temperatures were defined in this way.", "There was thus a tight link, apparently logically determined, between heat and temperature, though they were recognized as conceptually thoroughly distinct, especially by Joseph Black in the later eighteenth century.", "There are important exceptions.", "They break the obviously apparent link between heat and temperature.", "They make it clear that empirical definitions of temperature are contingent on the peculiar properties of particular thermometric substances, and are thus precluded from the title 'absolute'.", "For example, water contracts on being heated near 277 K. It cannot be used as a thermometric substance near that temperature.", "Also, over a certain temperature range, ice contracts on heating.", "Moreover, many substances can exist in metastable states, such as with negative pressure, that survive only transiently and in very special conditions.", "Such facts, sometimes called 'anomalous', are some of the reasons for the thermodynamic definition of absolute temperature.", "In the early days of measurement of high temperatures, another factor was important, and used by Josiah Wedgwood in his pyrometer.", "The temperature reached in a process was estimated by the shrinkage of a sample of clay.", "The higher the temperature, the more the shrinkage.", "This was the only available more or less reliable method of measurement of temperatures above 1000 °C (1,832 °F).", "But such shrinkage is irreversible.", "The clay does not expand again on cooling.", "That is why it could be used for the measurement.", "But only once.", "It is not a thermometric material in the usual sense of the word.", "Nevertheless, the thermodynamic definition of absolute temperature does make essential use of the concept of heat, with proper circumspection.", "According to Denbigh (1981), the property of hotness is a concern of thermodynamics that should be defined without reference to the concept of heat.", "Consideration of hotness leads to the concept of empirical temperature.", "All physical systems are capable of heating or cooling others.", "With reference to hotness, the comparative terms hotter and colder are defined by the rule that heat flows from the hotter body to the colder.", "If a physical system is inhomogeneous or very rapidly or irregularly changing, for example by turbulence, it may be impossible to characterize it by a temperature, but still there can be transfer of energy as heat between it and another system.", "If a system has a physical state that is regular enough, and persists long enough to allow it to reach thermal equilibrium with a specified thermometer, then it has a temperature according to that thermometer.", "An empirical thermometer registers degree of hotness for such a system.", "Such a temperature is called empirical.", "For example, Truesdell writes about classical thermodynamics: \"At each time, the body is assigned a real number called the \"temperature\".", "This number is a measure of how hot the body is.", "\"\nPhysical systems that are too turbulent to have temperatures may still differ in hotness.", "A physical system that passes heat to another physical system is said to be the hotter of the two.", "More is required for the system to have a thermodynamic temperature.", "Its behavior must be so regular that its empirical temperature is the same for all suitably calibrated and scaled thermometers, and then its hotness is said to lie on the one-dimensional hotness manifold.", "This is part of the reason why heat is defined following Carathéodory and Born, solely as occurring other than by work or transfer of matter; temperature is advisedly and deliberately not mentioned in this now widely accepted definition.", "This is also the reason that the zeroth law of thermodynamics is stated explicitly.", "If three physical systems, \"A\", \"B\", and \"C\" are each not in their own states of internal thermodynamic equilibrium, it is possible that, with suitable physical connections being made between them, \"A\" can heat \"B\" and \"B\" can heat \"C\" and \"C\" can heat \"A\".", "In non-equilibrium situations, cycles of flow are possible.", "It is the special and uniquely distinguishing characteristic of internal thermodynamic equilibrium that this possibility is not open to thermodynamic systems (as distinguished amongst physical systems) which are in their own states of internal thermodynamic equilibrium; this is the reason why the zeroth law of thermodynamics needs explicit statement.", "That is to say, the relation 'is not colder than' between general non-equilibrium physical systems is not transitive, whereas, in contrast, the relation 'has no lower a temperature than' between thermodynamic systems in their own states of internal thermodynamic equilibrium is transitive.", "It follows from this that the relation 'is in thermal equilibrium with' is transitive, which is one way of stating the zeroth law.", "Just as temperature may be undefined for a sufficiently inhomogeneous system, so also may entropy be undefined for a system not in its own state of internal thermodynamic equilibrium.", "For example, 'the temperature of the solar system' is not a defined quantity.", "Likewise, 'the entropy of the solar system' is not defined in classical thermodynamics.", "It has not been possible to define non-equilibrium entropy, as a simple number for a whole system, in a clearly satisfactory way." ]

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[ "In thermodynamics, heat is energy in transfer to or from a thermodynamic system, by mechanisms other than thermodynamic work or transfer of matter (e.g. conduction, radiation, and friction).", "For the precise definition of heat, it is necessary that it occur by a path that does not include transfer of matter.", "As an amount of energy (being transferred), the SI unit of heat is the joule (J)." ]

[ "The mechanisms of energy transfer that define heat include conduction, through direct contact of immobile bodies, or through a wall or barrier that is impermeable to matter; or radiation between separated bodies; or friction due to isochoric mechanical or electrical or magnetic or gravitational work done by the surroundings on the system of interest, such as Joule heating due to an electric current driven through the system of interest by an external system, or through a magnetic stirrer.", "When there is a suitable path between two systems with different temperatures, heat transfer occurs necessarily, immediately, and spontaneously from the hotter to the colder system.", "Thermal conduction occurs by the stochastic (random) motion of microscopic particles (such as atoms or molecules).", "In contrast, thermodynamic work is defined by mechanisms that act macroscopically and directly on the system's whole-body state variables; for example, change of the system's volume through a piston's motion with externally measurable force; or change of the system's internal electric polarization through an externally measurable change in electric field.", "The definition of heat transfer does not require that the process be in any sense smooth.", "For example, a bolt of lightning may transfer heat to a body.", "Convective circulation allows one body to heat another, through an intermediate circulating fluid that carries energy from a boundary of one to a boundary of the other; the actual heat transfer is by conduction and radiation between the fluid and the respective bodies.", "Convective circulation, though spontaneous, does not necessarily and immediately occur simply because of some slight temperature difference; for it to occur in a given arrangement of systems, there is a threshold that must be crossed.", "Although heat flows spontaneously from a hotter body to a cooler one, it is possible to construct a heat pump which expends work to transfer energy from a colder body to a hotter body.", "In contrast, a heat engine reduces an existing temperature difference to supply work to another system.", "Another thermodynamic type of heat transfer device is an active heat spreader, which expends work to speed up transfer of energy to colder surroundings from a hotter body, for example a computer component.", "As a form of energy, heat has the unit joule (J) in the International System of Units (SI).", "However, in many applied fields in engineering the British thermal unit (BTU) and the calorie are often used.", "The standard unit for the rate of heat transferred is the watt (W), defined as one joule per second.", "The symbol for the total amount of energy transferred as heat was used by Rudolf Clausius in 1850:\n\"Let the amount of heat which must be imparted during the transition of the gas in a definite manner from any given state to another, in which its volume is \"v\" and its temperature \"t\", be called \"Q\"\"\nHeat released by a system into its surroundings is by convention a negative quantity (); when a system absorbs heat from its surroundings, it is positive ().", "Heat transfer rate, or heat flow per unit time, is denoted by formula_1.", "This should not be confused with a time derivative of a function of state (which can also be written with the dot notation) since heat is not a function of state.", "Heat flux is defined as rate of heat transfer per unit cross-sectional area (units watts per square metre).", "In 1856, Rudolf Clausius, referring to closed systems, in which transfers of matter do not occur, defined the \"second fundamental theorem\" (the second law of thermodynamics) in the mechanical theory of heat (thermodynamics): \"if two transformations which, without necessitating any other permanent change, can mutually replace one another, be called equivalent, then the generations of the quantity of heat \"Q\" from work at the temperature \"T\", has the \"equivalence-value\":\"\nformula_2\nIn 1865, he came to define the entropy symbolized by \"S\", such that, due to the supply of the amount of heat \"Q\" at temperature \"T\" the entropy of the system is increased by\nIn a transfer of energy as heat without work being done, there are changes of entropy in both the surroundings which lose heat and the system which gains it.", "The increase, , of entropy in the system may be considered to consist of two parts, an increment, that matches, or 'compensates', the change, , of entropy in the surroundings, and a further increment, that may be considered to be 'generated' or 'produced' in the system, and is said therefore to be 'uncompensated'.", "Thus\nformula_3\nThis may also be written\nformula_4\nThe total change of entropy in the system and surroundings is thus\nformula_5\nThis may also be written\nformula_6\nIt is then said that an amount of entropy has been transferred from the surroundings to the system.", "Because entropy is not a conserved quantity, this is an exception to the general way of speaking, in which an amount transferred is of a conserved quantity.", "From the second law of thermodynamics follows that in a spontaneous transfer of heat, in which the temperature of the system is different from that of the surroundings:\nformula_7\nFor purposes of mathematical analysis of transfers, one thinks of fictive processes that are called \"reversible\", with the temperature of the system being hardly less than that of the surroundings, and the transfer taking place at an imperceptibly slow rate.", "Following the definition above in formula (), for such a fictive reversible process, a quantity of transferred heat (an inexact differential) is analyzed as a quantity , with (an exact differential):\nformula_8\nThis equality is only valid for a fictive transfer in which there is no production of entropy, that is to say, in which there is no uncompensated entropy.", "If, in contrast, the process is natural, and can really occur, with irreversibility, then there is entropy production, with .", "The quantity was termed by Clausius the \"uncompensated heat\", though that does not accord with present-day terminology.", "Then one has\nformula_9\nThis leads to the statement\nformula_10\nwhich is the second law of thermodynamics for closed systems.", "In non-equilibrium thermodynamics that makes the approximation of assuming the hypothesis of local thermodynamic equilibrium, there is a special notation for this.", "The transfer of energy as heat is assumed to take place across an infinitesimal temperature difference, so that the system element and its surroundings have near enough the same temperature .", "Then one writes\nformula_11\nwhere by definition\nformula_12\nThe second law for a natural process asserts that\nformula_13", "For a closed system (a system from which no matter can enter or exit), one version of the first law of thermodynamics states that the change in internal energy of the system is equal to the amount of heat supplied to the system minus the amount of thermodynamic work done by system on its surroundings.", "The foregoing sign convention for work is used in the present article, but an alternate sign convention, followed by IUPAC, for work, is to consider the work performed on the system by its surroundings as positive.", "This is the convention adopted by many modern textbooks of physical chemistry, such as those by Peter Atkins and Ira Levine, but many textbooks on physics define work as work done by the system.", "formula_14\nThis formula can be re-written so as to express a definition of quantity of energy transferred as heat, based purely on the concept of adiabatic work, if it is supposed that is defined and measured solely by processes of adiabatic work:\nformula_15\nThe thermodynamic work done by the system is through mechanisms defined by its thermodynamic state variables, for example, its volume , not through variables that necessarily involve mechanisms in the surroundings.", "The latter are such as shaft work, and include isochoric work.", "The internal energy, , is a state function.", "In cyclical processes, such as the operation of a heat engine, state functions of the working substance return to their initial values upon completion of a cycle.", "The differential, or infinitesimal increment, for the internal energy in an infinitesimal process is an exact differential .", "The symbol for exact differentials is the lowercase letter .", "In contrast, neither of the infinitesimal increments nor in an infinitesimal process represents the change in a state function of the system.", "Thus, infinitesimal increments of heat and work are inexact differentials.", "The lowercase Greek letter delta, , is the symbol for inexact differentials.", "The integral of any inexact differential in a process where the system leaves and then returns to the same thermodynamic state does not necessarily equal zero.", "As recounted above, in the section headed \"heat and entropy\", the second law of thermodynamics observes that if heat is supplied to a system in a reversible process, the increment of heat and the temperature form the exact differential\nformula_16\nand that , the entropy of the working body, is a state function.", "Likewise, with a well-defined pressure, , behind a slowly moving (quasistatic) boundary, the work differential, , and the pressure, , combine to form the exact differential\nformula_17\nwith the volume of the system, which is a state variable.", "In general, for systems of uniform pressure and temperature without composition change,\nformula_18\nAssociated with this differential equation is the concept that the internal energy may be considered to be a function of its natural variables and .", "The internal energy representation of the fundamental thermodynamic relation is written as\nformula_19\nIf is constant\nformula_20\nand if is constant\nformula_21\nwith the enthalpy defined by\nformula_22\nThe enthalpy may be considered to be a function of its natural variables and .", "The enthalpy representation of the fundamental thermodynamic relation is written\nformula_23\nThe internal energy representation and the enthalpy representation are partial Legendre transforms of one another.", "They contain the same physical information, written in different ways.", "Like the internal energy, the enthalpy stated as a function of its natural variables is a thermodynamic potential and contains all thermodynamic information about a body.", "If a quantity of heat is added to a body while it does only expansion work on its surroundings, one has\nformula_24\nIf this is constrained to happen at constant pressure, i.e. with , the expansion work done by the body is given by ; recalling the first law of thermodynamics, one has\nformula_25\nConsequently, by substitution one has\nformula_26\nIn this scenario, the increase in enthalpy is equal to the quantity of heat added to the system.", "This is the basis of the determination of enthalpy changes in chemical reactions by calorimetry.", "Since many processes do take place at constant atmospheric pressure, the enthalpy is sometimes given the misleading name of 'heat content' or heat function, while it actually depends strongly on the energies of covalent bonds and intermolecular forces.", "In terms of the natural variables of the state function , this process of change of state from state 1 to state 2 can be expressed as\nformula_27\nIt is known that the temperature is identically stated by\nformula_28\nConsequently,\nformula_29\nIn this case, the integral specifies a quantity of heat transferred at constant pressure.", "As a common noun, English \"heat\" or \"warmth\" (just as French \"chaleur\", German \"Wärme\", Latin \"calor\", Greek θάλπος, etc.) refers to (the human perception of) either thermal energy or temperature.", "Speculation on thermal energy or \"heat\" as a separate form of matter has a long history, see caloric theory, phlogiston and fire (classical element).", "The modern understanding of thermal energy originates with Thompson's 1798 mechanical theory of heat (\"An Experimental Enquiry Concerning the Source of the Heat which is Excited by Friction\"), postulating a mechanical equivalent of heat.", "A collaboration between Nicolas Clément and Sadi Carnot (\"Reflections on the Motive Power of Fire\") in the 1820s had some related thinking along similar lines.", "In 1845, Joule published a paper entitled \"The Mechanical Equivalent of Heat\", in which he specified a numerical value for the amount of mechanical work required to \"produce a unit of heat\".", "The theory of classical thermodynamics matured in the 1850s to 1860s.", "John Tyndall's \"Heat Considered as Mode of Motion\" (1863) was instrumental in popularizing the idea of heat as motion to the English-speaking public.", "The theory was developed in academic publications in French, English and German.", "From an early time, the French technical term \"chaleur\" used by Carnot was taken as equivalent to the English \"heat\" and German \"Wärme\" (lit.", "\"warmth\", while the equivalent of \"heat\" would be German \"Hitze\").", "The process function was introduced by Rudolf Clausius in 1850.", "Clausius described it with the German compound \"Wärmemenge\", translated as \"amount of heat\".", "James Clerk Maxwell in his 1871 \"Theory of Heat\" outlines four stipulations for the definition of heat:\n\n\nThe process function is referred to as \"Wärmemenge\" by Clausius, or as \"amount of heat\" in translation.", "Use of \"heat\" as an abbreviated form of the specific concept of \"quantity of energy transferred as heat\" led to some terminological confusion by the early 20th century.", "The generic meaning of \"heat\", even in classical thermodynamics, is just \"thermal energy\".", "Since the 1920s, it has been recommended practice to use enthalpy to refer to the \"heat content at constant volume\", and to thermal energy when \"heat\" in the general sense is intended, while \"heat\" is reserved for the very specific context of the transfer of thermal energy between two systems.", "Leonard Benedict Loeb in his \"Kinetic Theory of Gases\" (1927) makes a point of using \"quantity of heat\"\nor \"heat–quantity\" when referring to :", "After the perfection of thermometry [...] the next great advance made in the field of heat was the definition of a term which is called the quantity of heat.", "[... after the abandonment of caloric theory,] It still remains to interpret this very definite concept, the quantity of heat, in terms of a theory ascribing all heat to the kinetics of gas molecules.", "A frequent definition of heat is based on the work of Carathéodory (1909), referring to processes in a closed system.", "The internal energy of a body in an arbitrary state can be determined by amounts of work adiabatically performed by the body on its surroundings when it starts from a reference state .", "Such work is assessed through quantities defined in the surroundings of the body.", "It is supposed that such work can be assessed accurately, without error due to friction in the surroundings; friction in the body is not excluded by this definition.", "The adiabatic performance of work is defined in terms of adiabatic walls, which allow transfer of energy as work, but no other transfer, of energy or matter.", "In particular they do not allow the passage of energy as heat.", "According to this definition, work performed adiabatically is in general accompanied by friction within the thermodynamic system or body.", "On the other hand, according to Carathéodory (1909), there also exist non-adiabatic, \"diathermal\" walls, which are postulated to be permeable only to heat.", "For the definition of quantity of energy transferred as heat, it is customarily envisaged that an arbitrary state of interest is reached from state by a process with two components, one adiabatic and the other not adiabatic.", "For convenience one may say that the adiabatic component was the sum of work done by the body through volume change through movement of the walls while the non-adiabatic wall was temporarily rendered adiabatic, and of isochoric adiabatic work.", "Then the non-adiabatic component is a process of energy transfer through the wall that passes only heat, newly made accessible for the purpose of this transfer, from the surroundings to the body.", "The change in internal energy to reach the state from the state is the difference of the two amounts of energy transferred.", "Although Carathéodory himself did not state such a definition, following his work it is customary in theoretical studies to define heat, , to the body from its surroundings, in the combined process of change to state from the state , as the change in internal energy, , minus the amount of work, , done by the body on its surrounds by the adiabatic process, so that .", "In this definition, for the sake of conceptual rigour, the quantity of energy transferred as heat is not specified directly in terms of the non-adiabatic process.", "It is defined through knowledge of precisely two variables, the change of internal energy and the amount of adiabatic work done, for the combined process of change from the reference state to the arbitrary state .", "It is important that this does not explicitly involve the amount of energy transferred in the non-adiabatic component of the combined process.", "It is assumed here that the amount of energy required to pass from state to state , the change of internal energy, is known, independently of the combined process, by a determination through a purely adiabatic process, like that for the determination of the internal energy of state above.", "The rigour that is prized in this definition is that there is one and only one kind of energy transfer admitted as fundamental: energy transferred as work.", "Energy transfer as heat is considered as a derived quantity.", "The uniqueness of work in this scheme is considered to guarantee rigor and purity of conception.", "The conceptual purity of this definition, based on the concept of energy transferred as work as an ideal notion, relies on the idea that some frictionless and otherwise non-dissipative processes of energy transfer can be realized in physical actuality.", "The second law of thermodynamics, on the other hand, assures us that such processes are not found in nature.", "Before the rigorous mathematical definition of heat based on Carathéodory's 1909 paper,\nhistorically, heat, temperature, and thermal equilibrium were presented in thermodynamics textbooks as jointly primitive notions.", "Carathéodory introduced his 1909 paper thus: \"The proposition that the discipline of thermodynamics can be justified without recourse to any hypothesis that cannot be verified experimentally must be regarded as one of the most noteworthy results of the research in thermodynamics that was accomplished during the last century.\"", "Referring to the \"point of view adopted by most authors who were active in the last fifty years\", Carathéodory wrote: \"There exists a physical quantity called heat that is not identical with the mechanical quantities (mass, force, pressure, etc.) and whose variations can be determined by calorimetric measurements.\"", "James Serrin introduces an account of the theory of thermodynamics thus: \"In the following section, we shall use the classical notions of \"heat\", \"work\", and \"hotness\" as primitive elements, ...", "That heat is an appropriate and natural primitive for thermodynamics was already accepted by Carnot.", "Its continued validity as a primitive element of thermodynamical structure is due to the fact that it synthesizes an essential physical concept, as well as to its successful use in recent work to unify different constitutive theories.\"", "This traditional kind of presentation of the basis of thermodynamics includes ideas that may be summarized by the statement that heat transfer is purely due to spatial non-uniformity of temperature, and is by conduction and radiation, from hotter to colder bodies.", "It is sometimes proposed that this traditional kind of presentation necessarily rests on \"circular reasoning\"; against this proposal, there stands the rigorously logical mathematical development of the theory presented by Truesdell and Bharatha (1977).", "This alternative approach to the definition of quantity of energy transferred as heat differs in logical structure from that of Carathéodory, recounted just above.", "This alternative approach admits calorimetry as a primary or direct way to measure quantity of energy transferred as heat.", "It relies on temperature as one of its primitive concepts, and used in calorimetry.", "It is presupposed that enough processes exist physically to allow measurement of differences in internal energies.", "Such processes are not restricted to adiabatic transfers of energy as work.", "They include calorimetry, which is the commonest practical way of finding internal energy differences.", "The needed temperature can be either empirical or absolute thermodynamic.", "In contrast, the Carathéodory way recounted just above does not use calorimetry or temperature in its primary definition of quantity of energy transferred as heat.", "The Carathéodory way regards calorimetry only as a secondary or indirect way of measuring quantity of energy transferred as heat.", "As recounted in more detail just above, the Carathéodory way regards quantity of energy transferred as heat in a process as primarily or directly defined as a residual quantity.", "It is calculated from the difference of the internal energies of the initial and final states of the system, and from the actual work done by the system during the process.", "That internal energy difference is supposed to have been measured in advance through processes of purely adiabatic transfer of energy as work, processes that take the system between the initial and final states.", "By the Carathéodory way it is presupposed as known from experiment that there actually physically exist enough such adiabatic processes, so that there need be no recourse to calorimetry for measurement of quantity of energy transferred as heat.", "This presupposition is essential but is explicitly labeled neither as a law of thermodynamics nor as an axiom of the Carathéodory way.", "In fact, the actual physical existence of such adiabatic processes is indeed mostly supposition, and those supposed processes have in most cases not been actually verified empirically to exist.", "Referring to conduction, Partington writes: \"If a hot body is brought in conducting contact with a cold body, the temperature of the hot body falls and that of the cold body rises, and it is said that a \"quantity of heat\" has passed from the hot body to the cold body.", "\"\nReferring to radiation, Maxwell writes: \"In Radiation, the hotter body loses heat, and the colder body receives heat by means of a process occurring in some intervening medium which does not itself thereby become hot.\"\nMaxwell writes that convection as such \"is not a purely thermal phenomenon\".", "In thermodynamics, convection in general is regarded as transport of internal energy.", "If, however, the convection is enclosed and circulatory, then it may be regarded as an intermediary that transfers energy as heat between source and destination bodies, because it transfers only energy and not matter from the source to the destination body.", "In accordance with the first law for closed systems, energy transferred solely as heat leaves one body and enters another, changing the internal energies of each.", "Transfer, between bodies, of energy as work is a complementary way of changing internal energies.", "Though it is not logically rigorous from the viewpoint of strict physical concepts, a common form of words that expresses this is to say that heat and work are interconvertible.", "Cyclically operating engines that use only heat and work transfers have two thermal reservoirs, a hot and a cold one.", "They may be classified by the range of operating temperatures of the working body, relative to those reservoirs.", "In a heat engine, the working body is at all times colder than the hot reservoir and hotter than the cold reservoir.", "In a sense, it uses heat transfer to produce work.", "In a heat pump, the working body, at stages of the cycle, goes both hotter than the hot reservoir, and colder than the cold reservoir.", "In a sense, it uses work to produce heat transfer.", "In classical thermodynamics, a commonly considered model is the heat engine.", "It consists of four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir.", "A cyclic process leaves the working body in an unchanged state, and is envisaged as being repeated indefinitely often.", "Work transfers between the working body and the work reservoir are envisaged as reversible, and thus only one work reservoir is needed.", "But two thermal reservoirs are needed, because transfer of energy as heat is irreversible.", "A single cycle sees energy taken by the working body from the hot reservoir and sent to the two other reservoirs, the work reservoir and the cold reservoir.", "The hot reservoir always and only supplies energy and the cold reservoir always and only receives energy.", "The second law of thermodynamics requires that no cycle can occur in which no energy is received by the cold reservoir.", "Heat engines achieve higher efficiency when the ratio of the initial and final temperature is greater.", "Another commonly considered model is the heat pump or refrigerator.", "Again there are four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir.", "A single cycle starts with the working body colder than the cold reservoir, and then energy is taken in as heat by the working body from the cold reservoir.", "Then the work reservoir does work on the working body, adding more to its internal energy, making it hotter than the hot reservoir.", "The hot working body passes heat to the hot reservoir, but still remains hotter than the cold reservoir.", "Then, by allowing it to expand without passing heat to another body, the working body is made colder than the cold reservoir.", "It can now accept heat transfer from the cold reservoir to start another cycle.", "The device has transported energy from a colder to a hotter reservoir, but this is not regarded as by an inanimate agency; rather, it is regarded as by the harnessing of work .", "This is because work is supplied from the work reservoir, not just by a simple thermodynamic process, but by a cycle of thermodynamic operations and processes, which may be regarded as directed by an animate or harnessing agency.", "Accordingly, the cycle is still in accord with the second law of thermodynamics.", "The 'efficiency' of a heat pump (which exceeds unity) is best when the temperature difference between the hot and cold reservoirs is least.", "Functionally, such engines are used in two ways, distinguishing a target reservoir and a resource or surrounding reservoir.", "A heat pump transfers heat to the hot reservoir as the target from the resource or surrounding reservoir.", "A refrigerator transfers heat, from the cold reservoir as the target, to the resource or surrounding reservoir.", "The target reservoir may be regarded as leaking: when the target leaks heat to the surroundings, heat pumping is used; when the target leaks coldness to the surroundings, refrigeration is used.", "The engines harness work to overcome the leaks.", "According to Planck, there are three main conceptual approaches to heat.", "One is the microscopic or kinetic theory approach.", "The other two are macroscopic approaches.", "One is the approach through the law of conservation of energy taken as prior to thermodynamics, with a mechanical analysis of processes, for example in the work of Helmholtz.", "This mechanical view is taken in this article as currently customary for thermodynamic theory.", "The other macroscopic approach is the thermodynamic one, which admits heat as a primitive concept, which contributes, by scientific induction to knowledge of the law of conservation of energy.", "This view is widely taken as the practical one, quantity of heat being measured by calorimetry.", "Bailyn also distinguishes the two macroscopic approaches as the mechanical and the thermodynamic.", "The thermodynamic view was taken by the founders of thermodynamics in the nineteenth century.", "It regards quantity of energy transferred as heat as a primitive concept coherent with a primitive concept of temperature, measured primarily by calorimetry.", "A calorimeter is a body in the surroundings of the system, with its own temperature and internal energy; when it is connected to the system by a path for heat transfer, changes in it measure heat transfer.", "The mechanical view was pioneered by Helmholtz and developed and used in the twentieth century, largely through the influence of Max Born.", "It regards quantity of heat transferred as heat as a derived concept, defined for closed systems as quantity of heat transferred by mechanisms other than work transfer, the latter being regarded as primitive for thermodynamics, defined by macroscopic mechanics.", "According to Born, the transfer of internal energy between open systems that accompanies transfer of matter \"cannot be reduced to mechanics\".", "It follows that there is no well-founded definition of quantities of energy transferred as heat or as work associated with transfer of matter.", "Nevertheless, for the thermodynamical description of non-equilibrium processes, it is desired to consider the effect of a temperature gradient established by the surroundings across the system of interest when there is no physical barrier or wall between system and surroundings, that is to say, when they are open with respect to one another.", "The impossibility of a mechanical definition in terms of work for this circumstance does not alter the physical fact that a temperature gradient causes a diffusive flux of internal energy, a process that, in the thermodynamic view, might be proposed as a candidate concept for transfer of energy as heat.", "In this circumstance, it may be expected that there may also be active other drivers of diffusive flux of internal energy, such as gradient of chemical potential which drives transfer of matter, and gradient of electric potential which drives electric current and iontophoresis; such effects usually interact with diffusive flux of internal energy driven by temperature gradient, and such interactions are known as cross-effects.", "If cross-effects that result in diffusive transfer of internal energy were also labeled as heat transfers, they would sometimes violate the rule that pure heat transfer occurs only down a temperature gradient, never up one.", "They would also contradict the principle that all heat transfer is of one and the same kind, a principle founded on the idea of heat conduction between closed systems.", "One might to try to think narrowly of heat flux driven purely by temperature gradient as a conceptual component of diffusive internal energy flux, in the thermodynamic view, the concept resting specifically on careful calculations based on detailed knowledge of the processes and being indirectly assessed.", "In these circumstances, if perchance it happens that no transfer of matter is actualized, and there are no cross-effects, then the thermodynamic concept and the mechanical concept coincide, as if one were dealing with closed systems.", "But when there is transfer of matter, the exact laws by which temperature gradient drives diffusive flux of internal energy, rather than being exactly knowable, mostly need to be assumed, and in many cases are practically unverifiable.", "Consequently, when there is transfer of matter, the calculation of the pure 'heat flux' component of the diffusive flux of internal energy rests on practically unverifiable assumptions.", "This is a reason to think of heat as a specialized concept that relates primarily and precisely to closed systems, and applicable only in a very restricted way to open systems.", "In many writings in this context, the term \"heat flux\" is used when what is meant is therefore more accurately called diffusive flux of internal energy; such usage of the term \"heat flux\" is a residue of older and now obsolete language usage that allowed that a body may have a \"heat content\".", "In the kinetic theory, heat is explained in terms of the microscopic motions and interactions of constituent particles, such as electrons, atoms, and molecules.", "The immediate meaning of the kinetic energy of the constituent particles is not as heat.", "It is as a component of internal energy.", "In microscopic terms, heat is a transfer quantity, and is described by a transport theory, not as steadily localized kinetic energy of particles.", "Heat transfer arises from temperature gradients or differences, through the diffuse exchange of microscopic kinetic and potential particle energy, by particle collisions and other interactions.", "An early and vague expression of this was made by Francis Bacon.", "Precise and detailed versions of it were developed in the nineteenth century.", "In statistical mechanics, for a closed system (no transfer of matter), heat is the energy transfer associated with a disordered, microscopic action on the system, associated with jumps in occupation numbers of the energy levels of the system, without change in the values of the energy levels themselves.", "It is possible for macroscopic thermodynamic work to alter the occupation numbers without change in the values of the system energy levels themselves, but what distinguishes transfer as heat is that the transfer is entirely due to disordered, microscopic action, including radiative transfer.", "A mathematical definition can be formulated for small increments of quasi-static adiabatic work in terms of the statistical distribution of an ensemble of microstates.", "Quantity of heat transferred can be measured by calorimetry, or determined through calculations based on other quantities.", "Calorimetry is the empirical basis of the idea of quantity of heat transferred in a process.", "The transferred heat is measured by changes in a body of known properties, for example, temperature rise, change in volume or length, or phase change, such as melting of ice.", "A calculation of quantity of heat transferred can rely on a hypothetical quantity of energy transferred as adiabatic work and on the first law of thermodynamics.", "Such calculation is the primary approach of many theoretical studies of quantity of heat transferred.", "The discipline of heat transfer, typically considered an aspect of mechanical engineering and chemical engineering, deals with specific applied methods by which thermal energy in a system is generated, or converted, or transferred to another system.", "Although the definition of heat implicitly means the transfer of energy, the term \"heat transfer\" encompasses this traditional usage in many engineering disciplines and laymen language.", "\"Heat transfer\" is generally described as including the mechanisms of heat conduction, heat convection, thermal radiation, but may include mass transfer and heat in processes of phase changes.", "Convection may be described as the combined effects of conduction and fluid flow.", "From the thermodynamic point of view, heat flows into a fluid by diffusion to increase its energy, the fluid then transfers (advects) this increased internal energy (not heat) from one location to another, and this is then followed by a second thermal interaction which transfers heat to a second body or system, again by diffusion.", "This entire process is often regarded as an additional mechanism of heat transfer, although technically, \"heat transfer\" and thus heating and cooling occurs only on either end of such a conductive flow, but not as a result of flow.", "Thus, conduction can be said to \"transfer\" heat only as a net result of the process, but may not do so at every time within the complicated convective process.", "In an 1847 lecture entitled \"On Matter, Living Force, and Heat\", James Prescott Joule characterized the terms latent heat and sensible heat as components of heat each affecting distinct physical phenomena, namely the potential and kinetic energy of particles, respectively.", "He described latent energy as the energy possessed via a distancing of particles where attraction was over a greater distance, i.e. a form of potential energy, and the sensible heat as an energy involving the motion of particles, i.e. kinetic energy.", "Latent heat is the heat released or absorbed by a chemical substance or a thermodynamic system during a change of state that occurs without a change in temperature.", "Such a process may be a phase transition, such as the melting of ice or the boiling of water.", "Heat capacity is a measurable physical quantity equal to the ratio of the heat added to an object to the resulting temperature change.", "The \"molar heat capacity\" is the heat capacity per unit amount (SI unit: mole) of a pure substance, and the \"specific heat capacity\", often called simply \"specific heat\", is the heat capacity per unit mass of a material.", "Heat capacity is a physical property of a substance, which means that it depends on the state and properties of the substance under consideration.", "The specific heats of monatomic gases, such as helium, are nearly constant with temperature.", "Diatomic gases such as hydrogen display some temperature dependence, and triatomic gases (e.g., carbon dioxide) still more.", "Before the development of the laws of thermodynamics, heat was measured by changes in the states of the participating bodies.", "Some general rules, with important exceptions, can be stated as follows.", "In general, most bodies expand on heating.", "In this circumstance, heating a body at a constant volume increases the pressure it exerts on its constraining walls, while heating at a constant pressure increases its volume.", "Beyond this, most substances have three ordinarily recognized states of matter, solid, liquid, and gas.", "Some can also exist in a plasma.", "Many have further, more finely differentiated, states of matter, such as glass and liquid crystal.", "In many cases, at fixed temperature and pressure, a substance can exist in several distinct states of matter in what might be viewed as the same 'body'.", "For example, ice may float in a glass of water.", "Then the ice and the water are said to constitute two phases within the 'body'.", "Definite rules are known, telling how distinct phases may coexist in a 'body'.", "Mostly, at a fixed pressure, there is a definite temperature at which heating causes a solid to melt or evaporate, and a definite temperature at which heating causes a liquid to evaporate.", "In such cases, cooling has the reverse effects.", "All of these, the commonest cases, fit with a rule that heating can be measured by changes of state of a body.", "Such cases supply what are called \"thermometric bodies\", that allow the definition of empirical temperatures.", "Before 1848, all temperatures were defined in this way.", "There was thus a tight link, apparently logically determined, between heat and temperature, though they were recognized as conceptually thoroughly distinct, especially by Joseph Black in the later eighteenth century.", "There are important exceptions.", "They break the obviously apparent link between heat and temperature.", "They make it clear that empirical definitions of temperature are contingent on the peculiar properties of particular thermometric substances, and are thus precluded from the title 'absolute'.", "For example, water contracts on being heated near 277 K. It cannot be used as a thermometric substance near that temperature.", "Also, over a certain temperature range, ice contracts on heating.", "Moreover, many substances can exist in metastable states, such as with negative pressure, that survive only transiently and in very special conditions.", "Such facts, sometimes called 'anomalous', are some of the reasons for the thermodynamic definition of absolute temperature.", "In the early days of measurement of high temperatures, another factor was important, and used by Josiah Wedgwood in his pyrometer.", "The temperature reached in a process was estimated by the shrinkage of a sample of clay.", "The higher the temperature, the more the shrinkage.", "This was the only available more or less reliable method of measurement of temperatures above 1000 °C (1,832 °F).", "But such shrinkage is irreversible.", "The clay does not expand again on cooling.", "That is why it could be used for the measurement.", "But only once.", "It is not a thermometric material in the usual sense of the word.", "Nevertheless, the thermodynamic definition of absolute temperature does make essential use of the concept of heat, with proper circumspection.", "According to Denbigh (1981), the property of hotness is a concern of thermodynamics that should be defined without reference to the concept of heat.", "Consideration of hotness leads to the concept of empirical temperature.", "All physical systems are capable of heating or cooling others.", "With reference to hotness, the comparative terms hotter and colder are defined by the rule that heat flows from the hotter body to the colder.", "If a physical system is inhomogeneous or very rapidly or irregularly changing, for example by turbulence, it may be impossible to characterize it by a temperature, but still there can be transfer of energy as heat between it and another system.", "If a system has a physical state that is regular enough, and persists long enough to allow it to reach thermal equilibrium with a specified thermometer, then it has a temperature according to that thermometer.", "An empirical thermometer registers degree of hotness for such a system.", "Such a temperature is called empirical.", "For example, Truesdell writes about classical thermodynamics: \"At each time, the body is assigned a real number called the \"temperature\".", "This number is a measure of how hot the body is.", "\"\nPhysical systems that are too turbulent to have temperatures may still differ in hotness.", "A physical system that passes heat to another physical system is said to be the hotter of the two.", "More is required for the system to have a thermodynamic temperature.", "Its behavior must be so regular that its empirical temperature is the same for all suitably calibrated and scaled thermometers, and then its hotness is said to lie on the one-dimensional hotness manifold.", "This is part of the reason why heat is defined following Carathéodory and Born, solely as occurring other than by work or transfer of matter; temperature is advisedly and deliberately not mentioned in this now widely accepted definition.", "This is also the reason that the zeroth law of thermodynamics is stated explicitly.", "If three physical systems, \"A\", \"B\", and \"C\" are each not in their own states of internal thermodynamic equilibrium, it is possible that, with suitable physical connections being made between them, \"A\" can heat \"B\" and \"B\" can heat \"C\" and \"C\" can heat \"A\".", "In non-equilibrium situations, cycles of flow are possible.", "It is the special and uniquely distinguishing characteristic of internal thermodynamic equilibrium that this possibility is not open to thermodynamic systems (as distinguished amongst physical systems) which are in their own states of internal thermodynamic equilibrium; this is the reason why the zeroth law of thermodynamics needs explicit statement.", "That is to say, the relation 'is not colder than' between general non-equilibrium physical systems is not transitive, whereas, in contrast, the relation 'has no lower a temperature than' between thermodynamic systems in their own states of internal thermodynamic equilibrium is transitive.", "It follows from this that the relation 'is in thermal equilibrium with' is transitive, which is one way of stating the zeroth law.", "Just as temperature may be undefined for a sufficiently inhomogeneous system, so also may entropy be undefined for a system not in its own state of internal thermodynamic equilibrium.", "For example, 'the temperature of the solar system' is not a defined quantity.", "Likewise, 'the entropy of the solar system' is not defined in classical thermodynamics.", "It has not been possible to define non-equilibrium entropy, as a simple number for a whole system, in a clearly satisfactory way." ]

[ 11, 12, 13, 14, 15, 16, 17 ]

[ "The conventional symbol used to represent the amount of heat transferred in a thermodynamic process is or \"\".", "As an amount of energy (being transferred), the SI unit of heat is the joule (J)." ]

[ "The mechanisms of energy transfer that define heat include conduction, through direct contact of immobile bodies, or through a wall or barrier that is impermeable to matter; or radiation between separated bodies; or friction due to isochoric mechanical or electrical or magnetic or gravitational work done by the surroundings on the system of interest, such as Joule heating due to an electric current driven through the system of interest by an external system, or through a magnetic stirrer.", "When there is a suitable path between two systems with different temperatures, heat transfer occurs necessarily, immediately, and spontaneously from the hotter to the colder system.", "Thermal conduction occurs by the stochastic (random) motion of microscopic particles (such as atoms or molecules).", "In contrast, thermodynamic work is defined by mechanisms that act macroscopically and directly on the system's whole-body state variables; for example, change of the system's volume through a piston's motion with externally measurable force; or change of the system's internal electric polarization through an externally measurable change in electric field.", "The definition of heat transfer does not require that the process be in any sense smooth.", "For example, a bolt of lightning may transfer heat to a body.", "Convective circulation allows one body to heat another, through an intermediate circulating fluid that carries energy from a boundary of one to a boundary of the other; the actual heat transfer is by conduction and radiation between the fluid and the respective bodies.", "Convective circulation, though spontaneous, does not necessarily and immediately occur simply because of some slight temperature difference; for it to occur in a given arrangement of systems, there is a threshold that must be crossed.", "Although heat flows spontaneously from a hotter body to a cooler one, it is possible to construct a heat pump which expends work to transfer energy from a colder body to a hotter body.", "In contrast, a heat engine reduces an existing temperature difference to supply work to another system.", "Another thermodynamic type of heat transfer device is an active heat spreader, which expends work to speed up transfer of energy to colder surroundings from a hotter body, for example a computer component.", "As a form of energy, heat has the unit joule (J) in the International System of Units (SI).", "However, in many applied fields in engineering the British thermal unit (BTU) and the calorie are often used.", "The standard unit for the rate of heat transferred is the watt (W), defined as one joule per second.", "The symbol for the total amount of energy transferred as heat was used by Rudolf Clausius in 1850:\n\"Let the amount of heat which must be imparted during the transition of the gas in a definite manner from any given state to another, in which its volume is \"v\" and its temperature \"t\", be called \"Q\"\"\nHeat released by a system into its surroundings is by convention a negative quantity (); when a system absorbs heat from its surroundings, it is positive ().", "Heat transfer rate, or heat flow per unit time, is denoted by formula_1.", "This should not be confused with a time derivative of a function of state (which can also be written with the dot notation) since heat is not a function of state.", "Heat flux is defined as rate of heat transfer per unit cross-sectional area (units watts per square metre).", "In 1856, Rudolf Clausius, referring to closed systems, in which transfers of matter do not occur, defined the \"second fundamental theorem\" (the second law of thermodynamics) in the mechanical theory of heat (thermodynamics): \"if two transformations which, without necessitating any other permanent change, can mutually replace one another, be called equivalent, then the generations of the quantity of heat \"Q\" from work at the temperature \"T\", has the \"equivalence-value\":\"\nformula_2\nIn 1865, he came to define the entropy symbolized by \"S\", such that, due to the supply of the amount of heat \"Q\" at temperature \"T\" the entropy of the system is increased by\nIn a transfer of energy as heat without work being done, there are changes of entropy in both the surroundings which lose heat and the system which gains it.", "The increase, , of entropy in the system may be considered to consist of two parts, an increment, that matches, or 'compensates', the change, , of entropy in the surroundings, and a further increment, that may be considered to be 'generated' or 'produced' in the system, and is said therefore to be 'uncompensated'.", "Thus\nformula_3\nThis may also be written\nformula_4\nThe total change of entropy in the system and surroundings is thus\nformula_5\nThis may also be written\nformula_6\nIt is then said that an amount of entropy has been transferred from the surroundings to the system.", "Because entropy is not a conserved quantity, this is an exception to the general way of speaking, in which an amount transferred is of a conserved quantity.", "From the second law of thermodynamics follows that in a spontaneous transfer of heat, in which the temperature of the system is different from that of the surroundings:\nformula_7\nFor purposes of mathematical analysis of transfers, one thinks of fictive processes that are called \"reversible\", with the temperature of the system being hardly less than that of the surroundings, and the transfer taking place at an imperceptibly slow rate.", "Following the definition above in formula (), for such a fictive reversible process, a quantity of transferred heat (an inexact differential) is analyzed as a quantity , with (an exact differential):\nformula_8\nThis equality is only valid for a fictive transfer in which there is no production of entropy, that is to say, in which there is no uncompensated entropy.", "If, in contrast, the process is natural, and can really occur, with irreversibility, then there is entropy production, with .", "The quantity was termed by Clausius the \"uncompensated heat\", though that does not accord with present-day terminology.", "Then one has\nformula_9\nThis leads to the statement\nformula_10\nwhich is the second law of thermodynamics for closed systems.", "In non-equilibrium thermodynamics that makes the approximation of assuming the hypothesis of local thermodynamic equilibrium, there is a special notation for this.", "The transfer of energy as heat is assumed to take place across an infinitesimal temperature difference, so that the system element and its surroundings have near enough the same temperature .", "Then one writes\nformula_11\nwhere by definition\nformula_12\nThe second law for a natural process asserts that\nformula_13", "For a closed system (a system from which no matter can enter or exit), one version of the first law of thermodynamics states that the change in internal energy of the system is equal to the amount of heat supplied to the system minus the amount of thermodynamic work done by system on its surroundings.", "The foregoing sign convention for work is used in the present article, but an alternate sign convention, followed by IUPAC, for work, is to consider the work performed on the system by its surroundings as positive.", "This is the convention adopted by many modern textbooks of physical chemistry, such as those by Peter Atkins and Ira Levine, but many textbooks on physics define work as work done by the system.", "formula_14\nThis formula can be re-written so as to express a definition of quantity of energy transferred as heat, based purely on the concept of adiabatic work, if it is supposed that is defined and measured solely by processes of adiabatic work:\nformula_15\nThe thermodynamic work done by the system is through mechanisms defined by its thermodynamic state variables, for example, its volume , not through variables that necessarily involve mechanisms in the surroundings.", "The latter are such as shaft work, and include isochoric work.", "The internal energy, , is a state function.", "In cyclical processes, such as the operation of a heat engine, state functions of the working substance return to their initial values upon completion of a cycle.", "The differential, or infinitesimal increment, for the internal energy in an infinitesimal process is an exact differential .", "The symbol for exact differentials is the lowercase letter .", "In contrast, neither of the infinitesimal increments nor in an infinitesimal process represents the change in a state function of the system.", "Thus, infinitesimal increments of heat and work are inexact differentials.", "The lowercase Greek letter delta, , is the symbol for inexact differentials.", "The integral of any inexact differential in a process where the system leaves and then returns to the same thermodynamic state does not necessarily equal zero.", "As recounted above, in the section headed \"heat and entropy\", the second law of thermodynamics observes that if heat is supplied to a system in a reversible process, the increment of heat and the temperature form the exact differential\nformula_16\nand that , the entropy of the working body, is a state function.", "Likewise, with a well-defined pressure, , behind a slowly moving (quasistatic) boundary, the work differential, , and the pressure, , combine to form the exact differential\nformula_17\nwith the volume of the system, which is a state variable.", "In general, for systems of uniform pressure and temperature without composition change,\nformula_18\nAssociated with this differential equation is the concept that the internal energy may be considered to be a function of its natural variables and .", "The internal energy representation of the fundamental thermodynamic relation is written as\nformula_19\nIf is constant\nformula_20\nand if is constant\nformula_21\nwith the enthalpy defined by\nformula_22\nThe enthalpy may be considered to be a function of its natural variables and .", "The enthalpy representation of the fundamental thermodynamic relation is written\nformula_23\nThe internal energy representation and the enthalpy representation are partial Legendre transforms of one another.", "They contain the same physical information, written in different ways.", "Like the internal energy, the enthalpy stated as a function of its natural variables is a thermodynamic potential and contains all thermodynamic information about a body.", "If a quantity of heat is added to a body while it does only expansion work on its surroundings, one has\nformula_24\nIf this is constrained to happen at constant pressure, i.e. with , the expansion work done by the body is given by ; recalling the first law of thermodynamics, one has\nformula_25\nConsequently, by substitution one has\nformula_26\nIn this scenario, the increase in enthalpy is equal to the quantity of heat added to the system.", "This is the basis of the determination of enthalpy changes in chemical reactions by calorimetry.", "Since many processes do take place at constant atmospheric pressure, the enthalpy is sometimes given the misleading name of 'heat content' or heat function, while it actually depends strongly on the energies of covalent bonds and intermolecular forces.", "In terms of the natural variables of the state function , this process of change of state from state 1 to state 2 can be expressed as\nformula_27\nIt is known that the temperature is identically stated by\nformula_28\nConsequently,\nformula_29\nIn this case, the integral specifies a quantity of heat transferred at constant pressure.", "As a common noun, English \"heat\" or \"warmth\" (just as French \"chaleur\", German \"Wärme\", Latin \"calor\", Greek θάλπος, etc.) refers to (the human perception of) either thermal energy or temperature.", "Speculation on thermal energy or \"heat\" as a separate form of matter has a long history, see caloric theory, phlogiston and fire (classical element).", "The modern understanding of thermal energy originates with Thompson's 1798 mechanical theory of heat (\"An Experimental Enquiry Concerning the Source of the Heat which is Excited by Friction\"), postulating a mechanical equivalent of heat.", "A collaboration between Nicolas Clément and Sadi Carnot (\"Reflections on the Motive Power of Fire\") in the 1820s had some related thinking along similar lines.", "In 1845, Joule published a paper entitled \"The Mechanical Equivalent of Heat\", in which he specified a numerical value for the amount of mechanical work required to \"produce a unit of heat\".", "The theory of classical thermodynamics matured in the 1850s to 1860s.", "John Tyndall's \"Heat Considered as Mode of Motion\" (1863) was instrumental in popularizing the idea of heat as motion to the English-speaking public.", "The theory was developed in academic publications in French, English and German.", "From an early time, the French technical term \"chaleur\" used by Carnot was taken as equivalent to the English \"heat\" and German \"Wärme\" (lit.", "\"warmth\", while the equivalent of \"heat\" would be German \"Hitze\").", "The process function was introduced by Rudolf Clausius in 1850.", "Clausius described it with the German compound \"Wärmemenge\", translated as \"amount of heat\".", "James Clerk Maxwell in his 1871 \"Theory of Heat\" outlines four stipulations for the definition of heat:\n\n\nThe process function is referred to as \"Wärmemenge\" by Clausius, or as \"amount of heat\" in translation.", "Use of \"heat\" as an abbreviated form of the specific concept of \"quantity of energy transferred as heat\" led to some terminological confusion by the early 20th century.", "The generic meaning of \"heat\", even in classical thermodynamics, is just \"thermal energy\".", "Since the 1920s, it has been recommended practice to use enthalpy to refer to the \"heat content at constant volume\", and to thermal energy when \"heat\" in the general sense is intended, while \"heat\" is reserved for the very specific context of the transfer of thermal energy between two systems.", "Leonard Benedict Loeb in his \"Kinetic Theory of Gases\" (1927) makes a point of using \"quantity of heat\"\nor \"heat–quantity\" when referring to :", "After the perfection of thermometry [...] the next great advance made in the field of heat was the definition of a term which is called the quantity of heat.", "[... after the abandonment of caloric theory,] It still remains to interpret this very definite concept, the quantity of heat, in terms of a theory ascribing all heat to the kinetics of gas molecules.", "A frequent definition of heat is based on the work of Carathéodory (1909), referring to processes in a closed system.", "The internal energy of a body in an arbitrary state can be determined by amounts of work adiabatically performed by the body on its surroundings when it starts from a reference state .", "Such work is assessed through quantities defined in the surroundings of the body.", "It is supposed that such work can be assessed accurately, without error due to friction in the surroundings; friction in the body is not excluded by this definition.", "The adiabatic performance of work is defined in terms of adiabatic walls, which allow transfer of energy as work, but no other transfer, of energy or matter.", "In particular they do not allow the passage of energy as heat.", "According to this definition, work performed adiabatically is in general accompanied by friction within the thermodynamic system or body.", "On the other hand, according to Carathéodory (1909), there also exist non-adiabatic, \"diathermal\" walls, which are postulated to be permeable only to heat.", "For the definition of quantity of energy transferred as heat, it is customarily envisaged that an arbitrary state of interest is reached from state by a process with two components, one adiabatic and the other not adiabatic.", "For convenience one may say that the adiabatic component was the sum of work done by the body through volume change through movement of the walls while the non-adiabatic wall was temporarily rendered adiabatic, and of isochoric adiabatic work.", "Then the non-adiabatic component is a process of energy transfer through the wall that passes only heat, newly made accessible for the purpose of this transfer, from the surroundings to the body.", "The change in internal energy to reach the state from the state is the difference of the two amounts of energy transferred.", "Although Carathéodory himself did not state such a definition, following his work it is customary in theoretical studies to define heat, , to the body from its surroundings, in the combined process of change to state from the state , as the change in internal energy, , minus the amount of work, , done by the body on its surrounds by the adiabatic process, so that .", "In this definition, for the sake of conceptual rigour, the quantity of energy transferred as heat is not specified directly in terms of the non-adiabatic process.", "It is defined through knowledge of precisely two variables, the change of internal energy and the amount of adiabatic work done, for the combined process of change from the reference state to the arbitrary state .", "It is important that this does not explicitly involve the amount of energy transferred in the non-adiabatic component of the combined process.", "It is assumed here that the amount of energy required to pass from state to state , the change of internal energy, is known, independently of the combined process, by a determination through a purely adiabatic process, like that for the determination of the internal energy of state above.", "The rigour that is prized in this definition is that there is one and only one kind of energy transfer admitted as fundamental: energy transferred as work.", "Energy transfer as heat is considered as a derived quantity.", "The uniqueness of work in this scheme is considered to guarantee rigor and purity of conception.", "The conceptual purity of this definition, based on the concept of energy transferred as work as an ideal notion, relies on the idea that some frictionless and otherwise non-dissipative processes of energy transfer can be realized in physical actuality.", "The second law of thermodynamics, on the other hand, assures us that such processes are not found in nature.", "Before the rigorous mathematical definition of heat based on Carathéodory's 1909 paper,\nhistorically, heat, temperature, and thermal equilibrium were presented in thermodynamics textbooks as jointly primitive notions.", "Carathéodory introduced his 1909 paper thus: \"The proposition that the discipline of thermodynamics can be justified without recourse to any hypothesis that cannot be verified experimentally must be regarded as one of the most noteworthy results of the research in thermodynamics that was accomplished during the last century.\"", "Referring to the \"point of view adopted by most authors who were active in the last fifty years\", Carathéodory wrote: \"There exists a physical quantity called heat that is not identical with the mechanical quantities (mass, force, pressure, etc.) and whose variations can be determined by calorimetric measurements.\"", "James Serrin introduces an account of the theory of thermodynamics thus: \"In the following section, we shall use the classical notions of \"heat\", \"work\", and \"hotness\" as primitive elements, ...", "That heat is an appropriate and natural primitive for thermodynamics was already accepted by Carnot.", "Its continued validity as a primitive element of thermodynamical structure is due to the fact that it synthesizes an essential physical concept, as well as to its successful use in recent work to unify different constitutive theories.\"", "This traditional kind of presentation of the basis of thermodynamics includes ideas that may be summarized by the statement that heat transfer is purely due to spatial non-uniformity of temperature, and is by conduction and radiation, from hotter to colder bodies.", "It is sometimes proposed that this traditional kind of presentation necessarily rests on \"circular reasoning\"; against this proposal, there stands the rigorously logical mathematical development of the theory presented by Truesdell and Bharatha (1977).", "This alternative approach to the definition of quantity of energy transferred as heat differs in logical structure from that of Carathéodory, recounted just above.", "This alternative approach admits calorimetry as a primary or direct way to measure quantity of energy transferred as heat.", "It relies on temperature as one of its primitive concepts, and used in calorimetry.", "It is presupposed that enough processes exist physically to allow measurement of differences in internal energies.", "Such processes are not restricted to adiabatic transfers of energy as work.", "They include calorimetry, which is the commonest practical way of finding internal energy differences.", "The needed temperature can be either empirical or absolute thermodynamic.", "In contrast, the Carathéodory way recounted just above does not use calorimetry or temperature in its primary definition of quantity of energy transferred as heat.", "The Carathéodory way regards calorimetry only as a secondary or indirect way of measuring quantity of energy transferred as heat.", "As recounted in more detail just above, the Carathéodory way regards quantity of energy transferred as heat in a process as primarily or directly defined as a residual quantity.", "It is calculated from the difference of the internal energies of the initial and final states of the system, and from the actual work done by the system during the process.", "That internal energy difference is supposed to have been measured in advance through processes of purely adiabatic transfer of energy as work, processes that take the system between the initial and final states.", "By the Carathéodory way it is presupposed as known from experiment that there actually physically exist enough such adiabatic processes, so that there need be no recourse to calorimetry for measurement of quantity of energy transferred as heat.", "This presupposition is essential but is explicitly labeled neither as a law of thermodynamics nor as an axiom of the Carathéodory way.", "In fact, the actual physical existence of such adiabatic processes is indeed mostly supposition, and those supposed processes have in most cases not been actually verified empirically to exist.", "Referring to conduction, Partington writes: \"If a hot body is brought in conducting contact with a cold body, the temperature of the hot body falls and that of the cold body rises, and it is said that a \"quantity of heat\" has passed from the hot body to the cold body.", "\"\nReferring to radiation, Maxwell writes: \"In Radiation, the hotter body loses heat, and the colder body receives heat by means of a process occurring in some intervening medium which does not itself thereby become hot.\"\nMaxwell writes that convection as such \"is not a purely thermal phenomenon\".", "In thermodynamics, convection in general is regarded as transport of internal energy.", "If, however, the convection is enclosed and circulatory, then it may be regarded as an intermediary that transfers energy as heat between source and destination bodies, because it transfers only energy and not matter from the source to the destination body.", "In accordance with the first law for closed systems, energy transferred solely as heat leaves one body and enters another, changing the internal energies of each.", "Transfer, between bodies, of energy as work is a complementary way of changing internal energies.", "Though it is not logically rigorous from the viewpoint of strict physical concepts, a common form of words that expresses this is to say that heat and work are interconvertible.", "Cyclically operating engines that use only heat and work transfers have two thermal reservoirs, a hot and a cold one.", "They may be classified by the range of operating temperatures of the working body, relative to those reservoirs.", "In a heat engine, the working body is at all times colder than the hot reservoir and hotter than the cold reservoir.", "In a sense, it uses heat transfer to produce work.", "In a heat pump, the working body, at stages of the cycle, goes both hotter than the hot reservoir, and colder than the cold reservoir.", "In a sense, it uses work to produce heat transfer.", "In classical thermodynamics, a commonly considered model is the heat engine.", "It consists of four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir.", "A cyclic process leaves the working body in an unchanged state, and is envisaged as being repeated indefinitely often.", "Work transfers between the working body and the work reservoir are envisaged as reversible, and thus only one work reservoir is needed.", "But two thermal reservoirs are needed, because transfer of energy as heat is irreversible.", "A single cycle sees energy taken by the working body from the hot reservoir and sent to the two other reservoirs, the work reservoir and the cold reservoir.", "The hot reservoir always and only supplies energy and the cold reservoir always and only receives energy.", "The second law of thermodynamics requires that no cycle can occur in which no energy is received by the cold reservoir.", "Heat engines achieve higher efficiency when the ratio of the initial and final temperature is greater.", "Another commonly considered model is the heat pump or refrigerator.", "Again there are four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir.", "A single cycle starts with the working body colder than the cold reservoir, and then energy is taken in as heat by the working body from the cold reservoir.", "Then the work reservoir does work on the working body, adding more to its internal energy, making it hotter than the hot reservoir.", "The hot working body passes heat to the hot reservoir, but still remains hotter than the cold reservoir.", "Then, by allowing it to expand without passing heat to another body, the working body is made colder than the cold reservoir.", "It can now accept heat transfer from the cold reservoir to start another cycle.", "The device has transported energy from a colder to a hotter reservoir, but this is not regarded as by an inanimate agency; rather, it is regarded as by the harnessing of work .", "This is because work is supplied from the work reservoir, not just by a simple thermodynamic process, but by a cycle of thermodynamic operations and processes, which may be regarded as directed by an animate or harnessing agency.", "Accordingly, the cycle is still in accord with the second law of thermodynamics.", "The 'efficiency' of a heat pump (which exceeds unity) is best when the temperature difference between the hot and cold reservoirs is least.", "Functionally, such engines are used in two ways, distinguishing a target reservoir and a resource or surrounding reservoir.", "A heat pump transfers heat to the hot reservoir as the target from the resource or surrounding reservoir.", "A refrigerator transfers heat, from the cold reservoir as the target, to the resource or surrounding reservoir.", "The target reservoir may be regarded as leaking: when the target leaks heat to the surroundings, heat pumping is used; when the target leaks coldness to the surroundings, refrigeration is used.", "The engines harness work to overcome the leaks.", "According to Planck, there are three main conceptual approaches to heat.", "One is the microscopic or kinetic theory approach.", "The other two are macroscopic approaches.", "One is the approach through the law of conservation of energy taken as prior to thermodynamics, with a mechanical analysis of processes, for example in the work of Helmholtz.", "This mechanical view is taken in this article as currently customary for thermodynamic theory.", "The other macroscopic approach is the thermodynamic one, which admits heat as a primitive concept, which contributes, by scientific induction to knowledge of the law of conservation of energy.", "This view is widely taken as the practical one, quantity of heat being measured by calorimetry.", "Bailyn also distinguishes the two macroscopic approaches as the mechanical and the thermodynamic.", "The thermodynamic view was taken by the founders of thermodynamics in the nineteenth century.", "It regards quantity of energy transferred as heat as a primitive concept coherent with a primitive concept of temperature, measured primarily by calorimetry.", "A calorimeter is a body in the surroundings of the system, with its own temperature and internal energy; when it is connected to the system by a path for heat transfer, changes in it measure heat transfer.", "The mechanical view was pioneered by Helmholtz and developed and used in the twentieth century, largely through the influence of Max Born.", "It regards quantity of heat transferred as heat as a derived concept, defined for closed systems as quantity of heat transferred by mechanisms other than work transfer, the latter being regarded as primitive for thermodynamics, defined by macroscopic mechanics.", "According to Born, the transfer of internal energy between open systems that accompanies transfer of matter \"cannot be reduced to mechanics\".", "It follows that there is no well-founded definition of quantities of energy transferred as heat or as work associated with transfer of matter.", "Nevertheless, for the thermodynamical description of non-equilibrium processes, it is desired to consider the effect of a temperature gradient established by the surroundings across the system of interest when there is no physical barrier or wall between system and surroundings, that is to say, when they are open with respect to one another.", "The impossibility of a mechanical definition in terms of work for this circumstance does not alter the physical fact that a temperature gradient causes a diffusive flux of internal energy, a process that, in the thermodynamic view, might be proposed as a candidate concept for transfer of energy as heat.", "In this circumstance, it may be expected that there may also be active other drivers of diffusive flux of internal energy, such as gradient of chemical potential which drives transfer of matter, and gradient of electric potential which drives electric current and iontophoresis; such effects usually interact with diffusive flux of internal energy driven by temperature gradient, and such interactions are known as cross-effects.", "If cross-effects that result in diffusive transfer of internal energy were also labeled as heat transfers, they would sometimes violate the rule that pure heat transfer occurs only down a temperature gradient, never up one.", "They would also contradict the principle that all heat transfer is of one and the same kind, a principle founded on the idea of heat conduction between closed systems.", "One might to try to think narrowly of heat flux driven purely by temperature gradient as a conceptual component of diffusive internal energy flux, in the thermodynamic view, the concept resting specifically on careful calculations based on detailed knowledge of the processes and being indirectly assessed.", "In these circumstances, if perchance it happens that no transfer of matter is actualized, and there are no cross-effects, then the thermodynamic concept and the mechanical concept coincide, as if one were dealing with closed systems.", "But when there is transfer of matter, the exact laws by which temperature gradient drives diffusive flux of internal energy, rather than being exactly knowable, mostly need to be assumed, and in many cases are practically unverifiable.", "Consequently, when there is transfer of matter, the calculation of the pure 'heat flux' component of the diffusive flux of internal energy rests on practically unverifiable assumptions.", "This is a reason to think of heat as a specialized concept that relates primarily and precisely to closed systems, and applicable only in a very restricted way to open systems.", "In many writings in this context, the term \"heat flux\" is used when what is meant is therefore more accurately called diffusive flux of internal energy; such usage of the term \"heat flux\" is a residue of older and now obsolete language usage that allowed that a body may have a \"heat content\".", "In the kinetic theory, heat is explained in terms of the microscopic motions and interactions of constituent particles, such as electrons, atoms, and molecules.", "The immediate meaning of the kinetic energy of the constituent particles is not as heat.", "It is as a component of internal energy.", "In microscopic terms, heat is a transfer quantity, and is described by a transport theory, not as steadily localized kinetic energy of particles.", "Heat transfer arises from temperature gradients or differences, through the diffuse exchange of microscopic kinetic and potential particle energy, by particle collisions and other interactions.", "An early and vague expression of this was made by Francis Bacon.", "Precise and detailed versions of it were developed in the nineteenth century.", "In statistical mechanics, for a closed system (no transfer of matter), heat is the energy transfer associated with a disordered, microscopic action on the system, associated with jumps in occupation numbers of the energy levels of the system, without change in the values of the energy levels themselves.", "It is possible for macroscopic thermodynamic work to alter the occupation numbers without change in the values of the system energy levels themselves, but what distinguishes transfer as heat is that the transfer is entirely due to disordered, microscopic action, including radiative transfer.", "A mathematical definition can be formulated for small increments of quasi-static adiabatic work in terms of the statistical distribution of an ensemble of microstates.", "Quantity of heat transferred can be measured by calorimetry, or determined through calculations based on other quantities.", "Calorimetry is the empirical basis of the idea of quantity of heat transferred in a process.", "The transferred heat is measured by changes in a body of known properties, for example, temperature rise, change in volume or length, or phase change, such as melting of ice.", "A calculation of quantity of heat transferred can rely on a hypothetical quantity of energy transferred as adiabatic work and on the first law of thermodynamics.", "Such calculation is the primary approach of many theoretical studies of quantity of heat transferred.", "The discipline of heat transfer, typically considered an aspect of mechanical engineering and chemical engineering, deals with specific applied methods by which thermal energy in a system is generated, or converted, or transferred to another system.", "Although the definition of heat implicitly means the transfer of energy, the term \"heat transfer\" encompasses this traditional usage in many engineering disciplines and laymen language.", "\"Heat transfer\" is generally described as including the mechanisms of heat conduction, heat convection, thermal radiation, but may include mass transfer and heat in processes of phase changes.", "Convection may be described as the combined effects of conduction and fluid flow.", "From the thermodynamic point of view, heat flows into a fluid by diffusion to increase its energy, the fluid then transfers (advects) this increased internal energy (not heat) from one location to another, and this is then followed by a second thermal interaction which transfers heat to a second body or system, again by diffusion.", "This entire process is often regarded as an additional mechanism of heat transfer, although technically, \"heat transfer\" and thus heating and cooling occurs only on either end of such a conductive flow, but not as a result of flow.", "Thus, conduction can be said to \"transfer\" heat only as a net result of the process, but may not do so at every time within the complicated convective process.", "In an 1847 lecture entitled \"On Matter, Living Force, and Heat\", James Prescott Joule characterized the terms latent heat and sensible heat as components of heat each affecting distinct physical phenomena, namely the potential and kinetic energy of particles, respectively.", "He described latent energy as the energy possessed via a distancing of particles where attraction was over a greater distance, i.e. a form of potential energy, and the sensible heat as an energy involving the motion of particles, i.e. kinetic energy.", "Latent heat is the heat released or absorbed by a chemical substance or a thermodynamic system during a change of state that occurs without a change in temperature.", "Such a process may be a phase transition, such as the melting of ice or the boiling of water.", "Heat capacity is a measurable physical quantity equal to the ratio of the heat added to an object to the resulting temperature change.", "The \"molar heat capacity\" is the heat capacity per unit amount (SI unit: mole) of a pure substance, and the \"specific heat capacity\", often called simply \"specific heat\", is the heat capacity per unit mass of a material.", "Heat capacity is a physical property of a substance, which means that it depends on the state and properties of the substance under consideration.", "The specific heats of monatomic gases, such as helium, are nearly constant with temperature.", "Diatomic gases such as hydrogen display some temperature dependence, and triatomic gases (e.g., carbon dioxide) still more.", "Before the development of the laws of thermodynamics, heat was measured by changes in the states of the participating bodies.", "Some general rules, with important exceptions, can be stated as follows.", "In general, most bodies expand on heating.", "In this circumstance, heating a body at a constant volume increases the pressure it exerts on its constraining walls, while heating at a constant pressure increases its volume.", "Beyond this, most substances have three ordinarily recognized states of matter, solid, liquid, and gas.", "Some can also exist in a plasma.", "Many have further, more finely differentiated, states of matter, such as glass and liquid crystal.", "In many cases, at fixed temperature and pressure, a substance can exist in several distinct states of matter in what might be viewed as the same 'body'.", "For example, ice may float in a glass of water.", "Then the ice and the water are said to constitute two phases within the 'body'.", "Definite rules are known, telling how distinct phases may coexist in a 'body'.", "Mostly, at a fixed pressure, there is a definite temperature at which heating causes a solid to melt or evaporate, and a definite temperature at which heating causes a liquid to evaporate.", "In such cases, cooling has the reverse effects.", "All of these, the commonest cases, fit with a rule that heating can be measured by changes of state of a body.", "Such cases supply what are called \"thermometric bodies\", that allow the definition of empirical temperatures.", "Before 1848, all temperatures were defined in this way.", "There was thus a tight link, apparently logically determined, between heat and temperature, though they were recognized as conceptually thoroughly distinct, especially by Joseph Black in the later eighteenth century.", "There are important exceptions.", "They break the obviously apparent link between heat and temperature.", "They make it clear that empirical definitions of temperature are contingent on the peculiar properties of particular thermometric substances, and are thus precluded from the title 'absolute'.", "For example, water contracts on being heated near 277 K. It cannot be used as a thermometric substance near that temperature.", "Also, over a certain temperature range, ice contracts on heating.", "Moreover, many substances can exist in metastable states, such as with negative pressure, that survive only transiently and in very special conditions.", "Such facts, sometimes called 'anomalous', are some of the reasons for the thermodynamic definition of absolute temperature.", "In the early days of measurement of high temperatures, another factor was important, and used by Josiah Wedgwood in his pyrometer.", "The temperature reached in a process was estimated by the shrinkage of a sample of clay.", "The higher the temperature, the more the shrinkage.", "This was the only available more or less reliable method of measurement of temperatures above 1000 °C (1,832 °F).", "But such shrinkage is irreversible.", "The clay does not expand again on cooling.", "That is why it could be used for the measurement.", "But only once.", "It is not a thermometric material in the usual sense of the word.", "Nevertheless, the thermodynamic definition of absolute temperature does make essential use of the concept of heat, with proper circumspection.", "According to Denbigh (1981), the property of hotness is a concern of thermodynamics that should be defined without reference to the concept of heat.", "Consideration of hotness leads to the concept of empirical temperature.", "All physical systems are capable of heating or cooling others.", "With reference to hotness, the comparative terms hotter and colder are defined by the rule that heat flows from the hotter body to the colder.", "If a physical system is inhomogeneous or very rapidly or irregularly changing, for example by turbulence, it may be impossible to characterize it by a temperature, but still there can be transfer of energy as heat between it and another system.", "If a system has a physical state that is regular enough, and persists long enough to allow it to reach thermal equilibrium with a specified thermometer, then it has a temperature according to that thermometer.", "An empirical thermometer registers degree of hotness for such a system.", "Such a temperature is called empirical.", "For example, Truesdell writes about classical thermodynamics: \"At each time, the body is assigned a real number called the \"temperature\".", "This number is a measure of how hot the body is.", "\"\nPhysical systems that are too turbulent to have temperatures may still differ in hotness.", "A physical system that passes heat to another physical system is said to be the hotter of the two.", "More is required for the system to have a thermodynamic temperature.", "Its behavior must be so regular that its empirical temperature is the same for all suitably calibrated and scaled thermometers, and then its hotness is said to lie on the one-dimensional hotness manifold.", "This is part of the reason why heat is defined following Carathéodory and Born, solely as occurring other than by work or transfer of matter; temperature is advisedly and deliberately not mentioned in this now widely accepted definition.", "This is also the reason that the zeroth law of thermodynamics is stated explicitly.", "If three physical systems, \"A\", \"B\", and \"C\" are each not in their own states of internal thermodynamic equilibrium, it is possible that, with suitable physical connections being made between them, \"A\" can heat \"B\" and \"B\" can heat \"C\" and \"C\" can heat \"A\".", "In non-equilibrium situations, cycles of flow are possible.", "It is the special and uniquely distinguishing characteristic of internal thermodynamic equilibrium that this possibility is not open to thermodynamic systems (as distinguished amongst physical systems) which are in their own states of internal thermodynamic equilibrium; this is the reason why the zeroth law of thermodynamics needs explicit statement.", "That is to say, the relation 'is not colder than' between general non-equilibrium physical systems is not transitive, whereas, in contrast, the relation 'has no lower a temperature than' between thermodynamic systems in their own states of internal thermodynamic equilibrium is transitive.", "It follows from this that the relation 'is in thermal equilibrium with' is transitive, which is one way of stating the zeroth law.", "Just as temperature may be undefined for a sufficiently inhomogeneous system, so also may entropy be undefined for a system not in its own state of internal thermodynamic equilibrium.", "For example, 'the temperature of the solar system' is not a defined quantity.", "Likewise, 'the entropy of the solar system' is not defined in classical thermodynamics.", "It has not been possible to define non-equilibrium entropy, as a simple number for a whole system, in a clearly satisfactory way." ]

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[ "Like thermodynamic work, heat transfer involves the surroundings of a system, as well as the system itself, and so is not a property of the system alone, though it contributes to change in the system's internal energy, which is a property of the system alone.", "The quantity of energy transferred as heat in a process is the amount of transferred energy excluding any thermodynamic work that was done and any energy contained in matter transferred.", "For example, radiative heat transfer can co-occur with matter transfer.", "Though not immediately by the definition, but in special kinds of process, quantity of energy transferred as heat can be measured by its effect on the states of interacting bodies.", "The conventional symbol used to represent the amount of heat transferred in a thermodynamic process is or \"\"." ]

[ "The mechanisms of energy transfer that define heat include conduction, through direct contact of immobile bodies, or through a wall or barrier that is impermeable to matter; or radiation between separated bodies; or friction due to isochoric mechanical or electrical or magnetic or gravitational work done by the surroundings on the system of interest, such as Joule heating due to an electric current driven through the system of interest by an external system, or through a magnetic stirrer.", "When there is a suitable path between two systems with different temperatures, heat transfer occurs necessarily, immediately, and spontaneously from the hotter to the colder system.", "Thermal conduction occurs by the stochastic (random) motion of microscopic particles (such as atoms or molecules).", "In contrast, thermodynamic work is defined by mechanisms that act macroscopically and directly on the system's whole-body state variables; for example, change of the system's volume through a piston's motion with externally measurable force; or change of the system's internal electric polarization through an externally measurable change in electric field.", "The definition of heat transfer does not require that the process be in any sense smooth.", "For example, a bolt of lightning may transfer heat to a body.", "Convective circulation allows one body to heat another, through an intermediate circulating fluid that carries energy from a boundary of one to a boundary of the other; the actual heat transfer is by conduction and radiation between the fluid and the respective bodies.", "Convective circulation, though spontaneous, does not necessarily and immediately occur simply because of some slight temperature difference; for it to occur in a given arrangement of systems, there is a threshold that must be crossed.", "Although heat flows spontaneously from a hotter body to a cooler one, it is possible to construct a heat pump which expends work to transfer energy from a colder body to a hotter body.", "In contrast, a heat engine reduces an existing temperature difference to supply work to another system.", "Another thermodynamic type of heat transfer device is an active heat spreader, which expends work to speed up transfer of energy to colder surroundings from a hotter body, for example a computer component.", "As a form of energy, heat has the unit joule (J) in the International System of Units (SI).", "However, in many applied fields in engineering the British thermal unit (BTU) and the calorie are often used.", "The standard unit for the rate of heat transferred is the watt (W), defined as one joule per second.", "The symbol for the total amount of energy transferred as heat was used by Rudolf Clausius in 1850:\n\"Let the amount of heat which must be imparted during the transition of the gas in a definite manner from any given state to another, in which its volume is \"v\" and its temperature \"t\", be called \"Q\"\"\nHeat released by a system into its surroundings is by convention a negative quantity (); when a system absorbs heat from its surroundings, it is positive ().", "Heat transfer rate, or heat flow per unit time, is denoted by formula_1.", "This should not be confused with a time derivative of a function of state (which can also be written with the dot notation) since heat is not a function of state.", "Heat flux is defined as rate of heat transfer per unit cross-sectional area (units watts per square metre).", "In 1856, Rudolf Clausius, referring to closed systems, in which transfers of matter do not occur, defined the \"second fundamental theorem\" (the second law of thermodynamics) in the mechanical theory of heat (thermodynamics): \"if two transformations which, without necessitating any other permanent change, can mutually replace one another, be called equivalent, then the generations of the quantity of heat \"Q\" from work at the temperature \"T\", has the \"equivalence-value\":\"\nformula_2\nIn 1865, he came to define the entropy symbolized by \"S\", such that, due to the supply of the amount of heat \"Q\" at temperature \"T\" the entropy of the system is increased by\nIn a transfer of energy as heat without work being done, there are changes of entropy in both the surroundings which lose heat and the system which gains it.", "The increase, , of entropy in the system may be considered to consist of two parts, an increment, that matches, or 'compensates', the change, , of entropy in the surroundings, and a further increment, that may be considered to be 'generated' or 'produced' in the system, and is said therefore to be 'uncompensated'.", "Thus\nformula_3\nThis may also be written\nformula_4\nThe total change of entropy in the system and surroundings is thus\nformula_5\nThis may also be written\nformula_6\nIt is then said that an amount of entropy has been transferred from the surroundings to the system.", "Because entropy is not a conserved quantity, this is an exception to the general way of speaking, in which an amount transferred is of a conserved quantity.", "From the second law of thermodynamics follows that in a spontaneous transfer of heat, in which the temperature of the system is different from that of the surroundings:\nformula_7\nFor purposes of mathematical analysis of transfers, one thinks of fictive processes that are called \"reversible\", with the temperature of the system being hardly less than that of the surroundings, and the transfer taking place at an imperceptibly slow rate.", "Following the definition above in formula (), for such a fictive reversible process, a quantity of transferred heat (an inexact differential) is analyzed as a quantity , with (an exact differential):\nformula_8\nThis equality is only valid for a fictive transfer in which there is no production of entropy, that is to say, in which there is no uncompensated entropy.", "If, in contrast, the process is natural, and can really occur, with irreversibility, then there is entropy production, with .", "The quantity was termed by Clausius the \"uncompensated heat\", though that does not accord with present-day terminology.", "Then one has\nformula_9\nThis leads to the statement\nformula_10\nwhich is the second law of thermodynamics for closed systems.", "In non-equilibrium thermodynamics that makes the approximation of assuming the hypothesis of local thermodynamic equilibrium, there is a special notation for this.", "The transfer of energy as heat is assumed to take place across an infinitesimal temperature difference, so that the system element and its surroundings have near enough the same temperature .", "Then one writes\nformula_11\nwhere by definition\nformula_12\nThe second law for a natural process asserts that\nformula_13", "For a closed system (a system from which no matter can enter or exit), one version of the first law of thermodynamics states that the change in internal energy of the system is equal to the amount of heat supplied to the system minus the amount of thermodynamic work done by system on its surroundings.", "The foregoing sign convention for work is used in the present article, but an alternate sign convention, followed by IUPAC, for work, is to consider the work performed on the system by its surroundings as positive.", "This is the convention adopted by many modern textbooks of physical chemistry, such as those by Peter Atkins and Ira Levine, but many textbooks on physics define work as work done by the system.", "formula_14\nThis formula can be re-written so as to express a definition of quantity of energy transferred as heat, based purely on the concept of adiabatic work, if it is supposed that is defined and measured solely by processes of adiabatic work:\nformula_15\nThe thermodynamic work done by the system is through mechanisms defined by its thermodynamic state variables, for example, its volume , not through variables that necessarily involve mechanisms in the surroundings.", "The latter are such as shaft work, and include isochoric work.", "The internal energy, , is a state function.", "In cyclical processes, such as the operation of a heat engine, state functions of the working substance return to their initial values upon completion of a cycle.", "The differential, or infinitesimal increment, for the internal energy in an infinitesimal process is an exact differential .", "The symbol for exact differentials is the lowercase letter .", "In contrast, neither of the infinitesimal increments nor in an infinitesimal process represents the change in a state function of the system.", "Thus, infinitesimal increments of heat and work are inexact differentials.", "The lowercase Greek letter delta, , is the symbol for inexact differentials.", "The integral of any inexact differential in a process where the system leaves and then returns to the same thermodynamic state does not necessarily equal zero.", "As recounted above, in the section headed \"heat and entropy\", the second law of thermodynamics observes that if heat is supplied to a system in a reversible process, the increment of heat and the temperature form the exact differential\nformula_16\nand that , the entropy of the working body, is a state function.", "Likewise, with a well-defined pressure, , behind a slowly moving (quasistatic) boundary, the work differential, , and the pressure, , combine to form the exact differential\nformula_17\nwith the volume of the system, which is a state variable.", "In general, for systems of uniform pressure and temperature without composition change,\nformula_18\nAssociated with this differential equation is the concept that the internal energy may be considered to be a function of its natural variables and .", "The internal energy representation of the fundamental thermodynamic relation is written as\nformula_19\nIf is constant\nformula_20\nand if is constant\nformula_21\nwith the enthalpy defined by\nformula_22\nThe enthalpy may be considered to be a function of its natural variables and .", "The enthalpy representation of the fundamental thermodynamic relation is written\nformula_23\nThe internal energy representation and the enthalpy representation are partial Legendre transforms of one another.", "They contain the same physical information, written in different ways.", "Like the internal energy, the enthalpy stated as a function of its natural variables is a thermodynamic potential and contains all thermodynamic information about a body.", "If a quantity of heat is added to a body while it does only expansion work on its surroundings, one has\nformula_24\nIf this is constrained to happen at constant pressure, i.e. with , the expansion work done by the body is given by ; recalling the first law of thermodynamics, one has\nformula_25\nConsequently, by substitution one has\nformula_26\nIn this scenario, the increase in enthalpy is equal to the quantity of heat added to the system.", "This is the basis of the determination of enthalpy changes in chemical reactions by calorimetry.", "Since many processes do take place at constant atmospheric pressure, the enthalpy is sometimes given the misleading name of 'heat content' or heat function, while it actually depends strongly on the energies of covalent bonds and intermolecular forces.", "In terms of the natural variables of the state function , this process of change of state from state 1 to state 2 can be expressed as\nformula_27\nIt is known that the temperature is identically stated by\nformula_28\nConsequently,\nformula_29\nIn this case, the integral specifies a quantity of heat transferred at constant pressure.", "As a common noun, English \"heat\" or \"warmth\" (just as French \"chaleur\", German \"Wärme\", Latin \"calor\", Greek θάλπος, etc.) refers to (the human perception of) either thermal energy or temperature.", "Speculation on thermal energy or \"heat\" as a separate form of matter has a long history, see caloric theory, phlogiston and fire (classical element).", "The modern understanding of thermal energy originates with Thompson's 1798 mechanical theory of heat (\"An Experimental Enquiry Concerning the Source of the Heat which is Excited by Friction\"), postulating a mechanical equivalent of heat.", "A collaboration between Nicolas Clément and Sadi Carnot (\"Reflections on the Motive Power of Fire\") in the 1820s had some related thinking along similar lines.", "In 1845, Joule published a paper entitled \"The Mechanical Equivalent of Heat\", in which he specified a numerical value for the amount of mechanical work required to \"produce a unit of heat\".", "The theory of classical thermodynamics matured in the 1850s to 1860s.", "John Tyndall's \"Heat Considered as Mode of Motion\" (1863) was instrumental in popularizing the idea of heat as motion to the English-speaking public.", "The theory was developed in academic publications in French, English and German.", "From an early time, the French technical term \"chaleur\" used by Carnot was taken as equivalent to the English \"heat\" and German \"Wärme\" (lit.", "\"warmth\", while the equivalent of \"heat\" would be German \"Hitze\").", "The process function was introduced by Rudolf Clausius in 1850.", "Clausius described it with the German compound \"Wärmemenge\", translated as \"amount of heat\".", "James Clerk Maxwell in his 1871 \"Theory of Heat\" outlines four stipulations for the definition of heat:\n\n\nThe process function is referred to as \"Wärmemenge\" by Clausius, or as \"amount of heat\" in translation.", "Use of \"heat\" as an abbreviated form of the specific concept of \"quantity of energy transferred as heat\" led to some terminological confusion by the early 20th century.", "The generic meaning of \"heat\", even in classical thermodynamics, is just \"thermal energy\".", "Since the 1920s, it has been recommended practice to use enthalpy to refer to the \"heat content at constant volume\", and to thermal energy when \"heat\" in the general sense is intended, while \"heat\" is reserved for the very specific context of the transfer of thermal energy between two systems.", "Leonard Benedict Loeb in his \"Kinetic Theory of Gases\" (1927) makes a point of using \"quantity of heat\"\nor \"heat–quantity\" when referring to :", "After the perfection of thermometry [...] the next great advance made in the field of heat was the definition of a term which is called the quantity of heat.", "[... after the abandonment of caloric theory,] It still remains to interpret this very definite concept, the quantity of heat, in terms of a theory ascribing all heat to the kinetics of gas molecules.", "A frequent definition of heat is based on the work of Carathéodory (1909), referring to processes in a closed system.", "The internal energy of a body in an arbitrary state can be determined by amounts of work adiabatically performed by the body on its surroundings when it starts from a reference state .", "Such work is assessed through quantities defined in the surroundings of the body.", "It is supposed that such work can be assessed accurately, without error due to friction in the surroundings; friction in the body is not excluded by this definition.", "The adiabatic performance of work is defined in terms of adiabatic walls, which allow transfer of energy as work, but no other transfer, of energy or matter.", "In particular they do not allow the passage of energy as heat.", "According to this definition, work performed adiabatically is in general accompanied by friction within the thermodynamic system or body.", "On the other hand, according to Carathéodory (1909), there also exist non-adiabatic, \"diathermal\" walls, which are postulated to be permeable only to heat.", "For the definition of quantity of energy transferred as heat, it is customarily envisaged that an arbitrary state of interest is reached from state by a process with two components, one adiabatic and the other not adiabatic.", "For convenience one may say that the adiabatic component was the sum of work done by the body through volume change through movement of the walls while the non-adiabatic wall was temporarily rendered adiabatic, and of isochoric adiabatic work.", "Then the non-adiabatic component is a process of energy transfer through the wall that passes only heat, newly made accessible for the purpose of this transfer, from the surroundings to the body.", "The change in internal energy to reach the state from the state is the difference of the two amounts of energy transferred.", "Although Carathéodory himself did not state such a definition, following his work it is customary in theoretical studies to define heat, , to the body from its surroundings, in the combined process of change to state from the state , as the change in internal energy, , minus the amount of work, , done by the body on its surrounds by the adiabatic process, so that .", "In this definition, for the sake of conceptual rigour, the quantity of energy transferred as heat is not specified directly in terms of the non-adiabatic process.", "It is defined through knowledge of precisely two variables, the change of internal energy and the amount of adiabatic work done, for the combined process of change from the reference state to the arbitrary state .", "It is important that this does not explicitly involve the amount of energy transferred in the non-adiabatic component of the combined process.", "It is assumed here that the amount of energy required to pass from state to state , the change of internal energy, is known, independently of the combined process, by a determination through a purely adiabatic process, like that for the determination of the internal energy of state above.", "The rigour that is prized in this definition is that there is one and only one kind of energy transfer admitted as fundamental: energy transferred as work.", "Energy transfer as heat is considered as a derived quantity.", "The uniqueness of work in this scheme is considered to guarantee rigor and purity of conception.", "The conceptual purity of this definition, based on the concept of energy transferred as work as an ideal notion, relies on the idea that some frictionless and otherwise non-dissipative processes of energy transfer can be realized in physical actuality.", "The second law of thermodynamics, on the other hand, assures us that such processes are not found in nature.", "Before the rigorous mathematical definition of heat based on Carathéodory's 1909 paper,\nhistorically, heat, temperature, and thermal equilibrium were presented in thermodynamics textbooks as jointly primitive notions.", "Carathéodory introduced his 1909 paper thus: \"The proposition that the discipline of thermodynamics can be justified without recourse to any hypothesis that cannot be verified experimentally must be regarded as one of the most noteworthy results of the research in thermodynamics that was accomplished during the last century.\"", "Referring to the \"point of view adopted by most authors who were active in the last fifty years\", Carathéodory wrote: \"There exists a physical quantity called heat that is not identical with the mechanical quantities (mass, force, pressure, etc.) and whose variations can be determined by calorimetric measurements.\"", "James Serrin introduces an account of the theory of thermodynamics thus: \"In the following section, we shall use the classical notions of \"heat\", \"work\", and \"hotness\" as primitive elements, ...", "That heat is an appropriate and natural primitive for thermodynamics was already accepted by Carnot.", "Its continued validity as a primitive element of thermodynamical structure is due to the fact that it synthesizes an essential physical concept, as well as to its successful use in recent work to unify different constitutive theories.\"", "This traditional kind of presentation of the basis of thermodynamics includes ideas that may be summarized by the statement that heat transfer is purely due to spatial non-uniformity of temperature, and is by conduction and radiation, from hotter to colder bodies.", "It is sometimes proposed that this traditional kind of presentation necessarily rests on \"circular reasoning\"; against this proposal, there stands the rigorously logical mathematical development of the theory presented by Truesdell and Bharatha (1977).", "This alternative approach to the definition of quantity of energy transferred as heat differs in logical structure from that of Carathéodory, recounted just above.", "This alternative approach admits calorimetry as a primary or direct way to measure quantity of energy transferred as heat.", "It relies on temperature as one of its primitive concepts, and used in calorimetry.", "It is presupposed that enough processes exist physically to allow measurement of differences in internal energies.", "Such processes are not restricted to adiabatic transfers of energy as work.", "They include calorimetry, which is the commonest practical way of finding internal energy differences.", "The needed temperature can be either empirical or absolute thermodynamic.", "In contrast, the Carathéodory way recounted just above does not use calorimetry or temperature in its primary definition of quantity of energy transferred as heat.", "The Carathéodory way regards calorimetry only as a secondary or indirect way of measuring quantity of energy transferred as heat.", "As recounted in more detail just above, the Carathéodory way regards quantity of energy transferred as heat in a process as primarily or directly defined as a residual quantity.", "It is calculated from the difference of the internal energies of the initial and final states of the system, and from the actual work done by the system during the process.", "That internal energy difference is supposed to have been measured in advance through processes of purely adiabatic transfer of energy as work, processes that take the system between the initial and final states.", "By the Carathéodory way it is presupposed as known from experiment that there actually physically exist enough such adiabatic processes, so that there need be no recourse to calorimetry for measurement of quantity of energy transferred as heat.", "This presupposition is essential but is explicitly labeled neither as a law of thermodynamics nor as an axiom of the Carathéodory way.", "In fact, the actual physical existence of such adiabatic processes is indeed mostly supposition, and those supposed processes have in most cases not been actually verified empirically to exist.", "Referring to conduction, Partington writes: \"If a hot body is brought in conducting contact with a cold body, the temperature of the hot body falls and that of the cold body rises, and it is said that a \"quantity of heat\" has passed from the hot body to the cold body.", "\"\nReferring to radiation, Maxwell writes: \"In Radiation, the hotter body loses heat, and the colder body receives heat by means of a process occurring in some intervening medium which does not itself thereby become hot.\"\nMaxwell writes that convection as such \"is not a purely thermal phenomenon\".", "In thermodynamics, convection in general is regarded as transport of internal energy.", "If, however, the convection is enclosed and circulatory, then it may be regarded as an intermediary that transfers energy as heat between source and destination bodies, because it transfers only energy and not matter from the source to the destination body.", "In accordance with the first law for closed systems, energy transferred solely as heat leaves one body and enters another, changing the internal energies of each.", "Transfer, between bodies, of energy as work is a complementary way of changing internal energies.", "Though it is not logically rigorous from the viewpoint of strict physical concepts, a common form of words that expresses this is to say that heat and work are interconvertible.", "Cyclically operating engines that use only heat and work transfers have two thermal reservoirs, a hot and a cold one.", "They may be classified by the range of operating temperatures of the working body, relative to those reservoirs.", "In a heat engine, the working body is at all times colder than the hot reservoir and hotter than the cold reservoir.", "In a sense, it uses heat transfer to produce work.", "In a heat pump, the working body, at stages of the cycle, goes both hotter than the hot reservoir, and colder than the cold reservoir.", "In a sense, it uses work to produce heat transfer.", "In classical thermodynamics, a commonly considered model is the heat engine.", "It consists of four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir.", "A cyclic process leaves the working body in an unchanged state, and is envisaged as being repeated indefinitely often.", "Work transfers between the working body and the work reservoir are envisaged as reversible, and thus only one work reservoir is needed.", "But two thermal reservoirs are needed, because transfer of energy as heat is irreversible.", "A single cycle sees energy taken by the working body from the hot reservoir and sent to the two other reservoirs, the work reservoir and the cold reservoir.", "The hot reservoir always and only supplies energy and the cold reservoir always and only receives energy.", "The second law of thermodynamics requires that no cycle can occur in which no energy is received by the cold reservoir.", "Heat engines achieve higher efficiency when the ratio of the initial and final temperature is greater.", "Another commonly considered model is the heat pump or refrigerator.", "Again there are four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir.", "A single cycle starts with the working body colder than the cold reservoir, and then energy is taken in as heat by the working body from the cold reservoir.", "Then the work reservoir does work on the working body, adding more to its internal energy, making it hotter than the hot reservoir.", "The hot working body passes heat to the hot reservoir, but still remains hotter than the cold reservoir.", "Then, by allowing it to expand without passing heat to another body, the working body is made colder than the cold reservoir.", "It can now accept heat transfer from the cold reservoir to start another cycle.", "The device has transported energy from a colder to a hotter reservoir, but this is not regarded as by an inanimate agency; rather, it is regarded as by the harnessing of work .", "This is because work is supplied from the work reservoir, not just by a simple thermodynamic process, but by a cycle of thermodynamic operations and processes, which may be regarded as directed by an animate or harnessing agency.", "Accordingly, the cycle is still in accord with the second law of thermodynamics.", "The 'efficiency' of a heat pump (which exceeds unity) is best when the temperature difference between the hot and cold reservoirs is least.", "Functionally, such engines are used in two ways, distinguishing a target reservoir and a resource or surrounding reservoir.", "A heat pump transfers heat to the hot reservoir as the target from the resource or surrounding reservoir.", "A refrigerator transfers heat, from the cold reservoir as the target, to the resource or surrounding reservoir.", "The target reservoir may be regarded as leaking: when the target leaks heat to the surroundings, heat pumping is used; when the target leaks coldness to the surroundings, refrigeration is used.", "The engines harness work to overcome the leaks.", "According to Planck, there are three main conceptual approaches to heat.", "One is the microscopic or kinetic theory approach.", "The other two are macroscopic approaches.", "One is the approach through the law of conservation of energy taken as prior to thermodynamics, with a mechanical analysis of processes, for example in the work of Helmholtz.", "This mechanical view is taken in this article as currently customary for thermodynamic theory.", "The other macroscopic approach is the thermodynamic one, which admits heat as a primitive concept, which contributes, by scientific induction to knowledge of the law of conservation of energy.", "This view is widely taken as the practical one, quantity of heat being measured by calorimetry.", "Bailyn also distinguishes the two macroscopic approaches as the mechanical and the thermodynamic.", "The thermodynamic view was taken by the founders of thermodynamics in the nineteenth century.", "It regards quantity of energy transferred as heat as a primitive concept coherent with a primitive concept of temperature, measured primarily by calorimetry.", "A calorimeter is a body in the surroundings of the system, with its own temperature and internal energy; when it is connected to the system by a path for heat transfer, changes in it measure heat transfer.", "The mechanical view was pioneered by Helmholtz and developed and used in the twentieth century, largely through the influence of Max Born.", "It regards quantity of heat transferred as heat as a derived concept, defined for closed systems as quantity of heat transferred by mechanisms other than work transfer, the latter being regarded as primitive for thermodynamics, defined by macroscopic mechanics.", "According to Born, the transfer of internal energy between open systems that accompanies transfer of matter \"cannot be reduced to mechanics\".", "It follows that there is no well-founded definition of quantities of energy transferred as heat or as work associated with transfer of matter.", "Nevertheless, for the thermodynamical description of non-equilibrium processes, it is desired to consider the effect of a temperature gradient established by the surroundings across the system of interest when there is no physical barrier or wall between system and surroundings, that is to say, when they are open with respect to one another.", "The impossibility of a mechanical definition in terms of work for this circumstance does not alter the physical fact that a temperature gradient causes a diffusive flux of internal energy, a process that, in the thermodynamic view, might be proposed as a candidate concept for transfer of energy as heat.", "In this circumstance, it may be expected that there may also be active other drivers of diffusive flux of internal energy, such as gradient of chemical potential which drives transfer of matter, and gradient of electric potential which drives electric current and iontophoresis; such effects usually interact with diffusive flux of internal energy driven by temperature gradient, and such interactions are known as cross-effects.", "If cross-effects that result in diffusive transfer of internal energy were also labeled as heat transfers, they would sometimes violate the rule that pure heat transfer occurs only down a temperature gradient, never up one.", "They would also contradict the principle that all heat transfer is of one and the same kind, a principle founded on the idea of heat conduction between closed systems.", "One might to try to think narrowly of heat flux driven purely by temperature gradient as a conceptual component of diffusive internal energy flux, in the thermodynamic view, the concept resting specifically on careful calculations based on detailed knowledge of the processes and being indirectly assessed.", "In these circumstances, if perchance it happens that no transfer of matter is actualized, and there are no cross-effects, then the thermodynamic concept and the mechanical concept coincide, as if one were dealing with closed systems.", "But when there is transfer of matter, the exact laws by which temperature gradient drives diffusive flux of internal energy, rather than being exactly knowable, mostly need to be assumed, and in many cases are practically unverifiable.", "Consequently, when there is transfer of matter, the calculation of the pure 'heat flux' component of the diffusive flux of internal energy rests on practically unverifiable assumptions.", "This is a reason to think of heat as a specialized concept that relates primarily and precisely to closed systems, and applicable only in a very restricted way to open systems.", "In many writings in this context, the term \"heat flux\" is used when what is meant is therefore more accurately called diffusive flux of internal energy; such usage of the term \"heat flux\" is a residue of older and now obsolete language usage that allowed that a body may have a \"heat content\".", "In the kinetic theory, heat is explained in terms of the microscopic motions and interactions of constituent particles, such as electrons, atoms, and molecules.", "The immediate meaning of the kinetic energy of the constituent particles is not as heat.", "It is as a component of internal energy.", "In microscopic terms, heat is a transfer quantity, and is described by a transport theory, not as steadily localized kinetic energy of particles.", "Heat transfer arises from temperature gradients or differences, through the diffuse exchange of microscopic kinetic and potential particle energy, by particle collisions and other interactions.", "An early and vague expression of this was made by Francis Bacon.", "Precise and detailed versions of it were developed in the nineteenth century.", "In statistical mechanics, for a closed system (no transfer of matter), heat is the energy transfer associated with a disordered, microscopic action on the system, associated with jumps in occupation numbers of the energy levels of the system, without change in the values of the energy levels themselves.", "It is possible for macroscopic thermodynamic work to alter the occupation numbers without change in the values of the system energy levels themselves, but what distinguishes transfer as heat is that the transfer is entirely due to disordered, microscopic action, including radiative transfer.", "A mathematical definition can be formulated for small increments of quasi-static adiabatic work in terms of the statistical distribution of an ensemble of microstates.", "Quantity of heat transferred can be measured by calorimetry, or determined through calculations based on other quantities.", "Calorimetry is the empirical basis of the idea of quantity of heat transferred in a process.", "The transferred heat is measured by changes in a body of known properties, for example, temperature rise, change in volume or length, or phase change, such as melting of ice.", "A calculation of quantity of heat transferred can rely on a hypothetical quantity of energy transferred as adiabatic work and on the first law of thermodynamics.", "Such calculation is the primary approach of many theoretical studies of quantity of heat transferred.", "The discipline of heat transfer, typically considered an aspect of mechanical engineering and chemical engineering, deals with specific applied methods by which thermal energy in a system is generated, or converted, or transferred to another system.", "Although the definition of heat implicitly means the transfer of energy, the term \"heat transfer\" encompasses this traditional usage in many engineering disciplines and laymen language.", "\"Heat transfer\" is generally described as including the mechanisms of heat conduction, heat convection, thermal radiation, but may include mass transfer and heat in processes of phase changes.", "Convection may be described as the combined effects of conduction and fluid flow.", "From the thermodynamic point of view, heat flows into a fluid by diffusion to increase its energy, the fluid then transfers (advects) this increased internal energy (not heat) from one location to another, and this is then followed by a second thermal interaction which transfers heat to a second body or system, again by diffusion.", "This entire process is often regarded as an additional mechanism of heat transfer, although technically, \"heat transfer\" and thus heating and cooling occurs only on either end of such a conductive flow, but not as a result of flow.", "Thus, conduction can be said to \"transfer\" heat only as a net result of the process, but may not do so at every time within the complicated convective process.", "In an 1847 lecture entitled \"On Matter, Living Force, and Heat\", James Prescott Joule characterized the terms latent heat and sensible heat as components of heat each affecting distinct physical phenomena, namely the potential and kinetic energy of particles, respectively.", "He described latent energy as the energy possessed via a distancing of particles where attraction was over a greater distance, i.e. a form of potential energy, and the sensible heat as an energy involving the motion of particles, i.e. kinetic energy.", "Latent heat is the heat released or absorbed by a chemical substance or a thermodynamic system during a change of state that occurs without a change in temperature.", "Such a process may be a phase transition, such as the melting of ice or the boiling of water.", "Heat capacity is a measurable physical quantity equal to the ratio of the heat added to an object to the resulting temperature change.", "The \"molar heat capacity\" is the heat capacity per unit amount (SI unit: mole) of a pure substance, and the \"specific heat capacity\", often called simply \"specific heat\", is the heat capacity per unit mass of a material.", "Heat capacity is a physical property of a substance, which means that it depends on the state and properties of the substance under consideration.", "The specific heats of monatomic gases, such as helium, are nearly constant with temperature.", "Diatomic gases such as hydrogen display some temperature dependence, and triatomic gases (e.g., carbon dioxide) still more.", "Before the development of the laws of thermodynamics, heat was measured by changes in the states of the participating bodies.", "Some general rules, with important exceptions, can be stated as follows.", "In general, most bodies expand on heating.", "In this circumstance, heating a body at a constant volume increases the pressure it exerts on its constraining walls, while heating at a constant pressure increases its volume.", "Beyond this, most substances have three ordinarily recognized states of matter, solid, liquid, and gas.", "Some can also exist in a plasma.", "Many have further, more finely differentiated, states of matter, such as glass and liquid crystal.", "In many cases, at fixed temperature and pressure, a substance can exist in several distinct states of matter in what might be viewed as the same 'body'.", "For example, ice may float in a glass of water.", "Then the ice and the water are said to constitute two phases within the 'body'.", "Definite rules are known, telling how distinct phases may coexist in a 'body'.", "Mostly, at a fixed pressure, there is a definite temperature at which heating causes a solid to melt or evaporate, and a definite temperature at which heating causes a liquid to evaporate.", "In such cases, cooling has the reverse effects.", "All of these, the commonest cases, fit with a rule that heating can be measured by changes of state of a body.", "Such cases supply what are called \"thermometric bodies\", that allow the definition of empirical temperatures.", "Before 1848, all temperatures were defined in this way.", "There was thus a tight link, apparently logically determined, between heat and temperature, though they were recognized as conceptually thoroughly distinct, especially by Joseph Black in the later eighteenth century.", "There are important exceptions.", "They break the obviously apparent link between heat and temperature.", "They make it clear that empirical definitions of temperature are contingent on the peculiar properties of particular thermometric substances, and are thus precluded from the title 'absolute'.", "For example, water contracts on being heated near 277 K. It cannot be used as a thermometric substance near that temperature.", "Also, over a certain temperature range, ice contracts on heating.", "Moreover, many substances can exist in metastable states, such as with negative pressure, that survive only transiently and in very special conditions.", "Such facts, sometimes called 'anomalous', are some of the reasons for the thermodynamic definition of absolute temperature.", "In the early days of measurement of high temperatures, another factor was important, and used by Josiah Wedgwood in his pyrometer.", "The temperature reached in a process was estimated by the shrinkage of a sample of clay.", "The higher the temperature, the more the shrinkage.", "This was the only available more or less reliable method of measurement of temperatures above 1000 °C (1,832 °F).", "But such shrinkage is irreversible.", "The clay does not expand again on cooling.", "That is why it could be used for the measurement.", "But only once.", "It is not a thermometric material in the usual sense of the word.", "Nevertheless, the thermodynamic definition of absolute temperature does make essential use of the concept of heat, with proper circumspection.", "According to Denbigh (1981), the property of hotness is a concern of thermodynamics that should be defined without reference to the concept of heat.", "Consideration of hotness leads to the concept of empirical temperature.", "All physical systems are capable of heating or cooling others.", "With reference to hotness, the comparative terms hotter and colder are defined by the rule that heat flows from the hotter body to the colder.", "If a physical system is inhomogeneous or very rapidly or irregularly changing, for example by turbulence, it may be impossible to characterize it by a temperature, but still there can be transfer of energy as heat between it and another system.", "If a system has a physical state that is regular enough, and persists long enough to allow it to reach thermal equilibrium with a specified thermometer, then it has a temperature according to that thermometer.", "An empirical thermometer registers degree of hotness for such a system.", "Such a temperature is called empirical.", "For example, Truesdell writes about classical thermodynamics: \"At each time, the body is assigned a real number called the \"temperature\".", "This number is a measure of how hot the body is.", "\"\nPhysical systems that are too turbulent to have temperatures may still differ in hotness.", "A physical system that passes heat to another physical system is said to be the hotter of the two.", "More is required for the system to have a thermodynamic temperature.", "Its behavior must be so regular that its empirical temperature is the same for all suitably calibrated and scaled thermometers, and then its hotness is said to lie on the one-dimensional hotness manifold.", "This is part of the reason why heat is defined following Carathéodory and Born, solely as occurring other than by work or transfer of matter; temperature is advisedly and deliberately not mentioned in this now widely accepted definition.", "This is also the reason that the zeroth law of thermodynamics is stated explicitly.", "If three physical systems, \"A\", \"B\", and \"C\" are each not in their own states of internal thermodynamic equilibrium, it is possible that, with suitable physical connections being made between them, \"A\" can heat \"B\" and \"B\" can heat \"C\" and \"C\" can heat \"A\".", "In non-equilibrium situations, cycles of flow are possible.", "It is the special and uniquely distinguishing characteristic of internal thermodynamic equilibrium that this possibility is not open to thermodynamic systems (as distinguished amongst physical systems) which are in their own states of internal thermodynamic equilibrium; this is the reason why the zeroth law of thermodynamics needs explicit statement.", "That is to say, the relation 'is not colder than' between general non-equilibrium physical systems is not transitive, whereas, in contrast, the relation 'has no lower a temperature than' between thermodynamic systems in their own states of internal thermodynamic equilibrium is transitive.", "It follows from this that the relation 'is in thermal equilibrium with' is transitive, which is one way of stating the zeroth law.", "Just as temperature may be undefined for a sufficiently inhomogeneous system, so also may entropy be undefined for a system not in its own state of internal thermodynamic equilibrium.", "For example, 'the temperature of the solar system' is not a defined quantity.", "Likewise, 'the entropy of the solar system' is not defined in classical thermodynamics.", "It has not been possible to define non-equilibrium entropy, as a simple number for a whole system, in a clearly satisfactory way." ]

[ 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29 ]

[ "Like thermodynamic work, heat transfer involves the surroundings of a system, as well as the system itself, and so is not a property of the system alone, though it contributes to change in the system's internal energy, which is a property of the system alone.", "The quantity of energy transferred as heat in a process is the amount of transferred energy excluding any thermodynamic work that was done and any energy contained in matter transferred.", "For example, radiative heat transfer can co-occur with matter transfer.", "The conventional symbol used to represent the amount of heat transferred in a thermodynamic process is or \"\"." ]

[ "The mechanisms of energy transfer that define heat include conduction, through direct contact of immobile bodies, or through a wall or barrier that is impermeable to matter; or radiation between separated bodies; or friction due to isochoric mechanical or electrical or magnetic or gravitational work done by the surroundings on the system of interest, such as Joule heating due to an electric current driven through the system of interest by an external system, or through a magnetic stirrer.", "When there is a suitable path between two systems with different temperatures, heat transfer occurs necessarily, immediately, and spontaneously from the hotter to the colder system.", "Thermal conduction occurs by the stochastic (random) motion of microscopic particles (such as atoms or molecules).", "In contrast, thermodynamic work is defined by mechanisms that act macroscopically and directly on the system's whole-body state variables; for example, change of the system's volume through a piston's motion with externally measurable force; or change of the system's internal electric polarization through an externally measurable change in electric field.", "The definition of heat transfer does not require that the process be in any sense smooth.", "For example, a bolt of lightning may transfer heat to a body.", "Convective circulation allows one body to heat another, through an intermediate circulating fluid that carries energy from a boundary of one to a boundary of the other; the actual heat transfer is by conduction and radiation between the fluid and the respective bodies.", "Convective circulation, though spontaneous, does not necessarily and immediately occur simply because of some slight temperature difference; for it to occur in a given arrangement of systems, there is a threshold that must be crossed.", "Although heat flows spontaneously from a hotter body to a cooler one, it is possible to construct a heat pump which expends work to transfer energy from a colder body to a hotter body.", "In contrast, a heat engine reduces an existing temperature difference to supply work to another system.", "Another thermodynamic type of heat transfer device is an active heat spreader, which expends work to speed up transfer of energy to colder surroundings from a hotter body, for example a computer component.", "As a form of energy, heat has the unit joule (J) in the International System of Units (SI).", "However, in many applied fields in engineering the British thermal unit (BTU) and the calorie are often used.", "The standard unit for the rate of heat transferred is the watt (W), defined as one joule per second.", "The symbol for the total amount of energy transferred as heat was used by Rudolf Clausius in 1850:\n\"Let the amount of heat which must be imparted during the transition of the gas in a definite manner from any given state to another, in which its volume is \"v\" and its temperature \"t\", be called \"Q\"\"\nHeat released by a system into its surroundings is by convention a negative quantity (); when a system absorbs heat from its surroundings, it is positive ().", "Heat transfer rate, or heat flow per unit time, is denoted by formula_1.", "This should not be confused with a time derivative of a function of state (which can also be written with the dot notation) since heat is not a function of state.", "Heat flux is defined as rate of heat transfer per unit cross-sectional area (units watts per square metre).", "In 1856, Rudolf Clausius, referring to closed systems, in which transfers of matter do not occur, defined the \"second fundamental theorem\" (the second law of thermodynamics) in the mechanical theory of heat (thermodynamics): \"if two transformations which, without necessitating any other permanent change, can mutually replace one another, be called equivalent, then the generations of the quantity of heat \"Q\" from work at the temperature \"T\", has the \"equivalence-value\":\"\nformula_2\nIn 1865, he came to define the entropy symbolized by \"S\", such that, due to the supply of the amount of heat \"Q\" at temperature \"T\" the entropy of the system is increased by\nIn a transfer of energy as heat without work being done, there are changes of entropy in both the surroundings which lose heat and the system which gains it.", "The increase, , of entropy in the system may be considered to consist of two parts, an increment, that matches, or 'compensates', the change, , of entropy in the surroundings, and a further increment, that may be considered to be 'generated' or 'produced' in the system, and is said therefore to be 'uncompensated'.", "Thus\nformula_3\nThis may also be written\nformula_4\nThe total change of entropy in the system and surroundings is thus\nformula_5\nThis may also be written\nformula_6\nIt is then said that an amount of entropy has been transferred from the surroundings to the system.", "Because entropy is not a conserved quantity, this is an exception to the general way of speaking, in which an amount transferred is of a conserved quantity.", "From the second law of thermodynamics follows that in a spontaneous transfer of heat, in which the temperature of the system is different from that of the surroundings:\nformula_7\nFor purposes of mathematical analysis of transfers, one thinks of fictive processes that are called \"reversible\", with the temperature of the system being hardly less than that of the surroundings, and the transfer taking place at an imperceptibly slow rate.", "Following the definition above in formula (), for such a fictive reversible process, a quantity of transferred heat (an inexact differential) is analyzed as a quantity , with (an exact differential):\nformula_8\nThis equality is only valid for a fictive transfer in which there is no production of entropy, that is to say, in which there is no uncompensated entropy.", "If, in contrast, the process is natural, and can really occur, with irreversibility, then there is entropy production, with .", "The quantity was termed by Clausius the \"uncompensated heat\", though that does not accord with present-day terminology.", "Then one has\nformula_9\nThis leads to the statement\nformula_10\nwhich is the second law of thermodynamics for closed systems.", "In non-equilibrium thermodynamics that makes the approximation of assuming the hypothesis of local thermodynamic equilibrium, there is a special notation for this.", "The transfer of energy as heat is assumed to take place across an infinitesimal temperature difference, so that the system element and its surroundings have near enough the same temperature .", "Then one writes\nformula_11\nwhere by definition\nformula_12\nThe second law for a natural process asserts that\nformula_13", "For a closed system (a system from which no matter can enter or exit), one version of the first law of thermodynamics states that the change in internal energy of the system is equal to the amount of heat supplied to the system minus the amount of thermodynamic work done by system on its surroundings.", "The foregoing sign convention for work is used in the present article, but an alternate sign convention, followed by IUPAC, for work, is to consider the work performed on the system by its surroundings as positive.", "This is the convention adopted by many modern textbooks of physical chemistry, such as those by Peter Atkins and Ira Levine, but many textbooks on physics define work as work done by the system.", "formula_14\nThis formula can be re-written so as to express a definition of quantity of energy transferred as heat, based purely on the concept of adiabatic work, if it is supposed that is defined and measured solely by processes of adiabatic work:\nformula_15\nThe thermodynamic work done by the system is through mechanisms defined by its thermodynamic state variables, for example, its volume , not through variables that necessarily involve mechanisms in the surroundings.", "The latter are such as shaft work, and include isochoric work.", "The internal energy, , is a state function.", "In cyclical processes, such as the operation of a heat engine, state functions of the working substance return to their initial values upon completion of a cycle.", "The differential, or infinitesimal increment, for the internal energy in an infinitesimal process is an exact differential .", "The symbol for exact differentials is the lowercase letter .", "In contrast, neither of the infinitesimal increments nor in an infinitesimal process represents the change in a state function of the system.", "Thus, infinitesimal increments of heat and work are inexact differentials.", "The lowercase Greek letter delta, , is the symbol for inexact differentials.", "The integral of any inexact differential in a process where the system leaves and then returns to the same thermodynamic state does not necessarily equal zero.", "As recounted above, in the section headed \"heat and entropy\", the second law of thermodynamics observes that if heat is supplied to a system in a reversible process, the increment of heat and the temperature form the exact differential\nformula_16\nand that , the entropy of the working body, is a state function.", "Likewise, with a well-defined pressure, , behind a slowly moving (quasistatic) boundary, the work differential, , and the pressure, , combine to form the exact differential\nformula_17\nwith the volume of the system, which is a state variable.", "In general, for systems of uniform pressure and temperature without composition change,\nformula_18\nAssociated with this differential equation is the concept that the internal energy may be considered to be a function of its natural variables and .", "The internal energy representation of the fundamental thermodynamic relation is written as\nformula_19\nIf is constant\nformula_20\nand if is constant\nformula_21\nwith the enthalpy defined by\nformula_22\nThe enthalpy may be considered to be a function of its natural variables and .", "The enthalpy representation of the fundamental thermodynamic relation is written\nformula_23\nThe internal energy representation and the enthalpy representation are partial Legendre transforms of one another.", "They contain the same physical information, written in different ways.", "Like the internal energy, the enthalpy stated as a function of its natural variables is a thermodynamic potential and contains all thermodynamic information about a body.", "If a quantity of heat is added to a body while it does only expansion work on its surroundings, one has\nformula_24\nIf this is constrained to happen at constant pressure, i.e. with , the expansion work done by the body is given by ; recalling the first law of thermodynamics, one has\nformula_25\nConsequently, by substitution one has\nformula_26\nIn this scenario, the increase in enthalpy is equal to the quantity of heat added to the system.", "This is the basis of the determination of enthalpy changes in chemical reactions by calorimetry.", "Since many processes do take place at constant atmospheric pressure, the enthalpy is sometimes given the misleading name of 'heat content' or heat function, while it actually depends strongly on the energies of covalent bonds and intermolecular forces.", "In terms of the natural variables of the state function , this process of change of state from state 1 to state 2 can be expressed as\nformula_27\nIt is known that the temperature is identically stated by\nformula_28\nConsequently,\nformula_29\nIn this case, the integral specifies a quantity of heat transferred at constant pressure.", "As a common noun, English \"heat\" or \"warmth\" (just as French \"chaleur\", German \"Wärme\", Latin \"calor\", Greek θάλπος, etc.) refers to (the human perception of) either thermal energy or temperature.", "Speculation on thermal energy or \"heat\" as a separate form of matter has a long history, see caloric theory, phlogiston and fire (classical element).", "The modern understanding of thermal energy originates with Thompson's 1798 mechanical theory of heat (\"An Experimental Enquiry Concerning the Source of the Heat which is Excited by Friction\"), postulating a mechanical equivalent of heat.", "A collaboration between Nicolas Clément and Sadi Carnot (\"Reflections on the Motive Power of Fire\") in the 1820s had some related thinking along similar lines.", "In 1845, Joule published a paper entitled \"The Mechanical Equivalent of Heat\", in which he specified a numerical value for the amount of mechanical work required to \"produce a unit of heat\".", "The theory of classical thermodynamics matured in the 1850s to 1860s.", "John Tyndall's \"Heat Considered as Mode of Motion\" (1863) was instrumental in popularizing the idea of heat as motion to the English-speaking public.", "The theory was developed in academic publications in French, English and German.", "From an early time, the French technical term \"chaleur\" used by Carnot was taken as equivalent to the English \"heat\" and German \"Wärme\" (lit.", "\"warmth\", while the equivalent of \"heat\" would be German \"Hitze\").", "The process function was introduced by Rudolf Clausius in 1850.", "Clausius described it with the German compound \"Wärmemenge\", translated as \"amount of heat\".", "James Clerk Maxwell in his 1871 \"Theory of Heat\" outlines four stipulations for the definition of heat:\n\n\nThe process function is referred to as \"Wärmemenge\" by Clausius, or as \"amount of heat\" in translation.", "Use of \"heat\" as an abbreviated form of the specific concept of \"quantity of energy transferred as heat\" led to some terminological confusion by the early 20th century.", "The generic meaning of \"heat\", even in classical thermodynamics, is just \"thermal energy\".", "Since the 1920s, it has been recommended practice to use enthalpy to refer to the \"heat content at constant volume\", and to thermal energy when \"heat\" in the general sense is intended, while \"heat\" is reserved for the very specific context of the transfer of thermal energy between two systems.", "Leonard Benedict Loeb in his \"Kinetic Theory of Gases\" (1927) makes a point of using \"quantity of heat\"\nor \"heat–quantity\" when referring to :", "After the perfection of thermometry [...] the next great advance made in the field of heat was the definition of a term which is called the quantity of heat.", "[... after the abandonment of caloric theory,] It still remains to interpret this very definite concept, the quantity of heat, in terms of a theory ascribing all heat to the kinetics of gas molecules.", "A frequent definition of heat is based on the work of Carathéodory (1909), referring to processes in a closed system.", "The internal energy of a body in an arbitrary state can be determined by amounts of work adiabatically performed by the body on its surroundings when it starts from a reference state .", "Such work is assessed through quantities defined in the surroundings of the body.", "It is supposed that such work can be assessed accurately, without error due to friction in the surroundings; friction in the body is not excluded by this definition.", "The adiabatic performance of work is defined in terms of adiabatic walls, which allow transfer of energy as work, but no other transfer, of energy or matter.", "In particular they do not allow the passage of energy as heat.", "According to this definition, work performed adiabatically is in general accompanied by friction within the thermodynamic system or body.", "On the other hand, according to Carathéodory (1909), there also exist non-adiabatic, \"diathermal\" walls, which are postulated to be permeable only to heat.", "For the definition of quantity of energy transferred as heat, it is customarily envisaged that an arbitrary state of interest is reached from state by a process with two components, one adiabatic and the other not adiabatic.", "For convenience one may say that the adiabatic component was the sum of work done by the body through volume change through movement of the walls while the non-adiabatic wall was temporarily rendered adiabatic, and of isochoric adiabatic work.", "Then the non-adiabatic component is a process of energy transfer through the wall that passes only heat, newly made accessible for the purpose of this transfer, from the surroundings to the body.", "The change in internal energy to reach the state from the state is the difference of the two amounts of energy transferred.", "Although Carathéodory himself did not state such a definition, following his work it is customary in theoretical studies to define heat, , to the body from its surroundings, in the combined process of change to state from the state , as the change in internal energy, , minus the amount of work, , done by the body on its surrounds by the adiabatic process, so that .", "In this definition, for the sake of conceptual rigour, the quantity of energy transferred as heat is not specified directly in terms of the non-adiabatic process.", "It is defined through knowledge of precisely two variables, the change of internal energy and the amount of adiabatic work done, for the combined process of change from the reference state to the arbitrary state .", "It is important that this does not explicitly involve the amount of energy transferred in the non-adiabatic component of the combined process.", "It is assumed here that the amount of energy required to pass from state to state , the change of internal energy, is known, independently of the combined process, by a determination through a purely adiabatic process, like that for the determination of the internal energy of state above.", "The rigour that is prized in this definition is that there is one and only one kind of energy transfer admitted as fundamental: energy transferred as work.", "Energy transfer as heat is considered as a derived quantity.", "The uniqueness of work in this scheme is considered to guarantee rigor and purity of conception.", "The conceptual purity of this definition, based on the concept of energy transferred as work as an ideal notion, relies on the idea that some frictionless and otherwise non-dissipative processes of energy transfer can be realized in physical actuality.", "The second law of thermodynamics, on the other hand, assures us that such processes are not found in nature.", "Before the rigorous mathematical definition of heat based on Carathéodory's 1909 paper,\nhistorically, heat, temperature, and thermal equilibrium were presented in thermodynamics textbooks as jointly primitive notions.", "Carathéodory introduced his 1909 paper thus: \"The proposition that the discipline of thermodynamics can be justified without recourse to any hypothesis that cannot be verified experimentally must be regarded as one of the most noteworthy results of the research in thermodynamics that was accomplished during the last century.\"", "Referring to the \"point of view adopted by most authors who were active in the last fifty years\", Carathéodory wrote: \"There exists a physical quantity called heat that is not identical with the mechanical quantities (mass, force, pressure, etc.) and whose variations can be determined by calorimetric measurements.\"", "James Serrin introduces an account of the theory of thermodynamics thus: \"In the following section, we shall use the classical notions of \"heat\", \"work\", and \"hotness\" as primitive elements, ...", "That heat is an appropriate and natural primitive for thermodynamics was already accepted by Carnot.", "Its continued validity as a primitive element of thermodynamical structure is due to the fact that it synthesizes an essential physical concept, as well as to its successful use in recent work to unify different constitutive theories.\"", "This traditional kind of presentation of the basis of thermodynamics includes ideas that may be summarized by the statement that heat transfer is purely due to spatial non-uniformity of temperature, and is by conduction and radiation, from hotter to colder bodies.", "It is sometimes proposed that this traditional kind of presentation necessarily rests on \"circular reasoning\"; against this proposal, there stands the rigorously logical mathematical development of the theory presented by Truesdell and Bharatha (1977).", "This alternative approach to the definition of quantity of energy transferred as heat differs in logical structure from that of Carathéodory, recounted just above.", "This alternative approach admits calorimetry as a primary or direct way to measure quantity of energy transferred as heat.", "It relies on temperature as one of its primitive concepts, and used in calorimetry.", "It is presupposed that enough processes exist physically to allow measurement of differences in internal energies.", "Such processes are not restricted to adiabatic transfers of energy as work.", "They include calorimetry, which is the commonest practical way of finding internal energy differences.", "The needed temperature can be either empirical or absolute thermodynamic.", "In contrast, the Carathéodory way recounted just above does not use calorimetry or temperature in its primary definition of quantity of energy transferred as heat.", "The Carathéodory way regards calorimetry only as a secondary or indirect way of measuring quantity of energy transferred as heat.", "As recounted in more detail just above, the Carathéodory way regards quantity of energy transferred as heat in a process as primarily or directly defined as a residual quantity.", "It is calculated from the difference of the internal energies of the initial and final states of the system, and from the actual work done by the system during the process.", "That internal energy difference is supposed to have been measured in advance through processes of purely adiabatic transfer of energy as work, processes that take the system between the initial and final states.", "By the Carathéodory way it is presupposed as known from experiment that there actually physically exist enough such adiabatic processes, so that there need be no recourse to calorimetry for measurement of quantity of energy transferred as heat.", "This presupposition is essential but is explicitly labeled neither as a law of thermodynamics nor as an axiom of the Carathéodory way.", "In fact, the actual physical existence of such adiabatic processes is indeed mostly supposition, and those supposed processes have in most cases not been actually verified empirically to exist.", "Referring to conduction, Partington writes: \"If a hot body is brought in conducting contact with a cold body, the temperature of the hot body falls and that of the cold body rises, and it is said that a \"quantity of heat\" has passed from the hot body to the cold body.", "\"\nReferring to radiation, Maxwell writes: \"In Radiation, the hotter body loses heat, and the colder body receives heat by means of a process occurring in some intervening medium which does not itself thereby become hot.\"\nMaxwell writes that convection as such \"is not a purely thermal phenomenon\".", "In thermodynamics, convection in general is regarded as transport of internal energy.", "If, however, the convection is enclosed and circulatory, then it may be regarded as an intermediary that transfers energy as heat between source and destination bodies, because it transfers only energy and not matter from the source to the destination body.", "In accordance with the first law for closed systems, energy transferred solely as heat leaves one body and enters another, changing the internal energies of each.", "Transfer, between bodies, of energy as work is a complementary way of changing internal energies.", "Though it is not logically rigorous from the viewpoint of strict physical concepts, a common form of words that expresses this is to say that heat and work are interconvertible.", "Cyclically operating engines that use only heat and work transfers have two thermal reservoirs, a hot and a cold one.", "They may be classified by the range of operating temperatures of the working body, relative to those reservoirs.", "In a heat engine, the working body is at all times colder than the hot reservoir and hotter than the cold reservoir.", "In a sense, it uses heat transfer to produce work.", "In a heat pump, the working body, at stages of the cycle, goes both hotter than the hot reservoir, and colder than the cold reservoir.", "In a sense, it uses work to produce heat transfer.", "In classical thermodynamics, a commonly considered model is the heat engine.", "It consists of four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir.", "A cyclic process leaves the working body in an unchanged state, and is envisaged as being repeated indefinitely often.", "Work transfers between the working body and the work reservoir are envisaged as reversible, and thus only one work reservoir is needed.", "But two thermal reservoirs are needed, because transfer of energy as heat is irreversible.", "A single cycle sees energy taken by the working body from the hot reservoir and sent to the two other reservoirs, the work reservoir and the cold reservoir.", "The hot reservoir always and only supplies energy and the cold reservoir always and only receives energy.", "The second law of thermodynamics requires that no cycle can occur in which no energy is received by the cold reservoir.", "Heat engines achieve higher efficiency when the ratio of the initial and final temperature is greater.", "Another commonly considered model is the heat pump or refrigerator.", "Again there are four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir.", "A single cycle starts with the working body colder than the cold reservoir, and then energy is taken in as heat by the working body from the cold reservoir.", "Then the work reservoir does work on the working body, adding more to its internal energy, making it hotter than the hot reservoir.", "The hot working body passes heat to the hot reservoir, but still remains hotter than the cold reservoir.", "Then, by allowing it to expand without passing heat to another body, the working body is made colder than the cold reservoir.", "It can now accept heat transfer from the cold reservoir to start another cycle.", "The device has transported energy from a colder to a hotter reservoir, but this is not regarded as by an inanimate agency; rather, it is regarded as by the harnessing of work .", "This is because work is supplied from the work reservoir, not just by a simple thermodynamic process, but by a cycle of thermodynamic operations and processes, which may be regarded as directed by an animate or harnessing agency.", "Accordingly, the cycle is still in accord with the second law of thermodynamics.", "The 'efficiency' of a heat pump (which exceeds unity) is best when the temperature difference between the hot and cold reservoirs is least.", "Functionally, such engines are used in two ways, distinguishing a target reservoir and a resource or surrounding reservoir.", "A heat pump transfers heat to the hot reservoir as the target from the resource or surrounding reservoir.", "A refrigerator transfers heat, from the cold reservoir as the target, to the resource or surrounding reservoir.", "The target reservoir may be regarded as leaking: when the target leaks heat to the surroundings, heat pumping is used; when the target leaks coldness to the surroundings, refrigeration is used.", "The engines harness work to overcome the leaks.", "According to Planck, there are three main conceptual approaches to heat.", "One is the microscopic or kinetic theory approach.", "The other two are macroscopic approaches.", "One is the approach through the law of conservation of energy taken as prior to thermodynamics, with a mechanical analysis of processes, for example in the work of Helmholtz.", "This mechanical view is taken in this article as currently customary for thermodynamic theory.", "The other macroscopic approach is the thermodynamic one, which admits heat as a primitive concept, which contributes, by scientific induction to knowledge of the law of conservation of energy.", "This view is widely taken as the practical one, quantity of heat being measured by calorimetry.", "Bailyn also distinguishes the two macroscopic approaches as the mechanical and the thermodynamic.", "The thermodynamic view was taken by the founders of thermodynamics in the nineteenth century.", "It regards quantity of energy transferred as heat as a primitive concept coherent with a primitive concept of temperature, measured primarily by calorimetry.", "A calorimeter is a body in the surroundings of the system, with its own temperature and internal energy; when it is connected to the system by a path for heat transfer, changes in it measure heat transfer.", "The mechanical view was pioneered by Helmholtz and developed and used in the twentieth century, largely through the influence of Max Born.", "It regards quantity of heat transferred as heat as a derived concept, defined for closed systems as quantity of heat transferred by mechanisms other than work transfer, the latter being regarded as primitive for thermodynamics, defined by macroscopic mechanics.", "According to Born, the transfer of internal energy between open systems that accompanies transfer of matter \"cannot be reduced to mechanics\".", "It follows that there is no well-founded definition of quantities of energy transferred as heat or as work associated with transfer of matter.", "Nevertheless, for the thermodynamical description of non-equilibrium processes, it is desired to consider the effect of a temperature gradient established by the surroundings across the system of interest when there is no physical barrier or wall between system and surroundings, that is to say, when they are open with respect to one another.", "The impossibility of a mechanical definition in terms of work for this circumstance does not alter the physical fact that a temperature gradient causes a diffusive flux of internal energy, a process that, in the thermodynamic view, might be proposed as a candidate concept for transfer of energy as heat.", "In this circumstance, it may be expected that there may also be active other drivers of diffusive flux of internal energy, such as gradient of chemical potential which drives transfer of matter, and gradient of electric potential which drives electric current and iontophoresis; such effects usually interact with diffusive flux of internal energy driven by temperature gradient, and such interactions are known as cross-effects.", "If cross-effects that result in diffusive transfer of internal energy were also labeled as heat transfers, they would sometimes violate the rule that pure heat transfer occurs only down a temperature gradient, never up one.", "They would also contradict the principle that all heat transfer is of one and the same kind, a principle founded on the idea of heat conduction between closed systems.", "One might to try to think narrowly of heat flux driven purely by temperature gradient as a conceptual component of diffusive internal energy flux, in the thermodynamic view, the concept resting specifically on careful calculations based on detailed knowledge of the processes and being indirectly assessed.", "In these circumstances, if perchance it happens that no transfer of matter is actualized, and there are no cross-effects, then the thermodynamic concept and the mechanical concept coincide, as if one were dealing with closed systems.", "But when there is transfer of matter, the exact laws by which temperature gradient drives diffusive flux of internal energy, rather than being exactly knowable, mostly need to be assumed, and in many cases are practically unverifiable.", "Consequently, when there is transfer of matter, the calculation of the pure 'heat flux' component of the diffusive flux of internal energy rests on practically unverifiable assumptions.", "This is a reason to think of heat as a specialized concept that relates primarily and precisely to closed systems, and applicable only in a very restricted way to open systems.", "In many writings in this context, the term \"heat flux\" is used when what is meant is therefore more accurately called diffusive flux of internal energy; such usage of the term \"heat flux\" is a residue of older and now obsolete language usage that allowed that a body may have a \"heat content\".", "In the kinetic theory, heat is explained in terms of the microscopic motions and interactions of constituent particles, such as electrons, atoms, and molecules.", "The immediate meaning of the kinetic energy of the constituent particles is not as heat.", "It is as a component of internal energy.", "In microscopic terms, heat is a transfer quantity, and is described by a transport theory, not as steadily localized kinetic energy of particles.", "Heat transfer arises from temperature gradients or differences, through the diffuse exchange of microscopic kinetic and potential particle energy, by particle collisions and other interactions.", "An early and vague expression of this was made by Francis Bacon.", "Precise and detailed versions of it were developed in the nineteenth century.", "In statistical mechanics, for a closed system (no transfer of matter), heat is the energy transfer associated with a disordered, microscopic action on the system, associated with jumps in occupation numbers of the energy levels of the system, without change in the values of the energy levels themselves.", "It is possible for macroscopic thermodynamic work to alter the occupation numbers without change in the values of the system energy levels themselves, but what distinguishes transfer as heat is that the transfer is entirely due to disordered, microscopic action, including radiative transfer.", "A mathematical definition can be formulated for small increments of quasi-static adiabatic work in terms of the statistical distribution of an ensemble of microstates.", "Quantity of heat transferred can be measured by calorimetry, or determined through calculations based on other quantities.", "Calorimetry is the empirical basis of the idea of quantity of heat transferred in a process.", "The transferred heat is measured by changes in a body of known properties, for example, temperature rise, change in volume or length, or phase change, such as melting of ice.", "A calculation of quantity of heat transferred can rely on a hypothetical quantity of energy transferred as adiabatic work and on the first law of thermodynamics.", "Such calculation is the primary approach of many theoretical studies of quantity of heat transferred.", "The discipline of heat transfer, typically considered an aspect of mechanical engineering and chemical engineering, deals with specific applied methods by which thermal energy in a system is generated, or converted, or transferred to another system.", "Although the definition of heat implicitly means the transfer of energy, the term \"heat transfer\" encompasses this traditional usage in many engineering disciplines and laymen language.", "\"Heat transfer\" is generally described as including the mechanisms of heat conduction, heat convection, thermal radiation, but may include mass transfer and heat in processes of phase changes.", "Convection may be described as the combined effects of conduction and fluid flow.", "From the thermodynamic point of view, heat flows into a fluid by diffusion to increase its energy, the fluid then transfers (advects) this increased internal energy (not heat) from one location to another, and this is then followed by a second thermal interaction which transfers heat to a second body or system, again by diffusion.", "This entire process is often regarded as an additional mechanism of heat transfer, although technically, \"heat transfer\" and thus heating and cooling occurs only on either end of such a conductive flow, but not as a result of flow.", "Thus, conduction can be said to \"transfer\" heat only as a net result of the process, but may not do so at every time within the complicated convective process.", "In an 1847 lecture entitled \"On Matter, Living Force, and Heat\", James Prescott Joule characterized the terms latent heat and sensible heat as components of heat each affecting distinct physical phenomena, namely the potential and kinetic energy of particles, respectively.", "He described latent energy as the energy possessed via a distancing of particles where attraction was over a greater distance, i.e. a form of potential energy, and the sensible heat as an energy involving the motion of particles, i.e. kinetic energy.", "Latent heat is the heat released or absorbed by a chemical substance or a thermodynamic system during a change of state that occurs without a change in temperature.", "Such a process may be a phase transition, such as the melting of ice or the boiling of water.", "Heat capacity is a measurable physical quantity equal to the ratio of the heat added to an object to the resulting temperature change.", "The \"molar heat capacity\" is the heat capacity per unit amount (SI unit: mole) of a pure substance, and the \"specific heat capacity\", often called simply \"specific heat\", is the heat capacity per unit mass of a material.", "Heat capacity is a physical property of a substance, which means that it depends on the state and properties of the substance under consideration.", "The specific heats of monatomic gases, such as helium, are nearly constant with temperature.", "Diatomic gases such as hydrogen display some temperature dependence, and triatomic gases (e.g., carbon dioxide) still more.", "Before the development of the laws of thermodynamics, heat was measured by changes in the states of the participating bodies.", "Some general rules, with important exceptions, can be stated as follows.", "In general, most bodies expand on heating.", "In this circumstance, heating a body at a constant volume increases the pressure it exerts on its constraining walls, while heating at a constant pressure increases its volume.", "Beyond this, most substances have three ordinarily recognized states of matter, solid, liquid, and gas.", "Some can also exist in a plasma.", "Many have further, more finely differentiated, states of matter, such as glass and liquid crystal.", "In many cases, at fixed temperature and pressure, a substance can exist in several distinct states of matter in what might be viewed as the same 'body'.", "For example, ice may float in a glass of water.", "Then the ice and the water are said to constitute two phases within the 'body'.", "Definite rules are known, telling how distinct phases may coexist in a 'body'.", "Mostly, at a fixed pressure, there is a definite temperature at which heating causes a solid to melt or evaporate, and a definite temperature at which heating causes a liquid to evaporate.", "In such cases, cooling has the reverse effects.", "All of these, the commonest cases, fit with a rule that heating can be measured by changes of state of a body.", "Such cases supply what are called \"thermometric bodies\", that allow the definition of empirical temperatures.", "Before 1848, all temperatures were defined in this way.", "There was thus a tight link, apparently logically determined, between heat and temperature, though they were recognized as conceptually thoroughly distinct, especially by Joseph Black in the later eighteenth century.", "There are important exceptions.", "They break the obviously apparent link between heat and temperature.", "They make it clear that empirical definitions of temperature are contingent on the peculiar properties of particular thermometric substances, and are thus precluded from the title 'absolute'.", "For example, water contracts on being heated near 277 K. It cannot be used as a thermometric substance near that temperature.", "Also, over a certain temperature range, ice contracts on heating.", "Moreover, many substances can exist in metastable states, such as with negative pressure, that survive only transiently and in very special conditions.", "Such facts, sometimes called 'anomalous', are some of the reasons for the thermodynamic definition of absolute temperature.", "In the early days of measurement of high temperatures, another factor was important, and used by Josiah Wedgwood in his pyrometer.", "The temperature reached in a process was estimated by the shrinkage of a sample of clay.", "The higher the temperature, the more the shrinkage.", "This was the only available more or less reliable method of measurement of temperatures above 1000 °C (1,832 °F).", "But such shrinkage is irreversible.", "The clay does not expand again on cooling.", "That is why it could be used for the measurement.", "But only once.", "It is not a thermometric material in the usual sense of the word.", "Nevertheless, the thermodynamic definition of absolute temperature does make essential use of the concept of heat, with proper circumspection.", "According to Denbigh (1981), the property of hotness is a concern of thermodynamics that should be defined without reference to the concept of heat.", "Consideration of hotness leads to the concept of empirical temperature.", "All physical systems are capable of heating or cooling others.", "With reference to hotness, the comparative terms hotter and colder are defined by the rule that heat flows from the hotter body to the colder.", "If a physical system is inhomogeneous or very rapidly or irregularly changing, for example by turbulence, it may be impossible to characterize it by a temperature, but still there can be transfer of energy as heat between it and another system.", "If a system has a physical state that is regular enough, and persists long enough to allow it to reach thermal equilibrium with a specified thermometer, then it has a temperature according to that thermometer.", "An empirical thermometer registers degree of hotness for such a system.", "Such a temperature is called empirical.", "For example, Truesdell writes about classical thermodynamics: \"At each time, the body is assigned a real number called the \"temperature\".", "This number is a measure of how hot the body is.", "\"\nPhysical systems that are too turbulent to have temperatures may still differ in hotness.", "A physical system that passes heat to another physical system is said to be the hotter of the two.", "More is required for the system to have a thermodynamic temperature.", "Its behavior must be so regular that its empirical temperature is the same for all suitably calibrated and scaled thermometers, and then its hotness is said to lie on the one-dimensional hotness manifold.", "This is part of the reason why heat is defined following Carathéodory and Born, solely as occurring other than by work or transfer of matter; temperature is advisedly and deliberately not mentioned in this now widely accepted definition.", "This is also the reason that the zeroth law of thermodynamics is stated explicitly.", "If three physical systems, \"A\", \"B\", and \"C\" are each not in their own states of internal thermodynamic equilibrium, it is possible that, with suitable physical connections being made between them, \"A\" can heat \"B\" and \"B\" can heat \"C\" and \"C\" can heat \"A\".", "In non-equilibrium situations, cycles of flow are possible.", "It is the special and uniquely distinguishing characteristic of internal thermodynamic equilibrium that this possibility is not open to thermodynamic systems (as distinguished amongst physical systems) which are in their own states of internal thermodynamic equilibrium; this is the reason why the zeroth law of thermodynamics needs explicit statement.", "That is to say, the relation 'is not colder than' between general non-equilibrium physical systems is not transitive, whereas, in contrast, the relation 'has no lower a temperature than' between thermodynamic systems in their own states of internal thermodynamic equilibrium is transitive.", "It follows from this that the relation 'is in thermal equilibrium with' is transitive, which is one way of stating the zeroth law.", "Just as temperature may be undefined for a sufficiently inhomogeneous system, so also may entropy be undefined for a system not in its own state of internal thermodynamic equilibrium.", "For example, 'the temperature of the solar system' is not a defined quantity.", "Likewise, 'the entropy of the solar system' is not defined in classical thermodynamics.", "It has not been possible to define non-equilibrium entropy, as a simple number for a whole system, in a clearly satisfactory way." ]

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[ "Like thermodynamic work, heat transfer involves the surroundings of a system, as well as the system itself, and so is not a property of the system alone, though it contributes to change in the system's internal energy, which is a property of the system alone.", "Though not immediately by the definition, but in special kinds of process, quantity of energy transferred as heat can be measured by its effect on the states of interacting bodies." ]

[ "The mechanisms of energy transfer that define heat include conduction, through direct contact of immobile bodies, or through a wall or barrier that is impermeable to matter; or radiation between separated bodies; or friction due to isochoric mechanical or electrical or magnetic or gravitational work done by the surroundings on the system of interest, such as Joule heating due to an electric current driven through the system of interest by an external system, or through a magnetic stirrer.", "When there is a suitable path between two systems with different temperatures, heat transfer occurs necessarily, immediately, and spontaneously from the hotter to the colder system.", "Thermal conduction occurs by the stochastic (random) motion of microscopic particles (such as atoms or molecules).", "In contrast, thermodynamic work is defined by mechanisms that act macroscopically and directly on the system's whole-body state variables; for example, change of the system's volume through a piston's motion with externally measurable force; or change of the system's internal electric polarization through an externally measurable change in electric field.", "The definition of heat transfer does not require that the process be in any sense smooth.", "For example, a bolt of lightning may transfer heat to a body.", "Convective circulation allows one body to heat another, through an intermediate circulating fluid that carries energy from a boundary of one to a boundary of the other; the actual heat transfer is by conduction and radiation between the fluid and the respective bodies.", "Convective circulation, though spontaneous, does not necessarily and immediately occur simply because of some slight temperature difference; for it to occur in a given arrangement of systems, there is a threshold that must be crossed.", "Although heat flows spontaneously from a hotter body to a cooler one, it is possible to construct a heat pump which expends work to transfer energy from a colder body to a hotter body.", "In contrast, a heat engine reduces an existing temperature difference to supply work to another system.", "Another thermodynamic type of heat transfer device is an active heat spreader, which expends work to speed up transfer of energy to colder surroundings from a hotter body, for example a computer component.", "As a form of energy, heat has the unit joule (J) in the International System of Units (SI).", "However, in many applied fields in engineering the British thermal unit (BTU) and the calorie are often used.", "The standard unit for the rate of heat transferred is the watt (W), defined as one joule per second.", "The symbol for the total amount of energy transferred as heat was used by Rudolf Clausius in 1850:\n\"Let the amount of heat which must be imparted during the transition of the gas in a definite manner from any given state to another, in which its volume is \"v\" and its temperature \"t\", be called \"Q\"\"\nHeat released by a system into its surroundings is by convention a negative quantity (); when a system absorbs heat from its surroundings, it is positive ().", "Heat transfer rate, or heat flow per unit time, is denoted by formula_1.", "This should not be confused with a time derivative of a function of state (which can also be written with the dot notation) since heat is not a function of state.", "Heat flux is defined as rate of heat transfer per unit cross-sectional area (units watts per square metre).", "In 1856, Rudolf Clausius, referring to closed systems, in which transfers of matter do not occur, defined the \"second fundamental theorem\" (the second law of thermodynamics) in the mechanical theory of heat (thermodynamics): \"if two transformations which, without necessitating any other permanent change, can mutually replace one another, be called equivalent, then the generations of the quantity of heat \"Q\" from work at the temperature \"T\", has the \"equivalence-value\":\"\nformula_2\nIn 1865, he came to define the entropy symbolized by \"S\", such that, due to the supply of the amount of heat \"Q\" at temperature \"T\" the entropy of the system is increased by\nIn a transfer of energy as heat without work being done, there are changes of entropy in both the surroundings which lose heat and the system which gains it.", "The increase, , of entropy in the system may be considered to consist of two parts, an increment, that matches, or 'compensates', the change, , of entropy in the surroundings, and a further increment, that may be considered to be 'generated' or 'produced' in the system, and is said therefore to be 'uncompensated'.", "Thus\nformula_3\nThis may also be written\nformula_4\nThe total change of entropy in the system and surroundings is thus\nformula_5\nThis may also be written\nformula_6\nIt is then said that an amount of entropy has been transferred from the surroundings to the system.", "Because entropy is not a conserved quantity, this is an exception to the general way of speaking, in which an amount transferred is of a conserved quantity.", "From the second law of thermodynamics follows that in a spontaneous transfer of heat, in which the temperature of the system is different from that of the surroundings:\nformula_7\nFor purposes of mathematical analysis of transfers, one thinks of fictive processes that are called \"reversible\", with the temperature of the system being hardly less than that of the surroundings, and the transfer taking place at an imperceptibly slow rate.", "Following the definition above in formula (), for such a fictive reversible process, a quantity of transferred heat (an inexact differential) is analyzed as a quantity , with (an exact differential):\nformula_8\nThis equality is only valid for a fictive transfer in which there is no production of entropy, that is to say, in which there is no uncompensated entropy.", "If, in contrast, the process is natural, and can really occur, with irreversibility, then there is entropy production, with .", "The quantity was termed by Clausius the \"uncompensated heat\", though that does not accord with present-day terminology.", "Then one has\nformula_9\nThis leads to the statement\nformula_10\nwhich is the second law of thermodynamics for closed systems.", "In non-equilibrium thermodynamics that makes the approximation of assuming the hypothesis of local thermodynamic equilibrium, there is a special notation for this.", "The transfer of energy as heat is assumed to take place across an infinitesimal temperature difference, so that the system element and its surroundings have near enough the same temperature .", "Then one writes\nformula_11\nwhere by definition\nformula_12\nThe second law for a natural process asserts that\nformula_13", "For a closed system (a system from which no matter can enter or exit), one version of the first law of thermodynamics states that the change in internal energy of the system is equal to the amount of heat supplied to the system minus the amount of thermodynamic work done by system on its surroundings.", "The foregoing sign convention for work is used in the present article, but an alternate sign convention, followed by IUPAC, for work, is to consider the work performed on the system by its surroundings as positive.", "This is the convention adopted by many modern textbooks of physical chemistry, such as those by Peter Atkins and Ira Levine, but many textbooks on physics define work as work done by the system.", "formula_14\nThis formula can be re-written so as to express a definition of quantity of energy transferred as heat, based purely on the concept of adiabatic work, if it is supposed that is defined and measured solely by processes of adiabatic work:\nformula_15\nThe thermodynamic work done by the system is through mechanisms defined by its thermodynamic state variables, for example, its volume , not through variables that necessarily involve mechanisms in the surroundings.", "The latter are such as shaft work, and include isochoric work.", "The internal energy, , is a state function.", "In cyclical processes, such as the operation of a heat engine, state functions of the working substance return to their initial values upon completion of a cycle.", "The differential, or infinitesimal increment, for the internal energy in an infinitesimal process is an exact differential .", "The symbol for exact differentials is the lowercase letter .", "In contrast, neither of the infinitesimal increments nor in an infinitesimal process represents the change in a state function of the system.", "Thus, infinitesimal increments of heat and work are inexact differentials.", "The lowercase Greek letter delta, , is the symbol for inexact differentials.", "The integral of any inexact differential in a process where the system leaves and then returns to the same thermodynamic state does not necessarily equal zero.", "As recounted above, in the section headed \"heat and entropy\", the second law of thermodynamics observes that if heat is supplied to a system in a reversible process, the increment of heat and the temperature form the exact differential\nformula_16\nand that , the entropy of the working body, is a state function.", "Likewise, with a well-defined pressure, , behind a slowly moving (quasistatic) boundary, the work differential, , and the pressure, , combine to form the exact differential\nformula_17\nwith the volume of the system, which is a state variable.", "In general, for systems of uniform pressure and temperature without composition change,\nformula_18\nAssociated with this differential equation is the concept that the internal energy may be considered to be a function of its natural variables and .", "The internal energy representation of the fundamental thermodynamic relation is written as\nformula_19\nIf is constant\nformula_20\nand if is constant\nformula_21\nwith the enthalpy defined by\nformula_22\nThe enthalpy may be considered to be a function of its natural variables and .", "The enthalpy representation of the fundamental thermodynamic relation is written\nformula_23\nThe internal energy representation and the enthalpy representation are partial Legendre transforms of one another.", "They contain the same physical information, written in different ways.", "Like the internal energy, the enthalpy stated as a function of its natural variables is a thermodynamic potential and contains all thermodynamic information about a body.", "If a quantity of heat is added to a body while it does only expansion work on its surroundings, one has\nformula_24\nIf this is constrained to happen at constant pressure, i.e. with , the expansion work done by the body is given by ; recalling the first law of thermodynamics, one has\nformula_25\nConsequently, by substitution one has\nformula_26\nIn this scenario, the increase in enthalpy is equal to the quantity of heat added to the system.", "This is the basis of the determination of enthalpy changes in chemical reactions by calorimetry.", "Since many processes do take place at constant atmospheric pressure, the enthalpy is sometimes given the misleading name of 'heat content' or heat function, while it actually depends strongly on the energies of covalent bonds and intermolecular forces.", "In terms of the natural variables of the state function , this process of change of state from state 1 to state 2 can be expressed as\nformula_27\nIt is known that the temperature is identically stated by\nformula_28\nConsequently,\nformula_29\nIn this case, the integral specifies a quantity of heat transferred at constant pressure.", "As a common noun, English \"heat\" or \"warmth\" (just as French \"chaleur\", German \"Wärme\", Latin \"calor\", Greek θάλπος, etc.) refers to (the human perception of) either thermal energy or temperature.", "Speculation on thermal energy or \"heat\" as a separate form of matter has a long history, see caloric theory, phlogiston and fire (classical element).", "The modern understanding of thermal energy originates with Thompson's 1798 mechanical theory of heat (\"An Experimental Enquiry Concerning the Source of the Heat which is Excited by Friction\"), postulating a mechanical equivalent of heat.", "A collaboration between Nicolas Clément and Sadi Carnot (\"Reflections on the Motive Power of Fire\") in the 1820s had some related thinking along similar lines.", "In 1845, Joule published a paper entitled \"The Mechanical Equivalent of Heat\", in which he specified a numerical value for the amount of mechanical work required to \"produce a unit of heat\".", "The theory of classical thermodynamics matured in the 1850s to 1860s.", "John Tyndall's \"Heat Considered as Mode of Motion\" (1863) was instrumental in popularizing the idea of heat as motion to the English-speaking public.", "The theory was developed in academic publications in French, English and German.", "From an early time, the French technical term \"chaleur\" used by Carnot was taken as equivalent to the English \"heat\" and German \"Wärme\" (lit.", "\"warmth\", while the equivalent of \"heat\" would be German \"Hitze\").", "The process function was introduced by Rudolf Clausius in 1850.", "Clausius described it with the German compound \"Wärmemenge\", translated as \"amount of heat\".", "James Clerk Maxwell in his 1871 \"Theory of Heat\" outlines four stipulations for the definition of heat:\n\n\nThe process function is referred to as \"Wärmemenge\" by Clausius, or as \"amount of heat\" in translation.", "Use of \"heat\" as an abbreviated form of the specific concept of \"quantity of energy transferred as heat\" led to some terminological confusion by the early 20th century.", "The generic meaning of \"heat\", even in classical thermodynamics, is just \"thermal energy\".", "Since the 1920s, it has been recommended practice to use enthalpy to refer to the \"heat content at constant volume\", and to thermal energy when \"heat\" in the general sense is intended, while \"heat\" is reserved for the very specific context of the transfer of thermal energy between two systems.", "Leonard Benedict Loeb in his \"Kinetic Theory of Gases\" (1927) makes a point of using \"quantity of heat\"\nor \"heat–quantity\" when referring to :", "After the perfection of thermometry [...] the next great advance made in the field of heat was the definition of a term which is called the quantity of heat.", "[... after the abandonment of caloric theory,] It still remains to interpret this very definite concept, the quantity of heat, in terms of a theory ascribing all heat to the kinetics of gas molecules.", "A frequent definition of heat is based on the work of Carathéodory (1909), referring to processes in a closed system.", "The internal energy of a body in an arbitrary state can be determined by amounts of work adiabatically performed by the body on its surroundings when it starts from a reference state .", "Such work is assessed through quantities defined in the surroundings of the body.", "It is supposed that such work can be assessed accurately, without error due to friction in the surroundings; friction in the body is not excluded by this definition.", "The adiabatic performance of work is defined in terms of adiabatic walls, which allow transfer of energy as work, but no other transfer, of energy or matter.", "In particular they do not allow the passage of energy as heat.", "According to this definition, work performed adiabatically is in general accompanied by friction within the thermodynamic system or body.", "On the other hand, according to Carathéodory (1909), there also exist non-adiabatic, \"diathermal\" walls, which are postulated to be permeable only to heat.", "For the definition of quantity of energy transferred as heat, it is customarily envisaged that an arbitrary state of interest is reached from state by a process with two components, one adiabatic and the other not adiabatic.", "For convenience one may say that the adiabatic component was the sum of work done by the body through volume change through movement of the walls while the non-adiabatic wall was temporarily rendered adiabatic, and of isochoric adiabatic work.", "Then the non-adiabatic component is a process of energy transfer through the wall that passes only heat, newly made accessible for the purpose of this transfer, from the surroundings to the body.", "The change in internal energy to reach the state from the state is the difference of the two amounts of energy transferred.", "Although Carathéodory himself did not state such a definition, following his work it is customary in theoretical studies to define heat, , to the body from its surroundings, in the combined process of change to state from the state , as the change in internal energy, , minus the amount of work, , done by the body on its surrounds by the adiabatic process, so that .", "In this definition, for the sake of conceptual rigour, the quantity of energy transferred as heat is not specified directly in terms of the non-adiabatic process.", "It is defined through knowledge of precisely two variables, the change of internal energy and the amount of adiabatic work done, for the combined process of change from the reference state to the arbitrary state .", "It is important that this does not explicitly involve the amount of energy transferred in the non-adiabatic component of the combined process.", "It is assumed here that the amount of energy required to pass from state to state , the change of internal energy, is known, independently of the combined process, by a determination through a purely adiabatic process, like that for the determination of the internal energy of state above.", "The rigour that is prized in this definition is that there is one and only one kind of energy transfer admitted as fundamental: energy transferred as work.", "Energy transfer as heat is considered as a derived quantity.", "The uniqueness of work in this scheme is considered to guarantee rigor and purity of conception.", "The conceptual purity of this definition, based on the concept of energy transferred as work as an ideal notion, relies on the idea that some frictionless and otherwise non-dissipative processes of energy transfer can be realized in physical actuality.", "The second law of thermodynamics, on the other hand, assures us that such processes are not found in nature.", "Before the rigorous mathematical definition of heat based on Carathéodory's 1909 paper,\nhistorically, heat, temperature, and thermal equilibrium were presented in thermodynamics textbooks as jointly primitive notions.", "Carathéodory introduced his 1909 paper thus: \"The proposition that the discipline of thermodynamics can be justified without recourse to any hypothesis that cannot be verified experimentally must be regarded as one of the most noteworthy results of the research in thermodynamics that was accomplished during the last century.\"", "Referring to the \"point of view adopted by most authors who were active in the last fifty years\", Carathéodory wrote: \"There exists a physical quantity called heat that is not identical with the mechanical quantities (mass, force, pressure, etc.) and whose variations can be determined by calorimetric measurements.\"", "James Serrin introduces an account of the theory of thermodynamics thus: \"In the following section, we shall use the classical notions of \"heat\", \"work\", and \"hotness\" as primitive elements, ...", "That heat is an appropriate and natural primitive for thermodynamics was already accepted by Carnot.", "Its continued validity as a primitive element of thermodynamical structure is due to the fact that it synthesizes an essential physical concept, as well as to its successful use in recent work to unify different constitutive theories.\"", "This traditional kind of presentation of the basis of thermodynamics includes ideas that may be summarized by the statement that heat transfer is purely due to spatial non-uniformity of temperature, and is by conduction and radiation, from hotter to colder bodies.", "It is sometimes proposed that this traditional kind of presentation necessarily rests on \"circular reasoning\"; against this proposal, there stands the rigorously logical mathematical development of the theory presented by Truesdell and Bharatha (1977).", "This alternative approach to the definition of quantity of energy transferred as heat differs in logical structure from that of Carathéodory, recounted just above.", "This alternative approach admits calorimetry as a primary or direct way to measure quantity of energy transferred as heat.", "It relies on temperature as one of its primitive concepts, and used in calorimetry.", "It is presupposed that enough processes exist physically to allow measurement of differences in internal energies.", "Such processes are not restricted to adiabatic transfers of energy as work.", "They include calorimetry, which is the commonest practical way of finding internal energy differences.", "The needed temperature can be either empirical or absolute thermodynamic.", "In contrast, the Carathéodory way recounted just above does not use calorimetry or temperature in its primary definition of quantity of energy transferred as heat.", "The Carathéodory way regards calorimetry only as a secondary or indirect way of measuring quantity of energy transferred as heat.", "As recounted in more detail just above, the Carathéodory way regards quantity of energy transferred as heat in a process as primarily or directly defined as a residual quantity.", "It is calculated from the difference of the internal energies of the initial and final states of the system, and from the actual work done by the system during the process.", "That internal energy difference is supposed to have been measured in advance through processes of purely adiabatic transfer of energy as work, processes that take the system between the initial and final states.", "By the Carathéodory way it is presupposed as known from experiment that there actually physically exist enough such adiabatic processes, so that there need be no recourse to calorimetry for measurement of quantity of energy transferred as heat.", "This presupposition is essential but is explicitly labeled neither as a law of thermodynamics nor as an axiom of the Carathéodory way.", "In fact, the actual physical existence of such adiabatic processes is indeed mostly supposition, and those supposed processes have in most cases not been actually verified empirically to exist.", "Referring to conduction, Partington writes: \"If a hot body is brought in conducting contact with a cold body, the temperature of the hot body falls and that of the cold body rises, and it is said that a \"quantity of heat\" has passed from the hot body to the cold body.", "\"\nReferring to radiation, Maxwell writes: \"In Radiation, the hotter body loses heat, and the colder body receives heat by means of a process occurring in some intervening medium which does not itself thereby become hot.\"\nMaxwell writes that convection as such \"is not a purely thermal phenomenon\".", "In thermodynamics, convection in general is regarded as transport of internal energy.", "If, however, the convection is enclosed and circulatory, then it may be regarded as an intermediary that transfers energy as heat between source and destination bodies, because it transfers only energy and not matter from the source to the destination body.", "In accordance with the first law for closed systems, energy transferred solely as heat leaves one body and enters another, changing the internal energies of each.", "Transfer, between bodies, of energy as work is a complementary way of changing internal energies.", "Though it is not logically rigorous from the viewpoint of strict physical concepts, a common form of words that expresses this is to say that heat and work are interconvertible.", "Cyclically operating engines that use only heat and work transfers have two thermal reservoirs, a hot and a cold one.", "They may be classified by the range of operating temperatures of the working body, relative to those reservoirs.", "In a heat engine, the working body is at all times colder than the hot reservoir and hotter than the cold reservoir.", "In a sense, it uses heat transfer to produce work.", "In a heat pump, the working body, at stages of the cycle, goes both hotter than the hot reservoir, and colder than the cold reservoir.", "In a sense, it uses work to produce heat transfer.", "In classical thermodynamics, a commonly considered model is the heat engine.", "It consists of four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir.", "A cyclic process leaves the working body in an unchanged state, and is envisaged as being repeated indefinitely often.", "Work transfers between the working body and the work reservoir are envisaged as reversible, and thus only one work reservoir is needed.", "But two thermal reservoirs are needed, because transfer of energy as heat is irreversible.", "A single cycle sees energy taken by the working body from the hot reservoir and sent to the two other reservoirs, the work reservoir and the cold reservoir.", "The hot reservoir always and only supplies energy and the cold reservoir always and only receives energy.", "The second law of thermodynamics requires that no cycle can occur in which no energy is received by the cold reservoir.", "Heat engines achieve higher efficiency when the ratio of the initial and final temperature is greater.", "Another commonly considered model is the heat pump or refrigerator.", "Again there are four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir.", "A single cycle starts with the working body colder than the cold reservoir, and then energy is taken in as heat by the working body from the cold reservoir.", "Then the work reservoir does work on the working body, adding more to its internal energy, making it hotter than the hot reservoir.", "The hot working body passes heat to the hot reservoir, but still remains hotter than the cold reservoir.", "Then, by allowing it to expand without passing heat to another body, the working body is made colder than the cold reservoir.", "It can now accept heat transfer from the cold reservoir to start another cycle.", "The device has transported energy from a colder to a hotter reservoir, but this is not regarded as by an inanimate agency; rather, it is regarded as by the harnessing of work .", "This is because work is supplied from the work reservoir, not just by a simple thermodynamic process, but by a cycle of thermodynamic operations and processes, which may be regarded as directed by an animate or harnessing agency.", "Accordingly, the cycle is still in accord with the second law of thermodynamics.", "The 'efficiency' of a heat pump (which exceeds unity) is best when the temperature difference between the hot and cold reservoirs is least.", "Functionally, such engines are used in two ways, distinguishing a target reservoir and a resource or surrounding reservoir.", "A heat pump transfers heat to the hot reservoir as the target from the resource or surrounding reservoir.", "A refrigerator transfers heat, from the cold reservoir as the target, to the resource or surrounding reservoir.", "The target reservoir may be regarded as leaking: when the target leaks heat to the surroundings, heat pumping is used; when the target leaks coldness to the surroundings, refrigeration is used.", "The engines harness work to overcome the leaks.", "According to Planck, there are three main conceptual approaches to heat.", "One is the microscopic or kinetic theory approach.", "The other two are macroscopic approaches.", "One is the approach through the law of conservation of energy taken as prior to thermodynamics, with a mechanical analysis of processes, for example in the work of Helmholtz.", "This mechanical view is taken in this article as currently customary for thermodynamic theory.", "The other macroscopic approach is the thermodynamic one, which admits heat as a primitive concept, which contributes, by scientific induction to knowledge of the law of conservation of energy.", "This view is widely taken as the practical one, quantity of heat being measured by calorimetry.", "Bailyn also distinguishes the two macroscopic approaches as the mechanical and the thermodynamic.", "The thermodynamic view was taken by the founders of thermodynamics in the nineteenth century.", "It regards quantity of energy transferred as heat as a primitive concept coherent with a primitive concept of temperature, measured primarily by calorimetry.", "A calorimeter is a body in the surroundings of the system, with its own temperature and internal energy; when it is connected to the system by a path for heat transfer, changes in it measure heat transfer.", "The mechanical view was pioneered by Helmholtz and developed and used in the twentieth century, largely through the influence of Max Born.", "It regards quantity of heat transferred as heat as a derived concept, defined for closed systems as quantity of heat transferred by mechanisms other than work transfer, the latter being regarded as primitive for thermodynamics, defined by macroscopic mechanics.", "According to Born, the transfer of internal energy between open systems that accompanies transfer of matter \"cannot be reduced to mechanics\".", "It follows that there is no well-founded definition of quantities of energy transferred as heat or as work associated with transfer of matter.", "Nevertheless, for the thermodynamical description of non-equilibrium processes, it is desired to consider the effect of a temperature gradient established by the surroundings across the system of interest when there is no physical barrier or wall between system and surroundings, that is to say, when they are open with respect to one another.", "The impossibility of a mechanical definition in terms of work for this circumstance does not alter the physical fact that a temperature gradient causes a diffusive flux of internal energy, a process that, in the thermodynamic view, might be proposed as a candidate concept for transfer of energy as heat.", "In this circumstance, it may be expected that there may also be active other drivers of diffusive flux of internal energy, such as gradient of chemical potential which drives transfer of matter, and gradient of electric potential which drives electric current and iontophoresis; such effects usually interact with diffusive flux of internal energy driven by temperature gradient, and such interactions are known as cross-effects.", "If cross-effects that result in diffusive transfer of internal energy were also labeled as heat transfers, they would sometimes violate the rule that pure heat transfer occurs only down a temperature gradient, never up one.", "They would also contradict the principle that all heat transfer is of one and the same kind, a principle founded on the idea of heat conduction between closed systems.", "One might to try to think narrowly of heat flux driven purely by temperature gradient as a conceptual component of diffusive internal energy flux, in the thermodynamic view, the concept resting specifically on careful calculations based on detailed knowledge of the processes and being indirectly assessed.", "In these circumstances, if perchance it happens that no transfer of matter is actualized, and there are no cross-effects, then the thermodynamic concept and the mechanical concept coincide, as if one were dealing with closed systems.", "But when there is transfer of matter, the exact laws by which temperature gradient drives diffusive flux of internal energy, rather than being exactly knowable, mostly need to be assumed, and in many cases are practically unverifiable.", "Consequently, when there is transfer of matter, the calculation of the pure 'heat flux' component of the diffusive flux of internal energy rests on practically unverifiable assumptions.", "This is a reason to think of heat as a specialized concept that relates primarily and precisely to closed systems, and applicable only in a very restricted way to open systems.", "In many writings in this context, the term \"heat flux\" is used when what is meant is therefore more accurately called diffusive flux of internal energy; such usage of the term \"heat flux\" is a residue of older and now obsolete language usage that allowed that a body may have a \"heat content\".", "In the kinetic theory, heat is explained in terms of the microscopic motions and interactions of constituent particles, such as electrons, atoms, and molecules.", "The immediate meaning of the kinetic energy of the constituent particles is not as heat.", "It is as a component of internal energy.", "In microscopic terms, heat is a transfer quantity, and is described by a transport theory, not as steadily localized kinetic energy of particles.", "Heat transfer arises from temperature gradients or differences, through the diffuse exchange of microscopic kinetic and potential particle energy, by particle collisions and other interactions.", "An early and vague expression of this was made by Francis Bacon.", "Precise and detailed versions of it were developed in the nineteenth century.", "In statistical mechanics, for a closed system (no transfer of matter), heat is the energy transfer associated with a disordered, microscopic action on the system, associated with jumps in occupation numbers of the energy levels of the system, without change in the values of the energy levels themselves.", "It is possible for macroscopic thermodynamic work to alter the occupation numbers without change in the values of the system energy levels themselves, but what distinguishes transfer as heat is that the transfer is entirely due to disordered, microscopic action, including radiative transfer.", "A mathematical definition can be formulated for small increments of quasi-static adiabatic work in terms of the statistical distribution of an ensemble of microstates.", "Quantity of heat transferred can be measured by calorimetry, or determined through calculations based on other quantities.", "Calorimetry is the empirical basis of the idea of quantity of heat transferred in a process.", "The transferred heat is measured by changes in a body of known properties, for example, temperature rise, change in volume or length, or phase change, such as melting of ice.", "A calculation of quantity of heat transferred can rely on a hypothetical quantity of energy transferred as adiabatic work and on the first law of thermodynamics.", "Such calculation is the primary approach of many theoretical studies of quantity of heat transferred.", "The discipline of heat transfer, typically considered an aspect of mechanical engineering and chemical engineering, deals with specific applied methods by which thermal energy in a system is generated, or converted, or transferred to another system.", "Although the definition of heat implicitly means the transfer of energy, the term \"heat transfer\" encompasses this traditional usage in many engineering disciplines and laymen language.", "\"Heat transfer\" is generally described as including the mechanisms of heat conduction, heat convection, thermal radiation, but may include mass transfer and heat in processes of phase changes.", "Convection may be described as the combined effects of conduction and fluid flow.", "From the thermodynamic point of view, heat flows into a fluid by diffusion to increase its energy, the fluid then transfers (advects) this increased internal energy (not heat) from one location to another, and this is then followed by a second thermal interaction which transfers heat to a second body or system, again by diffusion.", "This entire process is often regarded as an additional mechanism of heat transfer, although technically, \"heat transfer\" and thus heating and cooling occurs only on either end of such a conductive flow, but not as a result of flow.", "Thus, conduction can be said to \"transfer\" heat only as a net result of the process, but may not do so at every time within the complicated convective process.", "In an 1847 lecture entitled \"On Matter, Living Force, and Heat\", James Prescott Joule characterized the terms latent heat and sensible heat as components of heat each affecting distinct physical phenomena, namely the potential and kinetic energy of particles, respectively.", "He described latent energy as the energy possessed via a distancing of particles where attraction was over a greater distance, i.e. a form of potential energy, and the sensible heat as an energy involving the motion of particles, i.e. kinetic energy.", "Latent heat is the heat released or absorbed by a chemical substance or a thermodynamic system during a change of state that occurs without a change in temperature.", "Such a process may be a phase transition, such as the melting of ice or the boiling of water.", "Heat capacity is a measurable physical quantity equal to the ratio of the heat added to an object to the resulting temperature change.", "The \"molar heat capacity\" is the heat capacity per unit amount (SI unit: mole) of a pure substance, and the \"specific heat capacity\", often called simply \"specific heat\", is the heat capacity per unit mass of a material.", "Heat capacity is a physical property of a substance, which means that it depends on the state and properties of the substance under consideration.", "The specific heats of monatomic gases, such as helium, are nearly constant with temperature.", "Diatomic gases such as hydrogen display some temperature dependence, and triatomic gases (e.g., carbon dioxide) still more.", "Before the development of the laws of thermodynamics, heat was measured by changes in the states of the participating bodies.", "Some general rules, with important exceptions, can be stated as follows.", "In general, most bodies expand on heating.", "In this circumstance, heating a body at a constant volume increases the pressure it exerts on its constraining walls, while heating at a constant pressure increases its volume.", "Beyond this, most substances have three ordinarily recognized states of matter, solid, liquid, and gas.", "Some can also exist in a plasma.", "Many have further, more finely differentiated, states of matter, such as glass and liquid crystal.", "In many cases, at fixed temperature and pressure, a substance can exist in several distinct states of matter in what might be viewed as the same 'body'.", "For example, ice may float in a glass of water.", "Then the ice and the water are said to constitute two phases within the 'body'.", "Definite rules are known, telling how distinct phases may coexist in a 'body'.", "Mostly, at a fixed pressure, there is a definite temperature at which heating causes a solid to melt or evaporate, and a definite temperature at which heating causes a liquid to evaporate.", "In such cases, cooling has the reverse effects.", "All of these, the commonest cases, fit with a rule that heating can be measured by changes of state of a body.", "Such cases supply what are called \"thermometric bodies\", that allow the definition of empirical temperatures.", "Before 1848, all temperatures were defined in this way.", "There was thus a tight link, apparently logically determined, between heat and temperature, though they were recognized as conceptually thoroughly distinct, especially by Joseph Black in the later eighteenth century.", "There are important exceptions.", "They break the obviously apparent link between heat and temperature.", "They make it clear that empirical definitions of temperature are contingent on the peculiar properties of particular thermometric substances, and are thus precluded from the title 'absolute'.", "For example, water contracts on being heated near 277 K. It cannot be used as a thermometric substance near that temperature.", "Also, over a certain temperature range, ice contracts on heating.", "Moreover, many substances can exist in metastable states, such as with negative pressure, that survive only transiently and in very special conditions.", "Such facts, sometimes called 'anomalous', are some of the reasons for the thermodynamic definition of absolute temperature.", "In the early days of measurement of high temperatures, another factor was important, and used by Josiah Wedgwood in his pyrometer.", "The temperature reached in a process was estimated by the shrinkage of a sample of clay.", "The higher the temperature, the more the shrinkage.", "This was the only available more or less reliable method of measurement of temperatures above 1000 °C (1,832 °F).", "But such shrinkage is irreversible.", "The clay does not expand again on cooling.", "That is why it could be used for the measurement.", "But only once.", "It is not a thermometric material in the usual sense of the word.", "Nevertheless, the thermodynamic definition of absolute temperature does make essential use of the concept of heat, with proper circumspection.", "According to Denbigh (1981), the property of hotness is a concern of thermodynamics that should be defined without reference to the concept of heat.", "Consideration of hotness leads to the concept of empirical temperature.", "All physical systems are capable of heating or cooling others.", "With reference to hotness, the comparative terms hotter and colder are defined by the rule that heat flows from the hotter body to the colder.", "If a physical system is inhomogeneous or very rapidly or irregularly changing, for example by turbulence, it may be impossible to characterize it by a temperature, but still there can be transfer of energy as heat between it and another system.", "If a system has a physical state that is regular enough, and persists long enough to allow it to reach thermal equilibrium with a specified thermometer, then it has a temperature according to that thermometer.", "An empirical thermometer registers degree of hotness for such a system.", "Such a temperature is called empirical.", "For example, Truesdell writes about classical thermodynamics: \"At each time, the body is assigned a real number called the \"temperature\".", "This number is a measure of how hot the body is.", "\"\nPhysical systems that are too turbulent to have temperatures may still differ in hotness.", "A physical system that passes heat to another physical system is said to be the hotter of the two.", "More is required for the system to have a thermodynamic temperature.", "Its behavior must be so regular that its empirical temperature is the same for all suitably calibrated and scaled thermometers, and then its hotness is said to lie on the one-dimensional hotness manifold.", "This is part of the reason why heat is defined following Carathéodory and Born, solely as occurring other than by work or transfer of matter; temperature is advisedly and deliberately not mentioned in this now widely accepted definition.", "This is also the reason that the zeroth law of thermodynamics is stated explicitly.", "If three physical systems, \"A\", \"B\", and \"C\" are each not in their own states of internal thermodynamic equilibrium, it is possible that, with suitable physical connections being made between them, \"A\" can heat \"B\" and \"B\" can heat \"C\" and \"C\" can heat \"A\".", "In non-equilibrium situations, cycles of flow are possible.", "It is the special and uniquely distinguishing characteristic of internal thermodynamic equilibrium that this possibility is not open to thermodynamic systems (as distinguished amongst physical systems) which are in their own states of internal thermodynamic equilibrium; this is the reason why the zeroth law of thermodynamics needs explicit statement.", "That is to say, the relation 'is not colder than' between general non-equilibrium physical systems is not transitive, whereas, in contrast, the relation 'has no lower a temperature than' between thermodynamic systems in their own states of internal thermodynamic equilibrium is transitive.", "It follows from this that the relation 'is in thermal equilibrium with' is transitive, which is one way of stating the zeroth law.", "Just as temperature may be undefined for a sufficiently inhomogeneous system, so also may entropy be undefined for a system not in its own state of internal thermodynamic equilibrium.", "For example, 'the temperature of the solar system' is not a defined quantity.", "Likewise, 'the entropy of the solar system' is not defined in classical thermodynamics.", "It has not been possible to define non-equilibrium entropy, as a simple number for a whole system, in a clearly satisfactory way." ]

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[ "This is distinct from the ordinary language usage of the word 'heat' as a property of a system in itself.", "For example, radiative heat transfer can co-occur with matter transfer.", "For example, respectively in special circumstances, heat transfer can be measured by the amount of ice melted, or by change in temperature of a body in the surroundings of the system." ]

[ "The mechanisms of energy transfer that define heat include conduction, through direct contact of immobile bodies, or through a wall or barrier that is impermeable to matter; or radiation between separated bodies; or friction due to isochoric mechanical or electrical or magnetic or gravitational work done by the surroundings on the system of interest, such as Joule heating due to an electric current driven through the system of interest by an external system, or through a magnetic stirrer.", "When there is a suitable path between two systems with different temperatures, heat transfer occurs necessarily, immediately, and spontaneously from the hotter to the colder system.", "Thermal conduction occurs by the stochastic (random) motion of microscopic particles (such as atoms or molecules).", "In contrast, thermodynamic work is defined by mechanisms that act macroscopically and directly on the system's whole-body state variables; for example, change of the system's volume through a piston's motion with externally measurable force; or change of the system's internal electric polarization through an externally measurable change in electric field.", "The definition of heat transfer does not require that the process be in any sense smooth.", "For example, a bolt of lightning may transfer heat to a body.", "Convective circulation allows one body to heat another, through an intermediate circulating fluid that carries energy from a boundary of one to a boundary of the other; the actual heat transfer is by conduction and radiation between the fluid and the respective bodies.", "Convective circulation, though spontaneous, does not necessarily and immediately occur simply because of some slight temperature difference; for it to occur in a given arrangement of systems, there is a threshold that must be crossed.", "Although heat flows spontaneously from a hotter body to a cooler one, it is possible to construct a heat pump which expends work to transfer energy from a colder body to a hotter body.", "In contrast, a heat engine reduces an existing temperature difference to supply work to another system.", "Another thermodynamic type of heat transfer device is an active heat spreader, which expends work to speed up transfer of energy to colder surroundings from a hotter body, for example a computer component.", "As a form of energy, heat has the unit joule (J) in the International System of Units (SI).", "However, in many applied fields in engineering the British thermal unit (BTU) and the calorie are often used.", "The standard unit for the rate of heat transferred is the watt (W), defined as one joule per second.", "The symbol for the total amount of energy transferred as heat was used by Rudolf Clausius in 1850:\n\"Let the amount of heat which must be imparted during the transition of the gas in a definite manner from any given state to another, in which its volume is \"v\" and its temperature \"t\", be called \"Q\"\"\nHeat released by a system into its surroundings is by convention a negative quantity (); when a system absorbs heat from its surroundings, it is positive ().", "Heat transfer rate, or heat flow per unit time, is denoted by formula_1.", "This should not be confused with a time derivative of a function of state (which can also be written with the dot notation) since heat is not a function of state.", "Heat flux is defined as rate of heat transfer per unit cross-sectional area (units watts per square metre).", "In 1856, Rudolf Clausius, referring to closed systems, in which transfers of matter do not occur, defined the \"second fundamental theorem\" (the second law of thermodynamics) in the mechanical theory of heat (thermodynamics): \"if two transformations which, without necessitating any other permanent change, can mutually replace one another, be called equivalent, then the generations of the quantity of heat \"Q\" from work at the temperature \"T\", has the \"equivalence-value\":\"\nformula_2\nIn 1865, he came to define the entropy symbolized by \"S\", such that, due to the supply of the amount of heat \"Q\" at temperature \"T\" the entropy of the system is increased by\nIn a transfer of energy as heat without work being done, there are changes of entropy in both the surroundings which lose heat and the system which gains it.", "The increase, , of entropy in the system may be considered to consist of two parts, an increment, that matches, or 'compensates', the change, , of entropy in the surroundings, and a further increment, that may be considered to be 'generated' or 'produced' in the system, and is said therefore to be 'uncompensated'.", "Thus\nformula_3\nThis may also be written\nformula_4\nThe total change of entropy in the system and surroundings is thus\nformula_5\nThis may also be written\nformula_6\nIt is then said that an amount of entropy has been transferred from the surroundings to the system.", "Because entropy is not a conserved quantity, this is an exception to the general way of speaking, in which an amount transferred is of a conserved quantity.", "From the second law of thermodynamics follows that in a spontaneous transfer of heat, in which the temperature of the system is different from that of the surroundings:\nformula_7\nFor purposes of mathematical analysis of transfers, one thinks of fictive processes that are called \"reversible\", with the temperature of the system being hardly less than that of the surroundings, and the transfer taking place at an imperceptibly slow rate.", "Following the definition above in formula (), for such a fictive reversible process, a quantity of transferred heat (an inexact differential) is analyzed as a quantity , with (an exact differential):\nformula_8\nThis equality is only valid for a fictive transfer in which there is no production of entropy, that is to say, in which there is no uncompensated entropy.", "If, in contrast, the process is natural, and can really occur, with irreversibility, then there is entropy production, with .", "The quantity was termed by Clausius the \"uncompensated heat\", though that does not accord with present-day terminology.", "Then one has\nformula_9\nThis leads to the statement\nformula_10\nwhich is the second law of thermodynamics for closed systems.", "In non-equilibrium thermodynamics that makes the approximation of assuming the hypothesis of local thermodynamic equilibrium, there is a special notation for this.", "The transfer of energy as heat is assumed to take place across an infinitesimal temperature difference, so that the system element and its surroundings have near enough the same temperature .", "Then one writes\nformula_11\nwhere by definition\nformula_12\nThe second law for a natural process asserts that\nformula_13", "For a closed system (a system from which no matter can enter or exit), one version of the first law of thermodynamics states that the change in internal energy of the system is equal to the amount of heat supplied to the system minus the amount of thermodynamic work done by system on its surroundings.", "The foregoing sign convention for work is used in the present article, but an alternate sign convention, followed by IUPAC, for work, is to consider the work performed on the system by its surroundings as positive.", "This is the convention adopted by many modern textbooks of physical chemistry, such as those by Peter Atkins and Ira Levine, but many textbooks on physics define work as work done by the system.", "formula_14\nThis formula can be re-written so as to express a definition of quantity of energy transferred as heat, based purely on the concept of adiabatic work, if it is supposed that is defined and measured solely by processes of adiabatic work:\nformula_15\nThe thermodynamic work done by the system is through mechanisms defined by its thermodynamic state variables, for example, its volume , not through variables that necessarily involve mechanisms in the surroundings.", "The latter are such as shaft work, and include isochoric work.", "The internal energy, , is a state function.", "In cyclical processes, such as the operation of a heat engine, state functions of the working substance return to their initial values upon completion of a cycle.", "The differential, or infinitesimal increment, for the internal energy in an infinitesimal process is an exact differential .", "The symbol for exact differentials is the lowercase letter .", "In contrast, neither of the infinitesimal increments nor in an infinitesimal process represents the change in a state function of the system.", "Thus, infinitesimal increments of heat and work are inexact differentials.", "The lowercase Greek letter delta, , is the symbol for inexact differentials.", "The integral of any inexact differential in a process where the system leaves and then returns to the same thermodynamic state does not necessarily equal zero.", "As recounted above, in the section headed \"heat and entropy\", the second law of thermodynamics observes that if heat is supplied to a system in a reversible process, the increment of heat and the temperature form the exact differential\nformula_16\nand that , the entropy of the working body, is a state function.", "Likewise, with a well-defined pressure, , behind a slowly moving (quasistatic) boundary, the work differential, , and the pressure, , combine to form the exact differential\nformula_17\nwith the volume of the system, which is a state variable.", "In general, for systems of uniform pressure and temperature without composition change,\nformula_18\nAssociated with this differential equation is the concept that the internal energy may be considered to be a function of its natural variables and .", "The internal energy representation of the fundamental thermodynamic relation is written as\nformula_19\nIf is constant\nformula_20\nand if is constant\nformula_21\nwith the enthalpy defined by\nformula_22\nThe enthalpy may be considered to be a function of its natural variables and .", "The enthalpy representation of the fundamental thermodynamic relation is written\nformula_23\nThe internal energy representation and the enthalpy representation are partial Legendre transforms of one another.", "They contain the same physical information, written in different ways.", "Like the internal energy, the enthalpy stated as a function of its natural variables is a thermodynamic potential and contains all thermodynamic information about a body.", "If a quantity of heat is added to a body while it does only expansion work on its surroundings, one has\nformula_24\nIf this is constrained to happen at constant pressure, i.e. with , the expansion work done by the body is given by ; recalling the first law of thermodynamics, one has\nformula_25\nConsequently, by substitution one has\nformula_26\nIn this scenario, the increase in enthalpy is equal to the quantity of heat added to the system.", "This is the basis of the determination of enthalpy changes in chemical reactions by calorimetry.", "Since many processes do take place at constant atmospheric pressure, the enthalpy is sometimes given the misleading name of 'heat content' or heat function, while it actually depends strongly on the energies of covalent bonds and intermolecular forces.", "In terms of the natural variables of the state function , this process of change of state from state 1 to state 2 can be expressed as\nformula_27\nIt is known that the temperature is identically stated by\nformula_28\nConsequently,\nformula_29\nIn this case, the integral specifies a quantity of heat transferred at constant pressure.", "As a common noun, English \"heat\" or \"warmth\" (just as French \"chaleur\", German \"Wärme\", Latin \"calor\", Greek θάλπος, etc.) refers to (the human perception of) either thermal energy or temperature.", "Speculation on thermal energy or \"heat\" as a separate form of matter has a long history, see caloric theory, phlogiston and fire (classical element).", "The modern understanding of thermal energy originates with Thompson's 1798 mechanical theory of heat (\"An Experimental Enquiry Concerning the Source of the Heat which is Excited by Friction\"), postulating a mechanical equivalent of heat.", "A collaboration between Nicolas Clément and Sadi Carnot (\"Reflections on the Motive Power of Fire\") in the 1820s had some related thinking along similar lines.", "In 1845, Joule published a paper entitled \"The Mechanical Equivalent of Heat\", in which he specified a numerical value for the amount of mechanical work required to \"produce a unit of heat\".", "The theory of classical thermodynamics matured in the 1850s to 1860s.", "John Tyndall's \"Heat Considered as Mode of Motion\" (1863) was instrumental in popularizing the idea of heat as motion to the English-speaking public.", "The theory was developed in academic publications in French, English and German.", "From an early time, the French technical term \"chaleur\" used by Carnot was taken as equivalent to the English \"heat\" and German \"Wärme\" (lit.", "\"warmth\", while the equivalent of \"heat\" would be German \"Hitze\").", "The process function was introduced by Rudolf Clausius in 1850.", "Clausius described it with the German compound \"Wärmemenge\", translated as \"amount of heat\".", "James Clerk Maxwell in his 1871 \"Theory of Heat\" outlines four stipulations for the definition of heat:\n\n\nThe process function is referred to as \"Wärmemenge\" by Clausius, or as \"amount of heat\" in translation.", "Use of \"heat\" as an abbreviated form of the specific concept of \"quantity of energy transferred as heat\" led to some terminological confusion by the early 20th century.", "The generic meaning of \"heat\", even in classical thermodynamics, is just \"thermal energy\".", "Since the 1920s, it has been recommended practice to use enthalpy to refer to the \"heat content at constant volume\", and to thermal energy when \"heat\" in the general sense is intended, while \"heat\" is reserved for the very specific context of the transfer of thermal energy between two systems.", "Leonard Benedict Loeb in his \"Kinetic Theory of Gases\" (1927) makes a point of using \"quantity of heat\"\nor \"heat–quantity\" when referring to :", "After the perfection of thermometry [...] the next great advance made in the field of heat was the definition of a term which is called the quantity of heat.", "[... after the abandonment of caloric theory,] It still remains to interpret this very definite concept, the quantity of heat, in terms of a theory ascribing all heat to the kinetics of gas molecules.", "A frequent definition of heat is based on the work of Carathéodory (1909), referring to processes in a closed system.", "The internal energy of a body in an arbitrary state can be determined by amounts of work adiabatically performed by the body on its surroundings when it starts from a reference state .", "Such work is assessed through quantities defined in the surroundings of the body.", "It is supposed that such work can be assessed accurately, without error due to friction in the surroundings; friction in the body is not excluded by this definition.", "The adiabatic performance of work is defined in terms of adiabatic walls, which allow transfer of energy as work, but no other transfer, of energy or matter.", "In particular they do not allow the passage of energy as heat.", "According to this definition, work performed adiabatically is in general accompanied by friction within the thermodynamic system or body.", "On the other hand, according to Carathéodory (1909), there also exist non-adiabatic, \"diathermal\" walls, which are postulated to be permeable only to heat.", "For the definition of quantity of energy transferred as heat, it is customarily envisaged that an arbitrary state of interest is reached from state by a process with two components, one adiabatic and the other not adiabatic.", "For convenience one may say that the adiabatic component was the sum of work done by the body through volume change through movement of the walls while the non-adiabatic wall was temporarily rendered adiabatic, and of isochoric adiabatic work.", "Then the non-adiabatic component is a process of energy transfer through the wall that passes only heat, newly made accessible for the purpose of this transfer, from the surroundings to the body.", "The change in internal energy to reach the state from the state is the difference of the two amounts of energy transferred.", "Although Carathéodory himself did not state such a definition, following his work it is customary in theoretical studies to define heat, , to the body from its surroundings, in the combined process of change to state from the state , as the change in internal energy, , minus the amount of work, , done by the body on its surrounds by the adiabatic process, so that .", "In this definition, for the sake of conceptual rigour, the quantity of energy transferred as heat is not specified directly in terms of the non-adiabatic process.", "It is defined through knowledge of precisely two variables, the change of internal energy and the amount of adiabatic work done, for the combined process of change from the reference state to the arbitrary state .", "It is important that this does not explicitly involve the amount of energy transferred in the non-adiabatic component of the combined process.", "It is assumed here that the amount of energy required to pass from state to state , the change of internal energy, is known, independently of the combined process, by a determination through a purely adiabatic process, like that for the determination of the internal energy of state above.", "The rigour that is prized in this definition is that there is one and only one kind of energy transfer admitted as fundamental: energy transferred as work.", "Energy transfer as heat is considered as a derived quantity.", "The uniqueness of work in this scheme is considered to guarantee rigor and purity of conception.", "The conceptual purity of this definition, based on the concept of energy transferred as work as an ideal notion, relies on the idea that some frictionless and otherwise non-dissipative processes of energy transfer can be realized in physical actuality.", "The second law of thermodynamics, on the other hand, assures us that such processes are not found in nature.", "Before the rigorous mathematical definition of heat based on Carathéodory's 1909 paper,\nhistorically, heat, temperature, and thermal equilibrium were presented in thermodynamics textbooks as jointly primitive notions.", "Carathéodory introduced his 1909 paper thus: \"The proposition that the discipline of thermodynamics can be justified without recourse to any hypothesis that cannot be verified experimentally must be regarded as one of the most noteworthy results of the research in thermodynamics that was accomplished during the last century.\"", "Referring to the \"point of view adopted by most authors who were active in the last fifty years\", Carathéodory wrote: \"There exists a physical quantity called heat that is not identical with the mechanical quantities (mass, force, pressure, etc.) and whose variations can be determined by calorimetric measurements.\"", "James Serrin introduces an account of the theory of thermodynamics thus: \"In the following section, we shall use the classical notions of \"heat\", \"work\", and \"hotness\" as primitive elements, ...", "That heat is an appropriate and natural primitive for thermodynamics was already accepted by Carnot.", "Its continued validity as a primitive element of thermodynamical structure is due to the fact that it synthesizes an essential physical concept, as well as to its successful use in recent work to unify different constitutive theories.\"", "This traditional kind of presentation of the basis of thermodynamics includes ideas that may be summarized by the statement that heat transfer is purely due to spatial non-uniformity of temperature, and is by conduction and radiation, from hotter to colder bodies.", "It is sometimes proposed that this traditional kind of presentation necessarily rests on \"circular reasoning\"; against this proposal, there stands the rigorously logical mathematical development of the theory presented by Truesdell and Bharatha (1977).", "This alternative approach to the definition of quantity of energy transferred as heat differs in logical structure from that of Carathéodory, recounted just above.", "This alternative approach admits calorimetry as a primary or direct way to measure quantity of energy transferred as heat.", "It relies on temperature as one of its primitive concepts, and used in calorimetry.", "It is presupposed that enough processes exist physically to allow measurement of differences in internal energies.", "Such processes are not restricted to adiabatic transfers of energy as work.", "They include calorimetry, which is the commonest practical way of finding internal energy differences.", "The needed temperature can be either empirical or absolute thermodynamic.", "In contrast, the Carathéodory way recounted just above does not use calorimetry or temperature in its primary definition of quantity of energy transferred as heat.", "The Carathéodory way regards calorimetry only as a secondary or indirect way of measuring quantity of energy transferred as heat.", "As recounted in more detail just above, the Carathéodory way regards quantity of energy transferred as heat in a process as primarily or directly defined as a residual quantity.", "It is calculated from the difference of the internal energies of the initial and final states of the system, and from the actual work done by the system during the process.", "That internal energy difference is supposed to have been measured in advance through processes of purely adiabatic transfer of energy as work, processes that take the system between the initial and final states.", "By the Carathéodory way it is presupposed as known from experiment that there actually physically exist enough such adiabatic processes, so that there need be no recourse to calorimetry for measurement of quantity of energy transferred as heat.", "This presupposition is essential but is explicitly labeled neither as a law of thermodynamics nor as an axiom of the Carathéodory way.", "In fact, the actual physical existence of such adiabatic processes is indeed mostly supposition, and those supposed processes have in most cases not been actually verified empirically to exist.", "Referring to conduction, Partington writes: \"If a hot body is brought in conducting contact with a cold body, the temperature of the hot body falls and that of the cold body rises, and it is said that a \"quantity of heat\" has passed from the hot body to the cold body.", "\"\nReferring to radiation, Maxwell writes: \"In Radiation, the hotter body loses heat, and the colder body receives heat by means of a process occurring in some intervening medium which does not itself thereby become hot.\"\nMaxwell writes that convection as such \"is not a purely thermal phenomenon\".", "In thermodynamics, convection in general is regarded as transport of internal energy.", "If, however, the convection is enclosed and circulatory, then it may be regarded as an intermediary that transfers energy as heat between source and destination bodies, because it transfers only energy and not matter from the source to the destination body.", "In accordance with the first law for closed systems, energy transferred solely as heat leaves one body and enters another, changing the internal energies of each.", "Transfer, between bodies, of energy as work is a complementary way of changing internal energies.", "Though it is not logically rigorous from the viewpoint of strict physical concepts, a common form of words that expresses this is to say that heat and work are interconvertible.", "Cyclically operating engines that use only heat and work transfers have two thermal reservoirs, a hot and a cold one.", "They may be classified by the range of operating temperatures of the working body, relative to those reservoirs.", "In a heat engine, the working body is at all times colder than the hot reservoir and hotter than the cold reservoir.", "In a sense, it uses heat transfer to produce work.", "In a heat pump, the working body, at stages of the cycle, goes both hotter than the hot reservoir, and colder than the cold reservoir.", "In a sense, it uses work to produce heat transfer.", "In classical thermodynamics, a commonly considered model is the heat engine.", "It consists of four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir.", "A cyclic process leaves the working body in an unchanged state, and is envisaged as being repeated indefinitely often.", "Work transfers between the working body and the work reservoir are envisaged as reversible, and thus only one work reservoir is needed.", "But two thermal reservoirs are needed, because transfer of energy as heat is irreversible.", "A single cycle sees energy taken by the working body from the hot reservoir and sent to the two other reservoirs, the work reservoir and the cold reservoir.", "The hot reservoir always and only supplies energy and the cold reservoir always and only receives energy.", "The second law of thermodynamics requires that no cycle can occur in which no energy is received by the cold reservoir.", "Heat engines achieve higher efficiency when the ratio of the initial and final temperature is greater.", "Another commonly considered model is the heat pump or refrigerator.", "Again there are four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir.", "A single cycle starts with the working body colder than the cold reservoir, and then energy is taken in as heat by the working body from the cold reservoir.", "Then the work reservoir does work on the working body, adding more to its internal energy, making it hotter than the hot reservoir.", "The hot working body passes heat to the hot reservoir, but still remains hotter than the cold reservoir.", "Then, by allowing it to expand without passing heat to another body, the working body is made colder than the cold reservoir.", "It can now accept heat transfer from the cold reservoir to start another cycle.", "The device has transported energy from a colder to a hotter reservoir, but this is not regarded as by an inanimate agency; rather, it is regarded as by the harnessing of work .", "This is because work is supplied from the work reservoir, not just by a simple thermodynamic process, but by a cycle of thermodynamic operations and processes, which may be regarded as directed by an animate or harnessing agency.", "Accordingly, the cycle is still in accord with the second law of thermodynamics.", "The 'efficiency' of a heat pump (which exceeds unity) is best when the temperature difference between the hot and cold reservoirs is least.", "Functionally, such engines are used in two ways, distinguishing a target reservoir and a resource or surrounding reservoir.", "A heat pump transfers heat to the hot reservoir as the target from the resource or surrounding reservoir.", "A refrigerator transfers heat, from the cold reservoir as the target, to the resource or surrounding reservoir.", "The target reservoir may be regarded as leaking: when the target leaks heat to the surroundings, heat pumping is used; when the target leaks coldness to the surroundings, refrigeration is used.", "The engines harness work to overcome the leaks.", "According to Planck, there are three main conceptual approaches to heat.", "One is the microscopic or kinetic theory approach.", "The other two are macroscopic approaches.", "One is the approach through the law of conservation of energy taken as prior to thermodynamics, with a mechanical analysis of processes, for example in the work of Helmholtz.", "This mechanical view is taken in this article as currently customary for thermodynamic theory.", "The other macroscopic approach is the thermodynamic one, which admits heat as a primitive concept, which contributes, by scientific induction to knowledge of the law of conservation of energy.", "This view is widely taken as the practical one, quantity of heat being measured by calorimetry.", "Bailyn also distinguishes the two macroscopic approaches as the mechanical and the thermodynamic.", "The thermodynamic view was taken by the founders of thermodynamics in the nineteenth century.", "It regards quantity of energy transferred as heat as a primitive concept coherent with a primitive concept of temperature, measured primarily by calorimetry.", "A calorimeter is a body in the surroundings of the system, with its own temperature and internal energy; when it is connected to the system by a path for heat transfer, changes in it measure heat transfer.", "The mechanical view was pioneered by Helmholtz and developed and used in the twentieth century, largely through the influence of Max Born.", "It regards quantity of heat transferred as heat as a derived concept, defined for closed systems as quantity of heat transferred by mechanisms other than work transfer, the latter being regarded as primitive for thermodynamics, defined by macroscopic mechanics.", "According to Born, the transfer of internal energy between open systems that accompanies transfer of matter \"cannot be reduced to mechanics\".", "It follows that there is no well-founded definition of quantities of energy transferred as heat or as work associated with transfer of matter.", "Nevertheless, for the thermodynamical description of non-equilibrium processes, it is desired to consider the effect of a temperature gradient established by the surroundings across the system of interest when there is no physical barrier or wall between system and surroundings, that is to say, when they are open with respect to one another.", "The impossibility of a mechanical definition in terms of work for this circumstance does not alter the physical fact that a temperature gradient causes a diffusive flux of internal energy, a process that, in the thermodynamic view, might be proposed as a candidate concept for transfer of energy as heat.", "In this circumstance, it may be expected that there may also be active other drivers of diffusive flux of internal energy, such as gradient of chemical potential which drives transfer of matter, and gradient of electric potential which drives electric current and iontophoresis; such effects usually interact with diffusive flux of internal energy driven by temperature gradient, and such interactions are known as cross-effects.", "If cross-effects that result in diffusive transfer of internal energy were also labeled as heat transfers, they would sometimes violate the rule that pure heat transfer occurs only down a temperature gradient, never up one.", "They would also contradict the principle that all heat transfer is of one and the same kind, a principle founded on the idea of heat conduction between closed systems.", "One might to try to think narrowly of heat flux driven purely by temperature gradient as a conceptual component of diffusive internal energy flux, in the thermodynamic view, the concept resting specifically on careful calculations based on detailed knowledge of the processes and being indirectly assessed.", "In these circumstances, if perchance it happens that no transfer of matter is actualized, and there are no cross-effects, then the thermodynamic concept and the mechanical concept coincide, as if one were dealing with closed systems.", "But when there is transfer of matter, the exact laws by which temperature gradient drives diffusive flux of internal energy, rather than being exactly knowable, mostly need to be assumed, and in many cases are practically unverifiable.", "Consequently, when there is transfer of matter, the calculation of the pure 'heat flux' component of the diffusive flux of internal energy rests on practically unverifiable assumptions.", "This is a reason to think of heat as a specialized concept that relates primarily and precisely to closed systems, and applicable only in a very restricted way to open systems.", "In many writings in this context, the term \"heat flux\" is used when what is meant is therefore more accurately called diffusive flux of internal energy; such usage of the term \"heat flux\" is a residue of older and now obsolete language usage that allowed that a body may have a \"heat content\".", "In the kinetic theory, heat is explained in terms of the microscopic motions and interactions of constituent particles, such as electrons, atoms, and molecules.", "The immediate meaning of the kinetic energy of the constituent particles is not as heat.", "It is as a component of internal energy.", "In microscopic terms, heat is a transfer quantity, and is described by a transport theory, not as steadily localized kinetic energy of particles.", "Heat transfer arises from temperature gradients or differences, through the diffuse exchange of microscopic kinetic and potential particle energy, by particle collisions and other interactions.", "An early and vague expression of this was made by Francis Bacon.", "Precise and detailed versions of it were developed in the nineteenth century.", "In statistical mechanics, for a closed system (no transfer of matter), heat is the energy transfer associated with a disordered, microscopic action on the system, associated with jumps in occupation numbers of the energy levels of the system, without change in the values of the energy levels themselves.", "It is possible for macroscopic thermodynamic work to alter the occupation numbers without change in the values of the system energy levels themselves, but what distinguishes transfer as heat is that the transfer is entirely due to disordered, microscopic action, including radiative transfer.", "A mathematical definition can be formulated for small increments of quasi-static adiabatic work in terms of the statistical distribution of an ensemble of microstates.", "Quantity of heat transferred can be measured by calorimetry, or determined through calculations based on other quantities.", "Calorimetry is the empirical basis of the idea of quantity of heat transferred in a process.", "The transferred heat is measured by changes in a body of known properties, for example, temperature rise, change in volume or length, or phase change, such as melting of ice.", "A calculation of quantity of heat transferred can rely on a hypothetical quantity of energy transferred as adiabatic work and on the first law of thermodynamics.", "Such calculation is the primary approach of many theoretical studies of quantity of heat transferred.", "The discipline of heat transfer, typically considered an aspect of mechanical engineering and chemical engineering, deals with specific applied methods by which thermal energy in a system is generated, or converted, or transferred to another system.", "Although the definition of heat implicitly means the transfer of energy, the term \"heat transfer\" encompasses this traditional usage in many engineering disciplines and laymen language.", "\"Heat transfer\" is generally described as including the mechanisms of heat conduction, heat convection, thermal radiation, but may include mass transfer and heat in processes of phase changes.", "Convection may be described as the combined effects of conduction and fluid flow.", "From the thermodynamic point of view, heat flows into a fluid by diffusion to increase its energy, the fluid then transfers (advects) this increased internal energy (not heat) from one location to another, and this is then followed by a second thermal interaction which transfers heat to a second body or system, again by diffusion.", "This entire process is often regarded as an additional mechanism of heat transfer, although technically, \"heat transfer\" and thus heating and cooling occurs only on either end of such a conductive flow, but not as a result of flow.", "Thus, conduction can be said to \"transfer\" heat only as a net result of the process, but may not do so at every time within the complicated convective process.", "In an 1847 lecture entitled \"On Matter, Living Force, and Heat\", James Prescott Joule characterized the terms latent heat and sensible heat as components of heat each affecting distinct physical phenomena, namely the potential and kinetic energy of particles, respectively.", "He described latent energy as the energy possessed via a distancing of particles where attraction was over a greater distance, i.e. a form of potential energy, and the sensible heat as an energy involving the motion of particles, i.e. kinetic energy.", "Latent heat is the heat released or absorbed by a chemical substance or a thermodynamic system during a change of state that occurs without a change in temperature.", "Such a process may be a phase transition, such as the melting of ice or the boiling of water.", "Heat capacity is a measurable physical quantity equal to the ratio of the heat added to an object to the resulting temperature change.", "The \"molar heat capacity\" is the heat capacity per unit amount (SI unit: mole) of a pure substance, and the \"specific heat capacity\", often called simply \"specific heat\", is the heat capacity per unit mass of a material.", "Heat capacity is a physical property of a substance, which means that it depends on the state and properties of the substance under consideration.", "The specific heats of monatomic gases, such as helium, are nearly constant with temperature.", "Diatomic gases such as hydrogen display some temperature dependence, and triatomic gases (e.g., carbon dioxide) still more.", "Before the development of the laws of thermodynamics, heat was measured by changes in the states of the participating bodies.", "Some general rules, with important exceptions, can be stated as follows.", "In general, most bodies expand on heating.", "In this circumstance, heating a body at a constant volume increases the pressure it exerts on its constraining walls, while heating at a constant pressure increases its volume.", "Beyond this, most substances have three ordinarily recognized states of matter, solid, liquid, and gas.", "Some can also exist in a plasma.", "Many have further, more finely differentiated, states of matter, such as glass and liquid crystal.", "In many cases, at fixed temperature and pressure, a substance can exist in several distinct states of matter in what might be viewed as the same 'body'.", "For example, ice may float in a glass of water.", "Then the ice and the water are said to constitute two phases within the 'body'.", "Definite rules are known, telling how distinct phases may coexist in a 'body'.", "Mostly, at a fixed pressure, there is a definite temperature at which heating causes a solid to melt or evaporate, and a definite temperature at which heating causes a liquid to evaporate.", "In such cases, cooling has the reverse effects.", "All of these, the commonest cases, fit with a rule that heating can be measured by changes of state of a body.", "Such cases supply what are called \"thermometric bodies\", that allow the definition of empirical temperatures.", "Before 1848, all temperatures were defined in this way.", "There was thus a tight link, apparently logically determined, between heat and temperature, though they were recognized as conceptually thoroughly distinct, especially by Joseph Black in the later eighteenth century.", "There are important exceptions.", "They break the obviously apparent link between heat and temperature.", "They make it clear that empirical definitions of temperature are contingent on the peculiar properties of particular thermometric substances, and are thus precluded from the title 'absolute'.", "For example, water contracts on being heated near 277 K. It cannot be used as a thermometric substance near that temperature.", "Also, over a certain temperature range, ice contracts on heating.", "Moreover, many substances can exist in metastable states, such as with negative pressure, that survive only transiently and in very special conditions.", "Such facts, sometimes called 'anomalous', are some of the reasons for the thermodynamic definition of absolute temperature.", "In the early days of measurement of high temperatures, another factor was important, and used by Josiah Wedgwood in his pyrometer.", "The temperature reached in a process was estimated by the shrinkage of a sample of clay.", "The higher the temperature, the more the shrinkage.", "This was the only available more or less reliable method of measurement of temperatures above 1000 °C (1,832 °F).", "But such shrinkage is irreversible.", "The clay does not expand again on cooling.", "That is why it could be used for the measurement.", "But only once.", "It is not a thermometric material in the usual sense of the word.", "Nevertheless, the thermodynamic definition of absolute temperature does make essential use of the concept of heat, with proper circumspection.", "According to Denbigh (1981), the property of hotness is a concern of thermodynamics that should be defined without reference to the concept of heat.", "Consideration of hotness leads to the concept of empirical temperature.", "All physical systems are capable of heating or cooling others.", "With reference to hotness, the comparative terms hotter and colder are defined by the rule that heat flows from the hotter body to the colder.", "If a physical system is inhomogeneous or very rapidly or irregularly changing, for example by turbulence, it may be impossible to characterize it by a temperature, but still there can be transfer of energy as heat between it and another system.", "If a system has a physical state that is regular enough, and persists long enough to allow it to reach thermal equilibrium with a specified thermometer, then it has a temperature according to that thermometer.", "An empirical thermometer registers degree of hotness for such a system.", "Such a temperature is called empirical.", "For example, Truesdell writes about classical thermodynamics: \"At each time, the body is assigned a real number called the \"temperature\".", "This number is a measure of how hot the body is.", "\"\nPhysical systems that are too turbulent to have temperatures may still differ in hotness.", "A physical system that passes heat to another physical system is said to be the hotter of the two.", "More is required for the system to have a thermodynamic temperature.", "Its behavior must be so regular that its empirical temperature is the same for all suitably calibrated and scaled thermometers, and then its hotness is said to lie on the one-dimensional hotness manifold.", "This is part of the reason why heat is defined following Carathéodory and Born, solely as occurring other than by work or transfer of matter; temperature is advisedly and deliberately not mentioned in this now widely accepted definition.", "This is also the reason that the zeroth law of thermodynamics is stated explicitly.", "If three physical systems, \"A\", \"B\", and \"C\" are each not in their own states of internal thermodynamic equilibrium, it is possible that, with suitable physical connections being made between them, \"A\" can heat \"B\" and \"B\" can heat \"C\" and \"C\" can heat \"A\".", "In non-equilibrium situations, cycles of flow are possible.", "It is the special and uniquely distinguishing characteristic of internal thermodynamic equilibrium that this possibility is not open to thermodynamic systems (as distinguished amongst physical systems) which are in their own states of internal thermodynamic equilibrium; this is the reason why the zeroth law of thermodynamics needs explicit statement.", "That is to say, the relation 'is not colder than' between general non-equilibrium physical systems is not transitive, whereas, in contrast, the relation 'has no lower a temperature than' between thermodynamic systems in their own states of internal thermodynamic equilibrium is transitive.", "It follows from this that the relation 'is in thermal equilibrium with' is transitive, which is one way of stating the zeroth law.", "Just as temperature may be undefined for a sufficiently inhomogeneous system, so also may entropy be undefined for a system not in its own state of internal thermodynamic equilibrium.", "For example, 'the temperature of the solar system' is not a defined quantity.", "Likewise, 'the entropy of the solar system' is not defined in classical thermodynamics.", "It has not been possible to define non-equilibrium entropy, as a simple number for a whole system, in a clearly satisfactory way." ]

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[ "For example, respectively in special circumstances, heat transfer can be measured by the amount of ice melted, or by change in temperature of a body in the surroundings of the system." ]

[ "The mechanisms of energy transfer that define heat include conduction, through direct contact of immobile bodies, or through a wall or barrier that is impermeable to matter; or radiation between separated bodies; or friction due to isochoric mechanical or electrical or magnetic or gravitational work done by the surroundings on the system of interest, such as Joule heating due to an electric current driven through the system of interest by an external system, or through a magnetic stirrer.", "When there is a suitable path between two systems with different temperatures, heat transfer occurs necessarily, immediately, and spontaneously from the hotter to the colder system.", "Thermal conduction occurs by the stochastic (random) motion of microscopic particles (such as atoms or molecules).", "In contrast, thermodynamic work is defined by mechanisms that act macroscopically and directly on the system's whole-body state variables; for example, change of the system's volume through a piston's motion with externally measurable force; or change of the system's internal electric polarization through an externally measurable change in electric field.", "The definition of heat transfer does not require that the process be in any sense smooth.", "For example, a bolt of lightning may transfer heat to a body.", "Convective circulation allows one body to heat another, through an intermediate circulating fluid that carries energy from a boundary of one to a boundary of the other; the actual heat transfer is by conduction and radiation between the fluid and the respective bodies.", "Convective circulation, though spontaneous, does not necessarily and immediately occur simply because of some slight temperature difference; for it to occur in a given arrangement of systems, there is a threshold that must be crossed.", "Although heat flows spontaneously from a hotter body to a cooler one, it is possible to construct a heat pump which expends work to transfer energy from a colder body to a hotter body.", "In contrast, a heat engine reduces an existing temperature difference to supply work to another system.", "Another thermodynamic type of heat transfer device is an active heat spreader, which expends work to speed up transfer of energy to colder surroundings from a hotter body, for example a computer component.", "As a form of energy, heat has the unit joule (J) in the International System of Units (SI).", "However, in many applied fields in engineering the British thermal unit (BTU) and the calorie are often used.", "The standard unit for the rate of heat transferred is the watt (W), defined as one joule per second.", "The symbol for the total amount of energy transferred as heat was used by Rudolf Clausius in 1850:\n\"Let the amount of heat which must be imparted during the transition of the gas in a definite manner from any given state to another, in which its volume is \"v\" and its temperature \"t\", be called \"Q\"\"\nHeat released by a system into its surroundings is by convention a negative quantity (); when a system absorbs heat from its surroundings, it is positive ().", "Heat transfer rate, or heat flow per unit time, is denoted by formula_1.", "This should not be confused with a time derivative of a function of state (which can also be written with the dot notation) since heat is not a function of state.", "Heat flux is defined as rate of heat transfer per unit cross-sectional area (units watts per square metre).", "In 1856, Rudolf Clausius, referring to closed systems, in which transfers of matter do not occur, defined the \"second fundamental theorem\" (the second law of thermodynamics) in the mechanical theory of heat (thermodynamics): \"if two transformations which, without necessitating any other permanent change, can mutually replace one another, be called equivalent, then the generations of the quantity of heat \"Q\" from work at the temperature \"T\", has the \"equivalence-value\":\"\nformula_2\nIn 1865, he came to define the entropy symbolized by \"S\", such that, due to the supply of the amount of heat \"Q\" at temperature \"T\" the entropy of the system is increased by\nIn a transfer of energy as heat without work being done, there are changes of entropy in both the surroundings which lose heat and the system which gains it.", "The increase, , of entropy in the system may be considered to consist of two parts, an increment, that matches, or 'compensates', the change, , of entropy in the surroundings, and a further increment, that may be considered to be 'generated' or 'produced' in the system, and is said therefore to be 'uncompensated'.", "Thus\nformula_3\nThis may also be written\nformula_4\nThe total change of entropy in the system and surroundings is thus\nformula_5\nThis may also be written\nformula_6\nIt is then said that an amount of entropy has been transferred from the surroundings to the system.", "Because entropy is not a conserved quantity, this is an exception to the general way of speaking, in which an amount transferred is of a conserved quantity.", "From the second law of thermodynamics follows that in a spontaneous transfer of heat, in which the temperature of the system is different from that of the surroundings:\nformula_7\nFor purposes of mathematical analysis of transfers, one thinks of fictive processes that are called \"reversible\", with the temperature of the system being hardly less than that of the surroundings, and the transfer taking place at an imperceptibly slow rate.", "Following the definition above in formula (), for such a fictive reversible process, a quantity of transferred heat (an inexact differential) is analyzed as a quantity , with (an exact differential):\nformula_8\nThis equality is only valid for a fictive transfer in which there is no production of entropy, that is to say, in which there is no uncompensated entropy.", "If, in contrast, the process is natural, and can really occur, with irreversibility, then there is entropy production, with .", "The quantity was termed by Clausius the \"uncompensated heat\", though that does not accord with present-day terminology.", "Then one has\nformula_9\nThis leads to the statement\nformula_10\nwhich is the second law of thermodynamics for closed systems.", "In non-equilibrium thermodynamics that makes the approximation of assuming the hypothesis of local thermodynamic equilibrium, there is a special notation for this.", "The transfer of energy as heat is assumed to take place across an infinitesimal temperature difference, so that the system element and its surroundings have near enough the same temperature .", "Then one writes\nformula_11\nwhere by definition\nformula_12\nThe second law for a natural process asserts that\nformula_13", "For a closed system (a system from which no matter can enter or exit), one version of the first law of thermodynamics states that the change in internal energy of the system is equal to the amount of heat supplied to the system minus the amount of thermodynamic work done by system on its surroundings.", "The foregoing sign convention for work is used in the present article, but an alternate sign convention, followed by IUPAC, for work, is to consider the work performed on the system by its surroundings as positive.", "This is the convention adopted by many modern textbooks of physical chemistry, such as those by Peter Atkins and Ira Levine, but many textbooks on physics define work as work done by the system.", "formula_14\nThis formula can be re-written so as to express a definition of quantity of energy transferred as heat, based purely on the concept of adiabatic work, if it is supposed that is defined and measured solely by processes of adiabatic work:\nformula_15\nThe thermodynamic work done by the system is through mechanisms defined by its thermodynamic state variables, for example, its volume , not through variables that necessarily involve mechanisms in the surroundings.", "The latter are such as shaft work, and include isochoric work.", "The internal energy, , is a state function.", "In cyclical processes, such as the operation of a heat engine, state functions of the working substance return to their initial values upon completion of a cycle.", "The differential, or infinitesimal increment, for the internal energy in an infinitesimal process is an exact differential .", "The symbol for exact differentials is the lowercase letter .", "In contrast, neither of the infinitesimal increments nor in an infinitesimal process represents the change in a state function of the system.", "Thus, infinitesimal increments of heat and work are inexact differentials.", "The lowercase Greek letter delta, , is the symbol for inexact differentials.", "The integral of any inexact differential in a process where the system leaves and then returns to the same thermodynamic state does not necessarily equal zero.", "As recounted above, in the section headed \"heat and entropy\", the second law of thermodynamics observes that if heat is supplied to a system in a reversible process, the increment of heat and the temperature form the exact differential\nformula_16\nand that , the entropy of the working body, is a state function.", "Likewise, with a well-defined pressure, , behind a slowly moving (quasistatic) boundary, the work differential, , and the pressure, , combine to form the exact differential\nformula_17\nwith the volume of the system, which is a state variable.", "In general, for systems of uniform pressure and temperature without composition change,\nformula_18\nAssociated with this differential equation is the concept that the internal energy may be considered to be a function of its natural variables and .", "The internal energy representation of the fundamental thermodynamic relation is written as\nformula_19\nIf is constant\nformula_20\nand if is constant\nformula_21\nwith the enthalpy defined by\nformula_22\nThe enthalpy may be considered to be a function of its natural variables and .", "The enthalpy representation of the fundamental thermodynamic relation is written\nformula_23\nThe internal energy representation and the enthalpy representation are partial Legendre transforms of one another.", "They contain the same physical information, written in different ways.", "Like the internal energy, the enthalpy stated as a function of its natural variables is a thermodynamic potential and contains all thermodynamic information about a body.", "If a quantity of heat is added to a body while it does only expansion work on its surroundings, one has\nformula_24\nIf this is constrained to happen at constant pressure, i.e. with , the expansion work done by the body is given by ; recalling the first law of thermodynamics, one has\nformula_25\nConsequently, by substitution one has\nformula_26\nIn this scenario, the increase in enthalpy is equal to the quantity of heat added to the system.", "This is the basis of the determination of enthalpy changes in chemical reactions by calorimetry.", "Since many processes do take place at constant atmospheric pressure, the enthalpy is sometimes given the misleading name of 'heat content' or heat function, while it actually depends strongly on the energies of covalent bonds and intermolecular forces.", "In terms of the natural variables of the state function , this process of change of state from state 1 to state 2 can be expressed as\nformula_27\nIt is known that the temperature is identically stated by\nformula_28\nConsequently,\nformula_29\nIn this case, the integral specifies a quantity of heat transferred at constant pressure.", "As a common noun, English \"heat\" or \"warmth\" (just as French \"chaleur\", German \"Wärme\", Latin \"calor\", Greek θάλπος, etc.) refers to (the human perception of) either thermal energy or temperature.", "Speculation on thermal energy or \"heat\" as a separate form of matter has a long history, see caloric theory, phlogiston and fire (classical element).", "The modern understanding of thermal energy originates with Thompson's 1798 mechanical theory of heat (\"An Experimental Enquiry Concerning the Source of the Heat which is Excited by Friction\"), postulating a mechanical equivalent of heat.", "A collaboration between Nicolas Clément and Sadi Carnot (\"Reflections on the Motive Power of Fire\") in the 1820s had some related thinking along similar lines.", "In 1845, Joule published a paper entitled \"The Mechanical Equivalent of Heat\", in which he specified a numerical value for the amount of mechanical work required to \"produce a unit of heat\".", "The theory of classical thermodynamics matured in the 1850s to 1860s.", "John Tyndall's \"Heat Considered as Mode of Motion\" (1863) was instrumental in popularizing the idea of heat as motion to the English-speaking public.", "The theory was developed in academic publications in French, English and German.", "From an early time, the French technical term \"chaleur\" used by Carnot was taken as equivalent to the English \"heat\" and German \"Wärme\" (lit.", "\"warmth\", while the equivalent of \"heat\" would be German \"Hitze\").", "The process function was introduced by Rudolf Clausius in 1850.", "Clausius described it with the German compound \"Wärmemenge\", translated as \"amount of heat\".", "James Clerk Maxwell in his 1871 \"Theory of Heat\" outlines four stipulations for the definition of heat:\n\n\nThe process function is referred to as \"Wärmemenge\" by Clausius, or as \"amount of heat\" in translation.", "Use of \"heat\" as an abbreviated form of the specific concept of \"quantity of energy transferred as heat\" led to some terminological confusion by the early 20th century.", "The generic meaning of \"heat\", even in classical thermodynamics, is just \"thermal energy\".", "Since the 1920s, it has been recommended practice to use enthalpy to refer to the \"heat content at constant volume\", and to thermal energy when \"heat\" in the general sense is intended, while \"heat\" is reserved for the very specific context of the transfer of thermal energy between two systems.", "Leonard Benedict Loeb in his \"Kinetic Theory of Gases\" (1927) makes a point of using \"quantity of heat\"\nor \"heat–quantity\" when referring to :", "After the perfection of thermometry [...] the next great advance made in the field of heat was the definition of a term which is called the quantity of heat.", "[... after the abandonment of caloric theory,] It still remains to interpret this very definite concept, the quantity of heat, in terms of a theory ascribing all heat to the kinetics of gas molecules.", "A frequent definition of heat is based on the work of Carathéodory (1909), referring to processes in a closed system.", "The internal energy of a body in an arbitrary state can be determined by amounts of work adiabatically performed by the body on its surroundings when it starts from a reference state .", "Such work is assessed through quantities defined in the surroundings of the body.", "It is supposed that such work can be assessed accurately, without error due to friction in the surroundings; friction in the body is not excluded by this definition.", "The adiabatic performance of work is defined in terms of adiabatic walls, which allow transfer of energy as work, but no other transfer, of energy or matter.", "In particular they do not allow the passage of energy as heat.", "According to this definition, work performed adiabatically is in general accompanied by friction within the thermodynamic system or body.", "On the other hand, according to Carathéodory (1909), there also exist non-adiabatic, \"diathermal\" walls, which are postulated to be permeable only to heat.", "For the definition of quantity of energy transferred as heat, it is customarily envisaged that an arbitrary state of interest is reached from state by a process with two components, one adiabatic and the other not adiabatic.", "For convenience one may say that the adiabatic component was the sum of work done by the body through volume change through movement of the walls while the non-adiabatic wall was temporarily rendered adiabatic, and of isochoric adiabatic work.", "Then the non-adiabatic component is a process of energy transfer through the wall that passes only heat, newly made accessible for the purpose of this transfer, from the surroundings to the body.", "The change in internal energy to reach the state from the state is the difference of the two amounts of energy transferred.", "Although Carathéodory himself did not state such a definition, following his work it is customary in theoretical studies to define heat, , to the body from its surroundings, in the combined process of change to state from the state , as the change in internal energy, , minus the amount of work, , done by the body on its surrounds by the adiabatic process, so that .", "In this definition, for the sake of conceptual rigour, the quantity of energy transferred as heat is not specified directly in terms of the non-adiabatic process.", "It is defined through knowledge of precisely two variables, the change of internal energy and the amount of adiabatic work done, for the combined process of change from the reference state to the arbitrary state .", "It is important that this does not explicitly involve the amount of energy transferred in the non-adiabatic component of the combined process.", "It is assumed here that the amount of energy required to pass from state to state , the change of internal energy, is known, independently of the combined process, by a determination through a purely adiabatic process, like that for the determination of the internal energy of state above.", "The rigour that is prized in this definition is that there is one and only one kind of energy transfer admitted as fundamental: energy transferred as work.", "Energy transfer as heat is considered as a derived quantity.", "The uniqueness of work in this scheme is considered to guarantee rigor and purity of conception.", "The conceptual purity of this definition, based on the concept of energy transferred as work as an ideal notion, relies on the idea that some frictionless and otherwise non-dissipative processes of energy transfer can be realized in physical actuality.", "The second law of thermodynamics, on the other hand, assures us that such processes are not found in nature.", "Before the rigorous mathematical definition of heat based on Carathéodory's 1909 paper,\nhistorically, heat, temperature, and thermal equilibrium were presented in thermodynamics textbooks as jointly primitive notions.", "Carathéodory introduced his 1909 paper thus: \"The proposition that the discipline of thermodynamics can be justified without recourse to any hypothesis that cannot be verified experimentally must be regarded as one of the most noteworthy results of the research in thermodynamics that was accomplished during the last century.\"", "Referring to the \"point of view adopted by most authors who were active in the last fifty years\", Carathéodory wrote: \"There exists a physical quantity called heat that is not identical with the mechanical quantities (mass, force, pressure, etc.) and whose variations can be determined by calorimetric measurements.\"", "James Serrin introduces an account of the theory of thermodynamics thus: \"In the following section, we shall use the classical notions of \"heat\", \"work\", and \"hotness\" as primitive elements, ...", "That heat is an appropriate and natural primitive for thermodynamics was already accepted by Carnot.", "Its continued validity as a primitive element of thermodynamical structure is due to the fact that it synthesizes an essential physical concept, as well as to its successful use in recent work to unify different constitutive theories.\"", "This traditional kind of presentation of the basis of thermodynamics includes ideas that may be summarized by the statement that heat transfer is purely due to spatial non-uniformity of temperature, and is by conduction and radiation, from hotter to colder bodies.", "It is sometimes proposed that this traditional kind of presentation necessarily rests on \"circular reasoning\"; against this proposal, there stands the rigorously logical mathematical development of the theory presented by Truesdell and Bharatha (1977).", "This alternative approach to the definition of quantity of energy transferred as heat differs in logical structure from that of Carathéodory, recounted just above.", "This alternative approach admits calorimetry as a primary or direct way to measure quantity of energy transferred as heat.", "It relies on temperature as one of its primitive concepts, and used in calorimetry.", "It is presupposed that enough processes exist physically to allow measurement of differences in internal energies.", "Such processes are not restricted to adiabatic transfers of energy as work.", "They include calorimetry, which is the commonest practical way of finding internal energy differences.", "The needed temperature can be either empirical or absolute thermodynamic.", "In contrast, the Carathéodory way recounted just above does not use calorimetry or temperature in its primary definition of quantity of energy transferred as heat.", "The Carathéodory way regards calorimetry only as a secondary or indirect way of measuring quantity of energy transferred as heat.", "As recounted in more detail just above, the Carathéodory way regards quantity of energy transferred as heat in a process as primarily or directly defined as a residual quantity.", "It is calculated from the difference of the internal energies of the initial and final states of the system, and from the actual work done by the system during the process.", "That internal energy difference is supposed to have been measured in advance through processes of purely adiabatic transfer of energy as work, processes that take the system between the initial and final states.", "By the Carathéodory way it is presupposed as known from experiment that there actually physically exist enough such adiabatic processes, so that there need be no recourse to calorimetry for measurement of quantity of energy transferred as heat.", "This presupposition is essential but is explicitly labeled neither as a law of thermodynamics nor as an axiom of the Carathéodory way.", "In fact, the actual physical existence of such adiabatic processes is indeed mostly supposition, and those supposed processes have in most cases not been actually verified empirically to exist.", "Referring to conduction, Partington writes: \"If a hot body is brought in conducting contact with a cold body, the temperature of the hot body falls and that of the cold body rises, and it is said that a \"quantity of heat\" has passed from the hot body to the cold body.", "\"\nReferring to radiation, Maxwell writes: \"In Radiation, the hotter body loses heat, and the colder body receives heat by means of a process occurring in some intervening medium which does not itself thereby become hot.\"\nMaxwell writes that convection as such \"is not a purely thermal phenomenon\".", "In thermodynamics, convection in general is regarded as transport of internal energy.", "If, however, the convection is enclosed and circulatory, then it may be regarded as an intermediary that transfers energy as heat between source and destination bodies, because it transfers only energy and not matter from the source to the destination body.", "In accordance with the first law for closed systems, energy transferred solely as heat leaves one body and enters another, changing the internal energies of each.", "Transfer, between bodies, of energy as work is a complementary way of changing internal energies.", "Though it is not logically rigorous from the viewpoint of strict physical concepts, a common form of words that expresses this is to say that heat and work are interconvertible.", "Cyclically operating engines that use only heat and work transfers have two thermal reservoirs, a hot and a cold one.", "They may be classified by the range of operating temperatures of the working body, relative to those reservoirs.", "In a heat engine, the working body is at all times colder than the hot reservoir and hotter than the cold reservoir.", "In a sense, it uses heat transfer to produce work.", "In a heat pump, the working body, at stages of the cycle, goes both hotter than the hot reservoir, and colder than the cold reservoir.", "In a sense, it uses work to produce heat transfer.", "In classical thermodynamics, a commonly considered model is the heat engine.", "It consists of four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir.", "A cyclic process leaves the working body in an unchanged state, and is envisaged as being repeated indefinitely often.", "Work transfers between the working body and the work reservoir are envisaged as reversible, and thus only one work reservoir is needed.", "But two thermal reservoirs are needed, because transfer of energy as heat is irreversible.", "A single cycle sees energy taken by the working body from the hot reservoir and sent to the two other reservoirs, the work reservoir and the cold reservoir.", "The hot reservoir always and only supplies energy and the cold reservoir always and only receives energy.", "The second law of thermodynamics requires that no cycle can occur in which no energy is received by the cold reservoir.", "Heat engines achieve higher efficiency when the ratio of the initial and final temperature is greater.", "Another commonly considered model is the heat pump or refrigerator.", "Again there are four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir.", "A single cycle starts with the working body colder than the cold reservoir, and then energy is taken in as heat by the working body from the cold reservoir.", "Then the work reservoir does work on the working body, adding more to its internal energy, making it hotter than the hot reservoir.", "The hot working body passes heat to the hot reservoir, but still remains hotter than the cold reservoir.", "Then, by allowing it to expand without passing heat to another body, the working body is made colder than the cold reservoir.", "It can now accept heat transfer from the cold reservoir to start another cycle.", "The device has transported energy from a colder to a hotter reservoir, but this is not regarded as by an inanimate agency; rather, it is regarded as by the harnessing of work .", "This is because work is supplied from the work reservoir, not just by a simple thermodynamic process, but by a cycle of thermodynamic operations and processes, which may be regarded as directed by an animate or harnessing agency.", "Accordingly, the cycle is still in accord with the second law of thermodynamics.", "The 'efficiency' of a heat pump (which exceeds unity) is best when the temperature difference between the hot and cold reservoirs is least.", "Functionally, such engines are used in two ways, distinguishing a target reservoir and a resource or surrounding reservoir.", "A heat pump transfers heat to the hot reservoir as the target from the resource or surrounding reservoir.", "A refrigerator transfers heat, from the cold reservoir as the target, to the resource or surrounding reservoir.", "The target reservoir may be regarded as leaking: when the target leaks heat to the surroundings, heat pumping is used; when the target leaks coldness to the surroundings, refrigeration is used.", "The engines harness work to overcome the leaks.", "According to Planck, there are three main conceptual approaches to heat.", "One is the microscopic or kinetic theory approach.", "The other two are macroscopic approaches.", "One is the approach through the law of conservation of energy taken as prior to thermodynamics, with a mechanical analysis of processes, for example in the work of Helmholtz.", "This mechanical view is taken in this article as currently customary for thermodynamic theory.", "The other macroscopic approach is the thermodynamic one, which admits heat as a primitive concept, which contributes, by scientific induction to knowledge of the law of conservation of energy.", "This view is widely taken as the practical one, quantity of heat being measured by calorimetry.", "Bailyn also distinguishes the two macroscopic approaches as the mechanical and the thermodynamic.", "The thermodynamic view was taken by the founders of thermodynamics in the nineteenth century.", "It regards quantity of energy transferred as heat as a primitive concept coherent with a primitive concept of temperature, measured primarily by calorimetry.", "A calorimeter is a body in the surroundings of the system, with its own temperature and internal energy; when it is connected to the system by a path for heat transfer, changes in it measure heat transfer.", "The mechanical view was pioneered by Helmholtz and developed and used in the twentieth century, largely through the influence of Max Born.", "It regards quantity of heat transferred as heat as a derived concept, defined for closed systems as quantity of heat transferred by mechanisms other than work transfer, the latter being regarded as primitive for thermodynamics, defined by macroscopic mechanics.", "According to Born, the transfer of internal energy between open systems that accompanies transfer of matter \"cannot be reduced to mechanics\".", "It follows that there is no well-founded definition of quantities of energy transferred as heat or as work associated with transfer of matter.", "Nevertheless, for the thermodynamical description of non-equilibrium processes, it is desired to consider the effect of a temperature gradient established by the surroundings across the system of interest when there is no physical barrier or wall between system and surroundings, that is to say, when they are open with respect to one another.", "The impossibility of a mechanical definition in terms of work for this circumstance does not alter the physical fact that a temperature gradient causes a diffusive flux of internal energy, a process that, in the thermodynamic view, might be proposed as a candidate concept for transfer of energy as heat.", "In this circumstance, it may be expected that there may also be active other drivers of diffusive flux of internal energy, such as gradient of chemical potential which drives transfer of matter, and gradient of electric potential which drives electric current and iontophoresis; such effects usually interact with diffusive flux of internal energy driven by temperature gradient, and such interactions are known as cross-effects.", "If cross-effects that result in diffusive transfer of internal energy were also labeled as heat transfers, they would sometimes violate the rule that pure heat transfer occurs only down a temperature gradient, never up one.", "They would also contradict the principle that all heat transfer is of one and the same kind, a principle founded on the idea of heat conduction between closed systems.", "One might to try to think narrowly of heat flux driven purely by temperature gradient as a conceptual component of diffusive internal energy flux, in the thermodynamic view, the concept resting specifically on careful calculations based on detailed knowledge of the processes and being indirectly assessed.", "In these circumstances, if perchance it happens that no transfer of matter is actualized, and there are no cross-effects, then the thermodynamic concept and the mechanical concept coincide, as if one were dealing with closed systems.", "But when there is transfer of matter, the exact laws by which temperature gradient drives diffusive flux of internal energy, rather than being exactly knowable, mostly need to be assumed, and in many cases are practically unverifiable.", "Consequently, when there is transfer of matter, the calculation of the pure 'heat flux' component of the diffusive flux of internal energy rests on practically unverifiable assumptions.", "This is a reason to think of heat as a specialized concept that relates primarily and precisely to closed systems, and applicable only in a very restricted way to open systems.", "In many writings in this context, the term \"heat flux\" is used when what is meant is therefore more accurately called diffusive flux of internal energy; such usage of the term \"heat flux\" is a residue of older and now obsolete language usage that allowed that a body may have a \"heat content\".", "In the kinetic theory, heat is explained in terms of the microscopic motions and interactions of constituent particles, such as electrons, atoms, and molecules.", "The immediate meaning of the kinetic energy of the constituent particles is not as heat.", "It is as a component of internal energy.", "In microscopic terms, heat is a transfer quantity, and is described by a transport theory, not as steadily localized kinetic energy of particles.", "Heat transfer arises from temperature gradients or differences, through the diffuse exchange of microscopic kinetic and potential particle energy, by particle collisions and other interactions.", "An early and vague expression of this was made by Francis Bacon.", "Precise and detailed versions of it were developed in the nineteenth century.", "In statistical mechanics, for a closed system (no transfer of matter), heat is the energy transfer associated with a disordered, microscopic action on the system, associated with jumps in occupation numbers of the energy levels of the system, without change in the values of the energy levels themselves.", "It is possible for macroscopic thermodynamic work to alter the occupation numbers without change in the values of the system energy levels themselves, but what distinguishes transfer as heat is that the transfer is entirely due to disordered, microscopic action, including radiative transfer.", "A mathematical definition can be formulated for small increments of quasi-static adiabatic work in terms of the statistical distribution of an ensemble of microstates.", "Quantity of heat transferred can be measured by calorimetry, or determined through calculations based on other quantities.", "Calorimetry is the empirical basis of the idea of quantity of heat transferred in a process.", "The transferred heat is measured by changes in a body of known properties, for example, temperature rise, change in volume or length, or phase change, such as melting of ice.", "A calculation of quantity of heat transferred can rely on a hypothetical quantity of energy transferred as adiabatic work and on the first law of thermodynamics.", "Such calculation is the primary approach of many theoretical studies of quantity of heat transferred.", "The discipline of heat transfer, typically considered an aspect of mechanical engineering and chemical engineering, deals with specific applied methods by which thermal energy in a system is generated, or converted, or transferred to another system.", "Although the definition of heat implicitly means the transfer of energy, the term \"heat transfer\" encompasses this traditional usage in many engineering disciplines and laymen language.", "\"Heat transfer\" is generally described as including the mechanisms of heat conduction, heat convection, thermal radiation, but may include mass transfer and heat in processes of phase changes.", "Convection may be described as the combined effects of conduction and fluid flow.", "From the thermodynamic point of view, heat flows into a fluid by diffusion to increase its energy, the fluid then transfers (advects) this increased internal energy (not heat) from one location to another, and this is then followed by a second thermal interaction which transfers heat to a second body or system, again by diffusion.", "This entire process is often regarded as an additional mechanism of heat transfer, although technically, \"heat transfer\" and thus heating and cooling occurs only on either end of such a conductive flow, but not as a result of flow.", "Thus, conduction can be said to \"transfer\" heat only as a net result of the process, but may not do so at every time within the complicated convective process.", "In an 1847 lecture entitled \"On Matter, Living Force, and Heat\", James Prescott Joule characterized the terms latent heat and sensible heat as components of heat each affecting distinct physical phenomena, namely the potential and kinetic energy of particles, respectively.", "He described latent energy as the energy possessed via a distancing of particles where attraction was over a greater distance, i.e. a form of potential energy, and the sensible heat as an energy involving the motion of particles, i.e. kinetic energy.", "Latent heat is the heat released or absorbed by a chemical substance or a thermodynamic system during a change of state that occurs without a change in temperature.", "Such a process may be a phase transition, such as the melting of ice or the boiling of water.", "Heat capacity is a measurable physical quantity equal to the ratio of the heat added to an object to the resulting temperature change.", "The \"molar heat capacity\" is the heat capacity per unit amount (SI unit: mole) of a pure substance, and the \"specific heat capacity\", often called simply \"specific heat\", is the heat capacity per unit mass of a material.", "Heat capacity is a physical property of a substance, which means that it depends on the state and properties of the substance under consideration.", "The specific heats of monatomic gases, such as helium, are nearly constant with temperature.", "Diatomic gases such as hydrogen display some temperature dependence, and triatomic gases (e.g., carbon dioxide) still more.", "Before the development of the laws of thermodynamics, heat was measured by changes in the states of the participating bodies.", "Some general rules, with important exceptions, can be stated as follows.", "In general, most bodies expand on heating.", "In this circumstance, heating a body at a constant volume increases the pressure it exerts on its constraining walls, while heating at a constant pressure increases its volume.", "Beyond this, most substances have three ordinarily recognized states of matter, solid, liquid, and gas.", "Some can also exist in a plasma.", "Many have further, more finely differentiated, states of matter, such as glass and liquid crystal.", "In many cases, at fixed temperature and pressure, a substance can exist in several distinct states of matter in what might be viewed as the same 'body'.", "For example, ice may float in a glass of water.", "Then the ice and the water are said to constitute two phases within the 'body'.", "Definite rules are known, telling how distinct phases may coexist in a 'body'.", "Mostly, at a fixed pressure, there is a definite temperature at which heating causes a solid to melt or evaporate, and a definite temperature at which heating causes a liquid to evaporate.", "In such cases, cooling has the reverse effects.", "All of these, the commonest cases, fit with a rule that heating can be measured by changes of state of a body.", "Such cases supply what are called \"thermometric bodies\", that allow the definition of empirical temperatures.", "Before 1848, all temperatures were defined in this way.", "There was thus a tight link, apparently logically determined, between heat and temperature, though they were recognized as conceptually thoroughly distinct, especially by Joseph Black in the later eighteenth century.", "There are important exceptions.", "They break the obviously apparent link between heat and temperature.", "They make it clear that empirical definitions of temperature are contingent on the peculiar properties of particular thermometric substances, and are thus precluded from the title 'absolute'.", "For example, water contracts on being heated near 277 K. It cannot be used as a thermometric substance near that temperature.", "Also, over a certain temperature range, ice contracts on heating.", "Moreover, many substances can exist in metastable states, such as with negative pressure, that survive only transiently and in very special conditions.", "Such facts, sometimes called 'anomalous', are some of the reasons for the thermodynamic definition of absolute temperature.", "In the early days of measurement of high temperatures, another factor was important, and used by Josiah Wedgwood in his pyrometer.", "The temperature reached in a process was estimated by the shrinkage of a sample of clay.", "The higher the temperature, the more the shrinkage.", "This was the only available more or less reliable method of measurement of temperatures above 1000 °C (1,832 °F).", "But such shrinkage is irreversible.", "The clay does not expand again on cooling.", "That is why it could be used for the measurement.", "But only once.", "It is not a thermometric material in the usual sense of the word.", "Nevertheless, the thermodynamic definition of absolute temperature does make essential use of the concept of heat, with proper circumspection.", "According to Denbigh (1981), the property of hotness is a concern of thermodynamics that should be defined without reference to the concept of heat.", "Consideration of hotness leads to the concept of empirical temperature.", "All physical systems are capable of heating or cooling others.", "With reference to hotness, the comparative terms hotter and colder are defined by the rule that heat flows from the hotter body to the colder.", "If a physical system is inhomogeneous or very rapidly or irregularly changing, for example by turbulence, it may be impossible to characterize it by a temperature, but still there can be transfer of energy as heat between it and another system.", "If a system has a physical state that is regular enough, and persists long enough to allow it to reach thermal equilibrium with a specified thermometer, then it has a temperature according to that thermometer.", "An empirical thermometer registers degree of hotness for such a system.", "Such a temperature is called empirical.", "For example, Truesdell writes about classical thermodynamics: \"At each time, the body is assigned a real number called the \"temperature\".", "This number is a measure of how hot the body is.", "\"\nPhysical systems that are too turbulent to have temperatures may still differ in hotness.", "A physical system that passes heat to another physical system is said to be the hotter of the two.", "More is required for the system to have a thermodynamic temperature.", "Its behavior must be so regular that its empirical temperature is the same for all suitably calibrated and scaled thermometers, and then its hotness is said to lie on the one-dimensional hotness manifold.", "This is part of the reason why heat is defined following Carathéodory and Born, solely as occurring other than by work or transfer of matter; temperature is advisedly and deliberately not mentioned in this now widely accepted definition.", "This is also the reason that the zeroth law of thermodynamics is stated explicitly.", "If three physical systems, \"A\", \"B\", and \"C\" are each not in their own states of internal thermodynamic equilibrium, it is possible that, with suitable physical connections being made between them, \"A\" can heat \"B\" and \"B\" can heat \"C\" and \"C\" can heat \"A\".", "In non-equilibrium situations, cycles of flow are possible.", "It is the special and uniquely distinguishing characteristic of internal thermodynamic equilibrium that this possibility is not open to thermodynamic systems (as distinguished amongst physical systems) which are in their own states of internal thermodynamic equilibrium; this is the reason why the zeroth law of thermodynamics needs explicit statement.", "That is to say, the relation 'is not colder than' between general non-equilibrium physical systems is not transitive, whereas, in contrast, the relation 'has no lower a temperature than' between thermodynamic systems in their own states of internal thermodynamic equilibrium is transitive.", "It follows from this that the relation 'is in thermal equilibrium with' is transitive, which is one way of stating the zeroth law.", "Just as temperature may be undefined for a sufficiently inhomogeneous system, so also may entropy be undefined for a system not in its own state of internal thermodynamic equilibrium.", "For example, 'the temperature of the solar system' is not a defined quantity.", "Likewise, 'the entropy of the solar system' is not defined in classical thermodynamics.", "It has not been possible to define non-equilibrium entropy, as a simple number for a whole system, in a clearly satisfactory way." ]

[ 182, 183, 184, 185, 186, 187, 188, 189, 190, 191 ]

[ "For example, radiative heat transfer can co-occur with matter transfer." ]

[ "The mechanisms of energy transfer that define heat include conduction, through direct contact of immobile bodies, or through a wall or barrier that is impermeable to matter; or radiation between separated bodies; or friction due to isochoric mechanical or electrical or magnetic or gravitational work done by the surroundings on the system of interest, such as Joule heating due to an electric current driven through the system of interest by an external system, or through a magnetic stirrer.", "When there is a suitable path between two systems with different temperatures, heat transfer occurs necessarily, immediately, and spontaneously from the hotter to the colder system.", "Thermal conduction occurs by the stochastic (random) motion of microscopic particles (such as atoms or molecules).", "In contrast, thermodynamic work is defined by mechanisms that act macroscopically and directly on the system's whole-body state variables; for example, change of the system's volume through a piston's motion with externally measurable force; or change of the system's internal electric polarization through an externally measurable change in electric field.", "The definition of heat transfer does not require that the process be in any sense smooth.", "For example, a bolt of lightning may transfer heat to a body.", "Convective circulation allows one body to heat another, through an intermediate circulating fluid that carries energy from a boundary of one to a boundary of the other; the actual heat transfer is by conduction and radiation between the fluid and the respective bodies.", "Convective circulation, though spontaneous, does not necessarily and immediately occur simply because of some slight temperature difference; for it to occur in a given arrangement of systems, there is a threshold that must be crossed.", "Although heat flows spontaneously from a hotter body to a cooler one, it is possible to construct a heat pump which expends work to transfer energy from a colder body to a hotter body.", "In contrast, a heat engine reduces an existing temperature difference to supply work to another system.", "Another thermodynamic type of heat transfer device is an active heat spreader, which expends work to speed up transfer of energy to colder surroundings from a hotter body, for example a computer component.", "As a form of energy, heat has the unit joule (J) in the International System of Units (SI).", "However, in many applied fields in engineering the British thermal unit (BTU) and the calorie are often used.", "The standard unit for the rate of heat transferred is the watt (W), defined as one joule per second.", "The symbol for the total amount of energy transferred as heat was used by Rudolf Clausius in 1850:\n\"Let the amount of heat which must be imparted during the transition of the gas in a definite manner from any given state to another, in which its volume is \"v\" and its temperature \"t\", be called \"Q\"\"\nHeat released by a system into its surroundings is by convention a negative quantity (); when a system absorbs heat from its surroundings, it is positive ().", "Heat transfer rate, or heat flow per unit time, is denoted by formula_1.", "This should not be confused with a time derivative of a function of state (which can also be written with the dot notation) since heat is not a function of state.", "Heat flux is defined as rate of heat transfer per unit cross-sectional area (units watts per square metre).", "In 1856, Rudolf Clausius, referring to closed systems, in which transfers of matter do not occur, defined the \"second fundamental theorem\" (the second law of thermodynamics) in the mechanical theory of heat (thermodynamics): \"if two transformations which, without necessitating any other permanent change, can mutually replace one another, be called equivalent, then the generations of the quantity of heat \"Q\" from work at the temperature \"T\", has the \"equivalence-value\":\"\nformula_2\nIn 1865, he came to define the entropy symbolized by \"S\", such that, due to the supply of the amount of heat \"Q\" at temperature \"T\" the entropy of the system is increased by\nIn a transfer of energy as heat without work being done, there are changes of entropy in both the surroundings which lose heat and the system which gains it.", "The increase, , of entropy in the system may be considered to consist of two parts, an increment, that matches, or 'compensates', the change, , of entropy in the surroundings, and a further increment, that may be considered to be 'generated' or 'produced' in the system, and is said therefore to be 'uncompensated'.", "Thus\nformula_3\nThis may also be written\nformula_4\nThe total change of entropy in the system and surroundings is thus\nformula_5\nThis may also be written\nformula_6\nIt is then said that an amount of entropy has been transferred from the surroundings to the system.", "Because entropy is not a conserved quantity, this is an exception to the general way of speaking, in which an amount transferred is of a conserved quantity.", "From the second law of thermodynamics follows that in a spontaneous transfer of heat, in which the temperature of the system is different from that of the surroundings:\nformula_7\nFor purposes of mathematical analysis of transfers, one thinks of fictive processes that are called \"reversible\", with the temperature of the system being hardly less than that of the surroundings, and the transfer taking place at an imperceptibly slow rate.", "Following the definition above in formula (), for such a fictive reversible process, a quantity of transferred heat (an inexact differential) is analyzed as a quantity , with (an exact differential):\nformula_8\nThis equality is only valid for a fictive transfer in which there is no production of entropy, that is to say, in which there is no uncompensated entropy.", "If, in contrast, the process is natural, and can really occur, with irreversibility, then there is entropy production, with .", "The quantity was termed by Clausius the \"uncompensated heat\", though that does not accord with present-day terminology.", "Then one has\nformula_9\nThis leads to the statement\nformula_10\nwhich is the second law of thermodynamics for closed systems.", "In non-equilibrium thermodynamics that makes the approximation of assuming the hypothesis of local thermodynamic equilibrium, there is a special notation for this.", "The transfer of energy as heat is assumed to take place across an infinitesimal temperature difference, so that the system element and its surroundings have near enough the same temperature .", "Then one writes\nformula_11\nwhere by definition\nformula_12\nThe second law for a natural process asserts that\nformula_13", "For a closed system (a system from which no matter can enter or exit), one version of the first law of thermodynamics states that the change in internal energy of the system is equal to the amount of heat supplied to the system minus the amount of thermodynamic work done by system on its surroundings.", "The foregoing sign convention for work is used in the present article, but an alternate sign convention, followed by IUPAC, for work, is to consider the work performed on the system by its surroundings as positive.", "This is the convention adopted by many modern textbooks of physical chemistry, such as those by Peter Atkins and Ira Levine, but many textbooks on physics define work as work done by the system.", "formula_14\nThis formula can be re-written so as to express a definition of quantity of energy transferred as heat, based purely on the concept of adiabatic work, if it is supposed that is defined and measured solely by processes of adiabatic work:\nformula_15\nThe thermodynamic work done by the system is through mechanisms defined by its thermodynamic state variables, for example, its volume , not through variables that necessarily involve mechanisms in the surroundings.", "The latter are such as shaft work, and include isochoric work.", "The internal energy, , is a state function.", "In cyclical processes, such as the operation of a heat engine, state functions of the working substance return to their initial values upon completion of a cycle.", "The differential, or infinitesimal increment, for the internal energy in an infinitesimal process is an exact differential .", "The symbol for exact differentials is the lowercase letter .", "In contrast, neither of the infinitesimal increments nor in an infinitesimal process represents the change in a state function of the system.", "Thus, infinitesimal increments of heat and work are inexact differentials.", "The lowercase Greek letter delta, , is the symbol for inexact differentials.", "The integral of any inexact differential in a process where the system leaves and then returns to the same thermodynamic state does not necessarily equal zero.", "As recounted above, in the section headed \"heat and entropy\", the second law of thermodynamics observes that if heat is supplied to a system in a reversible process, the increment of heat and the temperature form the exact differential\nformula_16\nand that , the entropy of the working body, is a state function.", "Likewise, with a well-defined pressure, , behind a slowly moving (quasistatic) boundary, the work differential, , and the pressure, , combine to form the exact differential\nformula_17\nwith the volume of the system, which is a state variable.", "In general, for systems of uniform pressure and temperature without composition change,\nformula_18\nAssociated with this differential equation is the concept that the internal energy may be considered to be a function of its natural variables and .", "The internal energy representation of the fundamental thermodynamic relation is written as\nformula_19\nIf is constant\nformula_20\nand if is constant\nformula_21\nwith the enthalpy defined by\nformula_22\nThe enthalpy may be considered to be a function of its natural variables and .", "The enthalpy representation of the fundamental thermodynamic relation is written\nformula_23\nThe internal energy representation and the enthalpy representation are partial Legendre transforms of one another.", "They contain the same physical information, written in different ways.", "Like the internal energy, the enthalpy stated as a function of its natural variables is a thermodynamic potential and contains all thermodynamic information about a body.", "If a quantity of heat is added to a body while it does only expansion work on its surroundings, one has\nformula_24\nIf this is constrained to happen at constant pressure, i.e. with , the expansion work done by the body is given by ; recalling the first law of thermodynamics, one has\nformula_25\nConsequently, by substitution one has\nformula_26\nIn this scenario, the increase in enthalpy is equal to the quantity of heat added to the system.", "This is the basis of the determination of enthalpy changes in chemical reactions by calorimetry.", "Since many processes do take place at constant atmospheric pressure, the enthalpy is sometimes given the misleading name of 'heat content' or heat function, while it actually depends strongly on the energies of covalent bonds and intermolecular forces.", "In terms of the natural variables of the state function , this process of change of state from state 1 to state 2 can be expressed as\nformula_27\nIt is known that the temperature is identically stated by\nformula_28\nConsequently,\nformula_29\nIn this case, the integral specifies a quantity of heat transferred at constant pressure.", "As a common noun, English \"heat\" or \"warmth\" (just as French \"chaleur\", German \"Wärme\", Latin \"calor\", Greek θάλπος, etc.) refers to (the human perception of) either thermal energy or temperature.", "Speculation on thermal energy or \"heat\" as a separate form of matter has a long history, see caloric theory, phlogiston and fire (classical element).", "The modern understanding of thermal energy originates with Thompson's 1798 mechanical theory of heat (\"An Experimental Enquiry Concerning the Source of the Heat which is Excited by Friction\"), postulating a mechanical equivalent of heat.", "A collaboration between Nicolas Clément and Sadi Carnot (\"Reflections on the Motive Power of Fire\") in the 1820s had some related thinking along similar lines.", "In 1845, Joule published a paper entitled \"The Mechanical Equivalent of Heat\", in which he specified a numerical value for the amount of mechanical work required to \"produce a unit of heat\".", "The theory of classical thermodynamics matured in the 1850s to 1860s.", "John Tyndall's \"Heat Considered as Mode of Motion\" (1863) was instrumental in popularizing the idea of heat as motion to the English-speaking public.", "The theory was developed in academic publications in French, English and German.", "From an early time, the French technical term \"chaleur\" used by Carnot was taken as equivalent to the English \"heat\" and German \"Wärme\" (lit.", "\"warmth\", while the equivalent of \"heat\" would be German \"Hitze\").", "The process function was introduced by Rudolf Clausius in 1850.", "Clausius described it with the German compound \"Wärmemenge\", translated as \"amount of heat\".", "James Clerk Maxwell in his 1871 \"Theory of Heat\" outlines four stipulations for the definition of heat:\n\n\nThe process function is referred to as \"Wärmemenge\" by Clausius, or as \"amount of heat\" in translation.", "Use of \"heat\" as an abbreviated form of the specific concept of \"quantity of energy transferred as heat\" led to some terminological confusion by the early 20th century.", "The generic meaning of \"heat\", even in classical thermodynamics, is just \"thermal energy\".", "Since the 1920s, it has been recommended practice to use enthalpy to refer to the \"heat content at constant volume\", and to thermal energy when \"heat\" in the general sense is intended, while \"heat\" is reserved for the very specific context of the transfer of thermal energy between two systems.", "Leonard Benedict Loeb in his \"Kinetic Theory of Gases\" (1927) makes a point of using \"quantity of heat\"\nor \"heat–quantity\" when referring to :", "After the perfection of thermometry [...] the next great advance made in the field of heat was the definition of a term which is called the quantity of heat.", "[... after the abandonment of caloric theory,] It still remains to interpret this very definite concept, the quantity of heat, in terms of a theory ascribing all heat to the kinetics of gas molecules.", "A frequent definition of heat is based on the work of Carathéodory (1909), referring to processes in a closed system.", "The internal energy of a body in an arbitrary state can be determined by amounts of work adiabatically performed by the body on its surroundings when it starts from a reference state .", "Such work is assessed through quantities defined in the surroundings of the body.", "It is supposed that such work can be assessed accurately, without error due to friction in the surroundings; friction in the body is not excluded by this definition.", "The adiabatic performance of work is defined in terms of adiabatic walls, which allow transfer of energy as work, but no other transfer, of energy or matter.", "In particular they do not allow the passage of energy as heat.", "According to this definition, work performed adiabatically is in general accompanied by friction within the thermodynamic system or body.", "On the other hand, according to Carathéodory (1909), there also exist non-adiabatic, \"diathermal\" walls, which are postulated to be permeable only to heat.", "For the definition of quantity of energy transferred as heat, it is customarily envisaged that an arbitrary state of interest is reached from state by a process with two components, one adiabatic and the other not adiabatic.", "For convenience one may say that the adiabatic component was the sum of work done by the body through volume change through movement of the walls while the non-adiabatic wall was temporarily rendered adiabatic, and of isochoric adiabatic work.", "Then the non-adiabatic component is a process of energy transfer through the wall that passes only heat, newly made accessible for the purpose of this transfer, from the surroundings to the body.", "The change in internal energy to reach the state from the state is the difference of the two amounts of energy transferred.", "Although Carathéodory himself did not state such a definition, following his work it is customary in theoretical studies to define heat, , to the body from its surroundings, in the combined process of change to state from the state , as the change in internal energy, , minus the amount of work, , done by the body on its surrounds by the adiabatic process, so that .", "In this definition, for the sake of conceptual rigour, the quantity of energy transferred as heat is not specified directly in terms of the non-adiabatic process.", "It is defined through knowledge of precisely two variables, the change of internal energy and the amount of adiabatic work done, for the combined process of change from the reference state to the arbitrary state .", "It is important that this does not explicitly involve the amount of energy transferred in the non-adiabatic component of the combined process.", "It is assumed here that the amount of energy required to pass from state to state , the change of internal energy, is known, independently of the combined process, by a determination through a purely adiabatic process, like that for the determination of the internal energy of state above.", "The rigour that is prized in this definition is that there is one and only one kind of energy transfer admitted as fundamental: energy transferred as work.", "Energy transfer as heat is considered as a derived quantity.", "The uniqueness of work in this scheme is considered to guarantee rigor and purity of conception.", "The conceptual purity of this definition, based on the concept of energy transferred as work as an ideal notion, relies on the idea that some frictionless and otherwise non-dissipative processes of energy transfer can be realized in physical actuality.", "The second law of thermodynamics, on the other hand, assures us that such processes are not found in nature.", "Before the rigorous mathematical definition of heat based on Carathéodory's 1909 paper,\nhistorically, heat, temperature, and thermal equilibrium were presented in thermodynamics textbooks as jointly primitive notions.", "Carathéodory introduced his 1909 paper thus: \"The proposition that the discipline of thermodynamics can be justified without recourse to any hypothesis that cannot be verified experimentally must be regarded as one of the most noteworthy results of the research in thermodynamics that was accomplished during the last century.\"", "Referring to the \"point of view adopted by most authors who were active in the last fifty years\", Carathéodory wrote: \"There exists a physical quantity called heat that is not identical with the mechanical quantities (mass, force, pressure, etc.) and whose variations can be determined by calorimetric measurements.\"", "James Serrin introduces an account of the theory of thermodynamics thus: \"In the following section, we shall use the classical notions of \"heat\", \"work\", and \"hotness\" as primitive elements, ...", "That heat is an appropriate and natural primitive for thermodynamics was already accepted by Carnot.", "Its continued validity as a primitive element of thermodynamical structure is due to the fact that it synthesizes an essential physical concept, as well as to its successful use in recent work to unify different constitutive theories.\"", "This traditional kind of presentation of the basis of thermodynamics includes ideas that may be summarized by the statement that heat transfer is purely due to spatial non-uniformity of temperature, and is by conduction and radiation, from hotter to colder bodies.", "It is sometimes proposed that this traditional kind of presentation necessarily rests on \"circular reasoning\"; against this proposal, there stands the rigorously logical mathematical development of the theory presented by Truesdell and Bharatha (1977).", "This alternative approach to the definition of quantity of energy transferred as heat differs in logical structure from that of Carathéodory, recounted just above.", "This alternative approach admits calorimetry as a primary or direct way to measure quantity of energy transferred as heat.", "It relies on temperature as one of its primitive concepts, and used in calorimetry.", "It is presupposed that enough processes exist physically to allow measurement of differences in internal energies.", "Such processes are not restricted to adiabatic transfers of energy as work.", "They include calorimetry, which is the commonest practical way of finding internal energy differences.", "The needed temperature can be either empirical or absolute thermodynamic.", "In contrast, the Carathéodory way recounted just above does not use calorimetry or temperature in its primary definition of quantity of energy transferred as heat.", "The Carathéodory way regards calorimetry only as a secondary or indirect way of measuring quantity of energy transferred as heat.", "As recounted in more detail just above, the Carathéodory way regards quantity of energy transferred as heat in a process as primarily or directly defined as a residual quantity.", "It is calculated from the difference of the internal energies of the initial and final states of the system, and from the actual work done by the system during the process.", "That internal energy difference is supposed to have been measured in advance through processes of purely adiabatic transfer of energy as work, processes that take the system between the initial and final states.", "By the Carathéodory way it is presupposed as known from experiment that there actually physically exist enough such adiabatic processes, so that there need be no recourse to calorimetry for measurement of quantity of energy transferred as heat.", "This presupposition is essential but is explicitly labeled neither as a law of thermodynamics nor as an axiom of the Carathéodory way.", "In fact, the actual physical existence of such adiabatic processes is indeed mostly supposition, and those supposed processes have in most cases not been actually verified empirically to exist.", "Referring to conduction, Partington writes: \"If a hot body is brought in conducting contact with a cold body, the temperature of the hot body falls and that of the cold body rises, and it is said that a \"quantity of heat\" has passed from the hot body to the cold body.", "\"\nReferring to radiation, Maxwell writes: \"In Radiation, the hotter body loses heat, and the colder body receives heat by means of a process occurring in some intervening medium which does not itself thereby become hot.\"\nMaxwell writes that convection as such \"is not a purely thermal phenomenon\".", "In thermodynamics, convection in general is regarded as transport of internal energy.", "If, however, the convection is enclosed and circulatory, then it may be regarded as an intermediary that transfers energy as heat between source and destination bodies, because it transfers only energy and not matter from the source to the destination body.", "In accordance with the first law for closed systems, energy transferred solely as heat leaves one body and enters another, changing the internal energies of each.", "Transfer, between bodies, of energy as work is a complementary way of changing internal energies.", "Though it is not logically rigorous from the viewpoint of strict physical concepts, a common form of words that expresses this is to say that heat and work are interconvertible.", "Cyclically operating engines that use only heat and work transfers have two thermal reservoirs, a hot and a cold one.", "They may be classified by the range of operating temperatures of the working body, relative to those reservoirs.", "In a heat engine, the working body is at all times colder than the hot reservoir and hotter than the cold reservoir.", "In a sense, it uses heat transfer to produce work.", "In a heat pump, the working body, at stages of the cycle, goes both hotter than the hot reservoir, and colder than the cold reservoir.", "In a sense, it uses work to produce heat transfer.", "In classical thermodynamics, a commonly considered model is the heat engine.", "It consists of four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir.", "A cyclic process leaves the working body in an unchanged state, and is envisaged as being repeated indefinitely often.", "Work transfers between the working body and the work reservoir are envisaged as reversible, and thus only one work reservoir is needed.", "But two thermal reservoirs are needed, because transfer of energy as heat is irreversible.", "A single cycle sees energy taken by the working body from the hot reservoir and sent to the two other reservoirs, the work reservoir and the cold reservoir.", "The hot reservoir always and only supplies energy and the cold reservoir always and only receives energy.", "The second law of thermodynamics requires that no cycle can occur in which no energy is received by the cold reservoir.", "Heat engines achieve higher efficiency when the ratio of the initial and final temperature is greater.", "Another commonly considered model is the heat pump or refrigerator.", "Again there are four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir.", "A single cycle starts with the working body colder than the cold reservoir, and then energy is taken in as heat by the working body from the cold reservoir.", "Then the work reservoir does work on the working body, adding more to its internal energy, making it hotter than the hot reservoir.", "The hot working body passes heat to the hot reservoir, but still remains hotter than the cold reservoir.", "Then, by allowing it to expand without passing heat to another body, the working body is made colder than the cold reservoir.", "It can now accept heat transfer from the cold reservoir to start another cycle.", "The device has transported energy from a colder to a hotter reservoir, but this is not regarded as by an inanimate agency; rather, it is regarded as by the harnessing of work .", "This is because work is supplied from the work reservoir, not just by a simple thermodynamic process, but by a cycle of thermodynamic operations and processes, which may be regarded as directed by an animate or harnessing agency.", "Accordingly, the cycle is still in accord with the second law of thermodynamics.", "The 'efficiency' of a heat pump (which exceeds unity) is best when the temperature difference between the hot and cold reservoirs is least.", "Functionally, such engines are used in two ways, distinguishing a target reservoir and a resource or surrounding reservoir.", "A heat pump transfers heat to the hot reservoir as the target from the resource or surrounding reservoir.", "A refrigerator transfers heat, from the cold reservoir as the target, to the resource or surrounding reservoir.", "The target reservoir may be regarded as leaking: when the target leaks heat to the surroundings, heat pumping is used; when the target leaks coldness to the surroundings, refrigeration is used.", "The engines harness work to overcome the leaks.", "According to Planck, there are three main conceptual approaches to heat.", "One is the microscopic or kinetic theory approach.", "The other two are macroscopic approaches.", "One is the approach through the law of conservation of energy taken as prior to thermodynamics, with a mechanical analysis of processes, for example in the work of Helmholtz.", "This mechanical view is taken in this article as currently customary for thermodynamic theory.", "The other macroscopic approach is the thermodynamic one, which admits heat as a primitive concept, which contributes, by scientific induction to knowledge of the law of conservation of energy.", "This view is widely taken as the practical one, quantity of heat being measured by calorimetry.", "Bailyn also distinguishes the two macroscopic approaches as the mechanical and the thermodynamic.", "The thermodynamic view was taken by the founders of thermodynamics in the nineteenth century.", "It regards quantity of energy transferred as heat as a primitive concept coherent with a primitive concept of temperature, measured primarily by calorimetry.", "A calorimeter is a body in the surroundings of the system, with its own temperature and internal energy; when it is connected to the system by a path for heat transfer, changes in it measure heat transfer.", "The mechanical view was pioneered by Helmholtz and developed and used in the twentieth century, largely through the influence of Max Born.", "It regards quantity of heat transferred as heat as a derived concept, defined for closed systems as quantity of heat transferred by mechanisms other than work transfer, the latter being regarded as primitive for thermodynamics, defined by macroscopic mechanics.", "According to Born, the transfer of internal energy between open systems that accompanies transfer of matter \"cannot be reduced to mechanics\".", "It follows that there is no well-founded definition of quantities of energy transferred as heat or as work associated with transfer of matter.", "Nevertheless, for the thermodynamical description of non-equilibrium processes, it is desired to consider the effect of a temperature gradient established by the surroundings across the system of interest when there is no physical barrier or wall between system and surroundings, that is to say, when they are open with respect to one another.", "The impossibility of a mechanical definition in terms of work for this circumstance does not alter the physical fact that a temperature gradient causes a diffusive flux of internal energy, a process that, in the thermodynamic view, might be proposed as a candidate concept for transfer of energy as heat.", "In this circumstance, it may be expected that there may also be active other drivers of diffusive flux of internal energy, such as gradient of chemical potential which drives transfer of matter, and gradient of electric potential which drives electric current and iontophoresis; such effects usually interact with diffusive flux of internal energy driven by temperature gradient, and such interactions are known as cross-effects.", "If cross-effects that result in diffusive transfer of internal energy were also labeled as heat transfers, they would sometimes violate the rule that pure heat transfer occurs only down a temperature gradient, never up one.", "They would also contradict the principle that all heat transfer is of one and the same kind, a principle founded on the idea of heat conduction between closed systems.", "One might to try to think narrowly of heat flux driven purely by temperature gradient as a conceptual component of diffusive internal energy flux, in the thermodynamic view, the concept resting specifically on careful calculations based on detailed knowledge of the processes and being indirectly assessed.", "In these circumstances, if perchance it happens that no transfer of matter is actualized, and there are no cross-effects, then the thermodynamic concept and the mechanical concept coincide, as if one were dealing with closed systems.", "But when there is transfer of matter, the exact laws by which temperature gradient drives diffusive flux of internal energy, rather than being exactly knowable, mostly need to be assumed, and in many cases are practically unverifiable.", "Consequently, when there is transfer of matter, the calculation of the pure 'heat flux' component of the diffusive flux of internal energy rests on practically unverifiable assumptions.", "This is a reason to think of heat as a specialized concept that relates primarily and precisely to closed systems, and applicable only in a very restricted way to open systems.", "In many writings in this context, the term \"heat flux\" is used when what is meant is therefore more accurately called diffusive flux of internal energy; such usage of the term \"heat flux\" is a residue of older and now obsolete language usage that allowed that a body may have a \"heat content\".", "In the kinetic theory, heat is explained in terms of the microscopic motions and interactions of constituent particles, such as electrons, atoms, and molecules.", "The immediate meaning of the kinetic energy of the constituent particles is not as heat.", "It is as a component of internal energy.", "In microscopic terms, heat is a transfer quantity, and is described by a transport theory, not as steadily localized kinetic energy of particles.", "Heat transfer arises from temperature gradients or differences, through the diffuse exchange of microscopic kinetic and potential particle energy, by particle collisions and other interactions.", "An early and vague expression of this was made by Francis Bacon.", "Precise and detailed versions of it were developed in the nineteenth century.", "In statistical mechanics, for a closed system (no transfer of matter), heat is the energy transfer associated with a disordered, microscopic action on the system, associated with jumps in occupation numbers of the energy levels of the system, without change in the values of the energy levels themselves.", "It is possible for macroscopic thermodynamic work to alter the occupation numbers without change in the values of the system energy levels themselves, but what distinguishes transfer as heat is that the transfer is entirely due to disordered, microscopic action, including radiative transfer.", "A mathematical definition can be formulated for small increments of quasi-static adiabatic work in terms of the statistical distribution of an ensemble of microstates.", "Quantity of heat transferred can be measured by calorimetry, or determined through calculations based on other quantities.", "Calorimetry is the empirical basis of the idea of quantity of heat transferred in a process.", "The transferred heat is measured by changes in a body of known properties, for example, temperature rise, change in volume or length, or phase change, such as melting of ice.", "A calculation of quantity of heat transferred can rely on a hypothetical quantity of energy transferred as adiabatic work and on the first law of thermodynamics.", "Such calculation is the primary approach of many theoretical studies of quantity of heat transferred.", "The discipline of heat transfer, typically considered an aspect of mechanical engineering and chemical engineering, deals with specific applied methods by which thermal energy in a system is generated, or converted, or transferred to another system.", "Although the definition of heat implicitly means the transfer of energy, the term \"heat transfer\" encompasses this traditional usage in many engineering disciplines and laymen language.", "\"Heat transfer\" is generally described as including the mechanisms of heat conduction, heat convection, thermal radiation, but may include mass transfer and heat in processes of phase changes.", "Convection may be described as the combined effects of conduction and fluid flow.", "From the thermodynamic point of view, heat flows into a fluid by diffusion to increase its energy, the fluid then transfers (advects) this increased internal energy (not heat) from one location to another, and this is then followed by a second thermal interaction which transfers heat to a second body or system, again by diffusion.", "This entire process is often regarded as an additional mechanism of heat transfer, although technically, \"heat transfer\" and thus heating and cooling occurs only on either end of such a conductive flow, but not as a result of flow.", "Thus, conduction can be said to \"transfer\" heat only as a net result of the process, but may not do so at every time within the complicated convective process.", "In an 1847 lecture entitled \"On Matter, Living Force, and Heat\", James Prescott Joule characterized the terms latent heat and sensible heat as components of heat each affecting distinct physical phenomena, namely the potential and kinetic energy of particles, respectively.", "He described latent energy as the energy possessed via a distancing of particles where attraction was over a greater distance, i.e. a form of potential energy, and the sensible heat as an energy involving the motion of particles, i.e. kinetic energy.", "Latent heat is the heat released or absorbed by a chemical substance or a thermodynamic system during a change of state that occurs without a change in temperature.", "Such a process may be a phase transition, such as the melting of ice or the boiling of water.", "Heat capacity is a measurable physical quantity equal to the ratio of the heat added to an object to the resulting temperature change.", "The \"molar heat capacity\" is the heat capacity per unit amount (SI unit: mole) of a pure substance, and the \"specific heat capacity\", often called simply \"specific heat\", is the heat capacity per unit mass of a material.", "Heat capacity is a physical property of a substance, which means that it depends on the state and properties of the substance under consideration.", "The specific heats of monatomic gases, such as helium, are nearly constant with temperature.", "Diatomic gases such as hydrogen display some temperature dependence, and triatomic gases (e.g., carbon dioxide) still more.", "Before the development of the laws of thermodynamics, heat was measured by changes in the states of the participating bodies.", "Some general rules, with important exceptions, can be stated as follows.", "In general, most bodies expand on heating.", "In this circumstance, heating a body at a constant volume increases the pressure it exerts on its constraining walls, while heating at a constant pressure increases its volume.", "Beyond this, most substances have three ordinarily recognized states of matter, solid, liquid, and gas.", "Some can also exist in a plasma.", "Many have further, more finely differentiated, states of matter, such as glass and liquid crystal.", "In many cases, at fixed temperature and pressure, a substance can exist in several distinct states of matter in what might be viewed as the same 'body'.", "For example, ice may float in a glass of water.", "Then the ice and the water are said to constitute two phases within the 'body'.", "Definite rules are known, telling how distinct phases may coexist in a 'body'.", "Mostly, at a fixed pressure, there is a definite temperature at which heating causes a solid to melt or evaporate, and a definite temperature at which heating causes a liquid to evaporate.", "In such cases, cooling has the reverse effects.", "All of these, the commonest cases, fit with a rule that heating can be measured by changes of state of a body.", "Such cases supply what are called \"thermometric bodies\", that allow the definition of empirical temperatures.", "Before 1848, all temperatures were defined in this way.", "There was thus a tight link, apparently logically determined, between heat and temperature, though they were recognized as conceptually thoroughly distinct, especially by Joseph Black in the later eighteenth century.", "There are important exceptions.", "They break the obviously apparent link between heat and temperature.", "They make it clear that empirical definitions of temperature are contingent on the peculiar properties of particular thermometric substances, and are thus precluded from the title 'absolute'.", "For example, water contracts on being heated near 277 K. It cannot be used as a thermometric substance near that temperature.", "Also, over a certain temperature range, ice contracts on heating.", "Moreover, many substances can exist in metastable states, such as with negative pressure, that survive only transiently and in very special conditions.", "Such facts, sometimes called 'anomalous', are some of the reasons for the thermodynamic definition of absolute temperature.", "In the early days of measurement of high temperatures, another factor was important, and used by Josiah Wedgwood in his pyrometer.", "The temperature reached in a process was estimated by the shrinkage of a sample of clay.", "The higher the temperature, the more the shrinkage.", "This was the only available more or less reliable method of measurement of temperatures above 1000 °C (1,832 °F).", "But such shrinkage is irreversible.", "The clay does not expand again on cooling.", "That is why it could be used for the measurement.", "But only once.", "It is not a thermometric material in the usual sense of the word.", "Nevertheless, the thermodynamic definition of absolute temperature does make essential use of the concept of heat, with proper circumspection.", "According to Denbigh (1981), the property of hotness is a concern of thermodynamics that should be defined without reference to the concept of heat.", "Consideration of hotness leads to the concept of empirical temperature.", "All physical systems are capable of heating or cooling others.", "With reference to hotness, the comparative terms hotter and colder are defined by the rule that heat flows from the hotter body to the colder.", "If a physical system is inhomogeneous or very rapidly or irregularly changing, for example by turbulence, it may be impossible to characterize it by a temperature, but still there can be transfer of energy as heat between it and another system.", "If a system has a physical state that is regular enough, and persists long enough to allow it to reach thermal equilibrium with a specified thermometer, then it has a temperature according to that thermometer.", "An empirical thermometer registers degree of hotness for such a system.", "Such a temperature is called empirical.", "For example, Truesdell writes about classical thermodynamics: \"At each time, the body is assigned a real number called the \"temperature\".", "This number is a measure of how hot the body is.", "\"\nPhysical systems that are too turbulent to have temperatures may still differ in hotness.", "A physical system that passes heat to another physical system is said to be the hotter of the two.", "More is required for the system to have a thermodynamic temperature.", "Its behavior must be so regular that its empirical temperature is the same for all suitably calibrated and scaled thermometers, and then its hotness is said to lie on the one-dimensional hotness manifold.", "This is part of the reason why heat is defined following Carathéodory and Born, solely as occurring other than by work or transfer of matter; temperature is advisedly and deliberately not mentioned in this now widely accepted definition.", "This is also the reason that the zeroth law of thermodynamics is stated explicitly.", "If three physical systems, \"A\", \"B\", and \"C\" are each not in their own states of internal thermodynamic equilibrium, it is possible that, with suitable physical connections being made between them, \"A\" can heat \"B\" and \"B\" can heat \"C\" and \"C\" can heat \"A\".", "In non-equilibrium situations, cycles of flow are possible.", "It is the special and uniquely distinguishing characteristic of internal thermodynamic equilibrium that this possibility is not open to thermodynamic systems (as distinguished amongst physical systems) which are in their own states of internal thermodynamic equilibrium; this is the reason why the zeroth law of thermodynamics needs explicit statement.", "That is to say, the relation 'is not colder than' between general non-equilibrium physical systems is not transitive, whereas, in contrast, the relation 'has no lower a temperature than' between thermodynamic systems in their own states of internal thermodynamic equilibrium is transitive.", "It follows from this that the relation 'is in thermal equilibrium with' is transitive, which is one way of stating the zeroth law.", "Just as temperature may be undefined for a sufficiently inhomogeneous system, so also may entropy be undefined for a system not in its own state of internal thermodynamic equilibrium.", "For example, 'the temperature of the solar system' is not a defined quantity.", "Likewise, 'the entropy of the solar system' is not defined in classical thermodynamics.", "It has not been possible to define non-equilibrium entropy, as a simple number for a whole system, in a clearly satisfactory way." ]

[ 192, 193, 194, 195, 196 ]

[ "For example, respectively in special circumstances, heat transfer can be measured by the amount of ice melted, or by change in temperature of a body in the surroundings of the system." ]

[ "The mechanisms of energy transfer that define heat include conduction, through direct contact of immobile bodies, or through a wall or barrier that is impermeable to matter; or radiation between separated bodies; or friction due to isochoric mechanical or electrical or magnetic or gravitational work done by the surroundings on the system of interest, such as Joule heating due to an electric current driven through the system of interest by an external system, or through a magnetic stirrer.", "When there is a suitable path between two systems with different temperatures, heat transfer occurs necessarily, immediately, and spontaneously from the hotter to the colder system.", "Thermal conduction occurs by the stochastic (random) motion of microscopic particles (such as atoms or molecules).", "In contrast, thermodynamic work is defined by mechanisms that act macroscopically and directly on the system's whole-body state variables; for example, change of the system's volume through a piston's motion with externally measurable force; or change of the system's internal electric polarization through an externally measurable change in electric field.", "The definition of heat transfer does not require that the process be in any sense smooth.", "For example, a bolt of lightning may transfer heat to a body.", "Convective circulation allows one body to heat another, through an intermediate circulating fluid that carries energy from a boundary of one to a boundary of the other; the actual heat transfer is by conduction and radiation between the fluid and the respective bodies.", "Convective circulation, though spontaneous, does not necessarily and immediately occur simply because of some slight temperature difference; for it to occur in a given arrangement of systems, there is a threshold that must be crossed.", "Although heat flows spontaneously from a hotter body to a cooler one, it is possible to construct a heat pump which expends work to transfer energy from a colder body to a hotter body.", "In contrast, a heat engine reduces an existing temperature difference to supply work to another system.", "Another thermodynamic type of heat transfer device is an active heat spreader, which expends work to speed up transfer of energy to colder surroundings from a hotter body, for example a computer component.", "As a form of energy, heat has the unit joule (J) in the International System of Units (SI).", "However, in many applied fields in engineering the British thermal unit (BTU) and the calorie are often used.", "The standard unit for the rate of heat transferred is the watt (W), defined as one joule per second.", "The symbol for the total amount of energy transferred as heat was used by Rudolf Clausius in 1850:\n\"Let the amount of heat which must be imparted during the transition of the gas in a definite manner from any given state to another, in which its volume is \"v\" and its temperature \"t\", be called \"Q\"\"\nHeat released by a system into its surroundings is by convention a negative quantity (); when a system absorbs heat from its surroundings, it is positive ().", "Heat transfer rate, or heat flow per unit time, is denoted by formula_1.", "This should not be confused with a time derivative of a function of state (which can also be written with the dot notation) since heat is not a function of state.", "Heat flux is defined as rate of heat transfer per unit cross-sectional area (units watts per square metre).", "In 1856, Rudolf Clausius, referring to closed systems, in which transfers of matter do not occur, defined the \"second fundamental theorem\" (the second law of thermodynamics) in the mechanical theory of heat (thermodynamics): \"if two transformations which, without necessitating any other permanent change, can mutually replace one another, be called equivalent, then the generations of the quantity of heat \"Q\" from work at the temperature \"T\", has the \"equivalence-value\":\"\nformula_2\nIn 1865, he came to define the entropy symbolized by \"S\", such that, due to the supply of the amount of heat \"Q\" at temperature \"T\" the entropy of the system is increased by\nIn a transfer of energy as heat without work being done, there are changes of entropy in both the surroundings which lose heat and the system which gains it.", "The increase, , of entropy in the system may be considered to consist of two parts, an increment, that matches, or 'compensates', the change, , of entropy in the surroundings, and a further increment, that may be considered to be 'generated' or 'produced' in the system, and is said therefore to be 'uncompensated'.", "Thus\nformula_3\nThis may also be written\nformula_4\nThe total change of entropy in the system and surroundings is thus\nformula_5\nThis may also be written\nformula_6\nIt is then said that an amount of entropy has been transferred from the surroundings to the system.", "Because entropy is not a conserved quantity, this is an exception to the general way of speaking, in which an amount transferred is of a conserved quantity.", "From the second law of thermodynamics follows that in a spontaneous transfer of heat, in which the temperature of the system is different from that of the surroundings:\nformula_7\nFor purposes of mathematical analysis of transfers, one thinks of fictive processes that are called \"reversible\", with the temperature of the system being hardly less than that of the surroundings, and the transfer taking place at an imperceptibly slow rate.", "Following the definition above in formula (), for such a fictive reversible process, a quantity of transferred heat (an inexact differential) is analyzed as a quantity , with (an exact differential):\nformula_8\nThis equality is only valid for a fictive transfer in which there is no production of entropy, that is to say, in which there is no uncompensated entropy.", "If, in contrast, the process is natural, and can really occur, with irreversibility, then there is entropy production, with .", "The quantity was termed by Clausius the \"uncompensated heat\", though that does not accord with present-day terminology.", "Then one has\nformula_9\nThis leads to the statement\nformula_10\nwhich is the second law of thermodynamics for closed systems.", "In non-equilibrium thermodynamics that makes the approximation of assuming the hypothesis of local thermodynamic equilibrium, there is a special notation for this.", "The transfer of energy as heat is assumed to take place across an infinitesimal temperature difference, so that the system element and its surroundings have near enough the same temperature .", "Then one writes\nformula_11\nwhere by definition\nformula_12\nThe second law for a natural process asserts that\nformula_13", "For a closed system (a system from which no matter can enter or exit), one version of the first law of thermodynamics states that the change in internal energy of the system is equal to the amount of heat supplied to the system minus the amount of thermodynamic work done by system on its surroundings.", "The foregoing sign convention for work is used in the present article, but an alternate sign convention, followed by IUPAC, for work, is to consider the work performed on the system by its surroundings as positive.", "This is the convention adopted by many modern textbooks of physical chemistry, such as those by Peter Atkins and Ira Levine, but many textbooks on physics define work as work done by the system.", "formula_14\nThis formula can be re-written so as to express a definition of quantity of energy transferred as heat, based purely on the concept of adiabatic work, if it is supposed that is defined and measured solely by processes of adiabatic work:\nformula_15\nThe thermodynamic work done by the system is through mechanisms defined by its thermodynamic state variables, for example, its volume , not through variables that necessarily involve mechanisms in the surroundings.", "The latter are such as shaft work, and include isochoric work.", "The internal energy, , is a state function.", "In cyclical processes, such as the operation of a heat engine, state functions of the working substance return to their initial values upon completion of a cycle.", "The differential, or infinitesimal increment, for the internal energy in an infinitesimal process is an exact differential .", "The symbol for exact differentials is the lowercase letter .", "In contrast, neither of the infinitesimal increments nor in an infinitesimal process represents the change in a state function of the system.", "Thus, infinitesimal increments of heat and work are inexact differentials.", "The lowercase Greek letter delta, , is the symbol for inexact differentials.", "The integral of any inexact differential in a process where the system leaves and then returns to the same thermodynamic state does not necessarily equal zero.", "As recounted above, in the section headed \"heat and entropy\", the second law of thermodynamics observes that if heat is supplied to a system in a reversible process, the increment of heat and the temperature form the exact differential\nformula_16\nand that , the entropy of the working body, is a state function.", "Likewise, with a well-defined pressure, , behind a slowly moving (quasistatic) boundary, the work differential, , and the pressure, , combine to form the exact differential\nformula_17\nwith the volume of the system, which is a state variable.", "In general, for systems of uniform pressure and temperature without composition change,\nformula_18\nAssociated with this differential equation is the concept that the internal energy may be considered to be a function of its natural variables and .", "The internal energy representation of the fundamental thermodynamic relation is written as\nformula_19\nIf is constant\nformula_20\nand if is constant\nformula_21\nwith the enthalpy defined by\nformula_22\nThe enthalpy may be considered to be a function of its natural variables and .", "The enthalpy representation of the fundamental thermodynamic relation is written\nformula_23\nThe internal energy representation and the enthalpy representation are partial Legendre transforms of one another.", "They contain the same physical information, written in different ways.", "Like the internal energy, the enthalpy stated as a function of its natural variables is a thermodynamic potential and contains all thermodynamic information about a body.", "If a quantity of heat is added to a body while it does only expansion work on its surroundings, one has\nformula_24\nIf this is constrained to happen at constant pressure, i.e. with , the expansion work done by the body is given by ; recalling the first law of thermodynamics, one has\nformula_25\nConsequently, by substitution one has\nformula_26\nIn this scenario, the increase in enthalpy is equal to the quantity of heat added to the system.", "This is the basis of the determination of enthalpy changes in chemical reactions by calorimetry.", "Since many processes do take place at constant atmospheric pressure, the enthalpy is sometimes given the misleading name of 'heat content' or heat function, while it actually depends strongly on the energies of covalent bonds and intermolecular forces.", "In terms of the natural variables of the state function , this process of change of state from state 1 to state 2 can be expressed as\nformula_27\nIt is known that the temperature is identically stated by\nformula_28\nConsequently,\nformula_29\nIn this case, the integral specifies a quantity of heat transferred at constant pressure.", "As a common noun, English \"heat\" or \"warmth\" (just as French \"chaleur\", German \"Wärme\", Latin \"calor\", Greek θάλπος, etc.) refers to (the human perception of) either thermal energy or temperature.", "Speculation on thermal energy or \"heat\" as a separate form of matter has a long history, see caloric theory, phlogiston and fire (classical element).", "The modern understanding of thermal energy originates with Thompson's 1798 mechanical theory of heat (\"An Experimental Enquiry Concerning the Source of the Heat which is Excited by Friction\"), postulating a mechanical equivalent of heat.", "A collaboration between Nicolas Clément and Sadi Carnot (\"Reflections on the Motive Power of Fire\") in the 1820s had some related thinking along similar lines.", "In 1845, Joule published a paper entitled \"The Mechanical Equivalent of Heat\", in which he specified a numerical value for the amount of mechanical work required to \"produce a unit of heat\".", "The theory of classical thermodynamics matured in the 1850s to 1860s.", "John Tyndall's \"Heat Considered as Mode of Motion\" (1863) was instrumental in popularizing the idea of heat as motion to the English-speaking public.", "The theory was developed in academic publications in French, English and German.", "From an early time, the French technical term \"chaleur\" used by Carnot was taken as equivalent to the English \"heat\" and German \"Wärme\" (lit.", "\"warmth\", while the equivalent of \"heat\" would be German \"Hitze\").", "The process function was introduced by Rudolf Clausius in 1850.", "Clausius described it with the German compound \"Wärmemenge\", translated as \"amount of heat\".", "James Clerk Maxwell in his 1871 \"Theory of Heat\" outlines four stipulations for the definition of heat:\n\n\nThe process function is referred to as \"Wärmemenge\" by Clausius, or as \"amount of heat\" in translation.", "Use of \"heat\" as an abbreviated form of the specific concept of \"quantity of energy transferred as heat\" led to some terminological confusion by the early 20th century.", "The generic meaning of \"heat\", even in classical thermodynamics, is just \"thermal energy\".", "Since the 1920s, it has been recommended practice to use enthalpy to refer to the \"heat content at constant volume\", and to thermal energy when \"heat\" in the general sense is intended, while \"heat\" is reserved for the very specific context of the transfer of thermal energy between two systems.", "Leonard Benedict Loeb in his \"Kinetic Theory of Gases\" (1927) makes a point of using \"quantity of heat\"\nor \"heat–quantity\" when referring to :", "After the perfection of thermometry [...] the next great advance made in the field of heat was the definition of a term which is called the quantity of heat.", "[... after the abandonment of caloric theory,] It still remains to interpret this very definite concept, the quantity of heat, in terms of a theory ascribing all heat to the kinetics of gas molecules.", "A frequent definition of heat is based on the work of Carathéodory (1909), referring to processes in a closed system.", "The internal energy of a body in an arbitrary state can be determined by amounts of work adiabatically performed by the body on its surroundings when it starts from a reference state .", "Such work is assessed through quantities defined in the surroundings of the body.", "It is supposed that such work can be assessed accurately, without error due to friction in the surroundings; friction in the body is not excluded by this definition.", "The adiabatic performance of work is defined in terms of adiabatic walls, which allow transfer of energy as work, but no other transfer, of energy or matter.", "In particular they do not allow the passage of energy as heat.", "According to this definition, work performed adiabatically is in general accompanied by friction within the thermodynamic system or body.", "On the other hand, according to Carathéodory (1909), there also exist non-adiabatic, \"diathermal\" walls, which are postulated to be permeable only to heat.", "For the definition of quantity of energy transferred as heat, it is customarily envisaged that an arbitrary state of interest is reached from state by a process with two components, one adiabatic and the other not adiabatic.", "For convenience one may say that the adiabatic component was the sum of work done by the body through volume change through movement of the walls while the non-adiabatic wall was temporarily rendered adiabatic, and of isochoric adiabatic work.", "Then the non-adiabatic component is a process of energy transfer through the wall that passes only heat, newly made accessible for the purpose of this transfer, from the surroundings to the body.", "The change in internal energy to reach the state from the state is the difference of the two amounts of energy transferred.", "Although Carathéodory himself did not state such a definition, following his work it is customary in theoretical studies to define heat, , to the body from its surroundings, in the combined process of change to state from the state , as the change in internal energy, , minus the amount of work, , done by the body on its surrounds by the adiabatic process, so that .", "In this definition, for the sake of conceptual rigour, the quantity of energy transferred as heat is not specified directly in terms of the non-adiabatic process.", "It is defined through knowledge of precisely two variables, the change of internal energy and the amount of adiabatic work done, for the combined process of change from the reference state to the arbitrary state .", "It is important that this does not explicitly involve the amount of energy transferred in the non-adiabatic component of the combined process.", "It is assumed here that the amount of energy required to pass from state to state , the change of internal energy, is known, independently of the combined process, by a determination through a purely adiabatic process, like that for the determination of the internal energy of state above.", "The rigour that is prized in this definition is that there is one and only one kind of energy transfer admitted as fundamental: energy transferred as work.", "Energy transfer as heat is considered as a derived quantity.", "The uniqueness of work in this scheme is considered to guarantee rigor and purity of conception.", "The conceptual purity of this definition, based on the concept of energy transferred as work as an ideal notion, relies on the idea that some frictionless and otherwise non-dissipative processes of energy transfer can be realized in physical actuality.", "The second law of thermodynamics, on the other hand, assures us that such processes are not found in nature.", "Before the rigorous mathematical definition of heat based on Carathéodory's 1909 paper,\nhistorically, heat, temperature, and thermal equilibrium were presented in thermodynamics textbooks as jointly primitive notions.", "Carathéodory introduced his 1909 paper thus: \"The proposition that the discipline of thermodynamics can be justified without recourse to any hypothesis that cannot be verified experimentally must be regarded as one of the most noteworthy results of the research in thermodynamics that was accomplished during the last century.\"", "Referring to the \"point of view adopted by most authors who were active in the last fifty years\", Carathéodory wrote: \"There exists a physical quantity called heat that is not identical with the mechanical quantities (mass, force, pressure, etc.) and whose variations can be determined by calorimetric measurements.\"", "James Serrin introduces an account of the theory of thermodynamics thus: \"In the following section, we shall use the classical notions of \"heat\", \"work\", and \"hotness\" as primitive elements, ...", "That heat is an appropriate and natural primitive for thermodynamics was already accepted by Carnot.", "Its continued validity as a primitive element of thermodynamical structure is due to the fact that it synthesizes an essential physical concept, as well as to its successful use in recent work to unify different constitutive theories.\"", "This traditional kind of presentation of the basis of thermodynamics includes ideas that may be summarized by the statement that heat transfer is purely due to spatial non-uniformity of temperature, and is by conduction and radiation, from hotter to colder bodies.", "It is sometimes proposed that this traditional kind of presentation necessarily rests on \"circular reasoning\"; against this proposal, there stands the rigorously logical mathematical development of the theory presented by Truesdell and Bharatha (1977).", "This alternative approach to the definition of quantity of energy transferred as heat differs in logical structure from that of Carathéodory, recounted just above.", "This alternative approach admits calorimetry as a primary or direct way to measure quantity of energy transferred as heat.", "It relies on temperature as one of its primitive concepts, and used in calorimetry.", "It is presupposed that enough processes exist physically to allow measurement of differences in internal energies.", "Such processes are not restricted to adiabatic transfers of energy as work.", "They include calorimetry, which is the commonest practical way of finding internal energy differences.", "The needed temperature can be either empirical or absolute thermodynamic.", "In contrast, the Carathéodory way recounted just above does not use calorimetry or temperature in its primary definition of quantity of energy transferred as heat.", "The Carathéodory way regards calorimetry only as a secondary or indirect way of measuring quantity of energy transferred as heat.", "As recounted in more detail just above, the Carathéodory way regards quantity of energy transferred as heat in a process as primarily or directly defined as a residual quantity.", "It is calculated from the difference of the internal energies of the initial and final states of the system, and from the actual work done by the system during the process.", "That internal energy difference is supposed to have been measured in advance through processes of purely adiabatic transfer of energy as work, processes that take the system between the initial and final states.", "By the Carathéodory way it is presupposed as known from experiment that there actually physically exist enough such adiabatic processes, so that there need be no recourse to calorimetry for measurement of quantity of energy transferred as heat.", "This presupposition is essential but is explicitly labeled neither as a law of thermodynamics nor as an axiom of the Carathéodory way.", "In fact, the actual physical existence of such adiabatic processes is indeed mostly supposition, and those supposed processes have in most cases not been actually verified empirically to exist.", "Referring to conduction, Partington writes: \"If a hot body is brought in conducting contact with a cold body, the temperature of the hot body falls and that of the cold body rises, and it is said that a \"quantity of heat\" has passed from the hot body to the cold body.", "\"\nReferring to radiation, Maxwell writes: \"In Radiation, the hotter body loses heat, and the colder body receives heat by means of a process occurring in some intervening medium which does not itself thereby become hot.\"\nMaxwell writes that convection as such \"is not a purely thermal phenomenon\".", "In thermodynamics, convection in general is regarded as transport of internal energy.", "If, however, the convection is enclosed and circulatory, then it may be regarded as an intermediary that transfers energy as heat between source and destination bodies, because it transfers only energy and not matter from the source to the destination body.", "In accordance with the first law for closed systems, energy transferred solely as heat leaves one body and enters another, changing the internal energies of each.", "Transfer, between bodies, of energy as work is a complementary way of changing internal energies.", "Though it is not logically rigorous from the viewpoint of strict physical concepts, a common form of words that expresses this is to say that heat and work are interconvertible.", "Cyclically operating engines that use only heat and work transfers have two thermal reservoirs, a hot and a cold one.", "They may be classified by the range of operating temperatures of the working body, relative to those reservoirs.", "In a heat engine, the working body is at all times colder than the hot reservoir and hotter than the cold reservoir.", "In a sense, it uses heat transfer to produce work.", "In a heat pump, the working body, at stages of the cycle, goes both hotter than the hot reservoir, and colder than the cold reservoir.", "In a sense, it uses work to produce heat transfer.", "In classical thermodynamics, a commonly considered model is the heat engine.", "It consists of four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir.", "A cyclic process leaves the working body in an unchanged state, and is envisaged as being repeated indefinitely often.", "Work transfers between the working body and the work reservoir are envisaged as reversible, and thus only one work reservoir is needed.", "But two thermal reservoirs are needed, because transfer of energy as heat is irreversible.", "A single cycle sees energy taken by the working body from the hot reservoir and sent to the two other reservoirs, the work reservoir and the cold reservoir.", "The hot reservoir always and only supplies energy and the cold reservoir always and only receives energy.", "The second law of thermodynamics requires that no cycle can occur in which no energy is received by the cold reservoir.", "Heat engines achieve higher efficiency when the ratio of the initial and final temperature is greater.", "Another commonly considered model is the heat pump or refrigerator.", "Again there are four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir.", "A single cycle starts with the working body colder than the cold reservoir, and then energy is taken in as heat by the working body from the cold reservoir.", "Then the work reservoir does work on the working body, adding more to its internal energy, making it hotter than the hot reservoir.", "The hot working body passes heat to the hot reservoir, but still remains hotter than the cold reservoir.", "Then, by allowing it to expand without passing heat to another body, the working body is made colder than the cold reservoir.", "It can now accept heat transfer from the cold reservoir to start another cycle.", "The device has transported energy from a colder to a hotter reservoir, but this is not regarded as by an inanimate agency; rather, it is regarded as by the harnessing of work .", "This is because work is supplied from the work reservoir, not just by a simple thermodynamic process, but by a cycle of thermodynamic operations and processes, which may be regarded as directed by an animate or harnessing agency.", "Accordingly, the cycle is still in accord with the second law of thermodynamics.", "The 'efficiency' of a heat pump (which exceeds unity) is best when the temperature difference between the hot and cold reservoirs is least.", "Functionally, such engines are used in two ways, distinguishing a target reservoir and a resource or surrounding reservoir.", "A heat pump transfers heat to the hot reservoir as the target from the resource or surrounding reservoir.", "A refrigerator transfers heat, from the cold reservoir as the target, to the resource or surrounding reservoir.", "The target reservoir may be regarded as leaking: when the target leaks heat to the surroundings, heat pumping is used; when the target leaks coldness to the surroundings, refrigeration is used.", "The engines harness work to overcome the leaks.", "According to Planck, there are three main conceptual approaches to heat.", "One is the microscopic or kinetic theory approach.", "The other two are macroscopic approaches.", "One is the approach through the law of conservation of energy taken as prior to thermodynamics, with a mechanical analysis of processes, for example in the work of Helmholtz.", "This mechanical view is taken in this article as currently customary for thermodynamic theory.", "The other macroscopic approach is the thermodynamic one, which admits heat as a primitive concept, which contributes, by scientific induction to knowledge of the law of conservation of energy.", "This view is widely taken as the practical one, quantity of heat being measured by calorimetry.", "Bailyn also distinguishes the two macroscopic approaches as the mechanical and the thermodynamic.", "The thermodynamic view was taken by the founders of thermodynamics in the nineteenth century.", "It regards quantity of energy transferred as heat as a primitive concept coherent with a primitive concept of temperature, measured primarily by calorimetry.", "A calorimeter is a body in the surroundings of the system, with its own temperature and internal energy; when it is connected to the system by a path for heat transfer, changes in it measure heat transfer.", "The mechanical view was pioneered by Helmholtz and developed and used in the twentieth century, largely through the influence of Max Born.", "It regards quantity of heat transferred as heat as a derived concept, defined for closed systems as quantity of heat transferred by mechanisms other than work transfer, the latter being regarded as primitive for thermodynamics, defined by macroscopic mechanics.", "According to Born, the transfer of internal energy between open systems that accompanies transfer of matter \"cannot be reduced to mechanics\".", "It follows that there is no well-founded definition of quantities of energy transferred as heat or as work associated with transfer of matter.", "Nevertheless, for the thermodynamical description of non-equilibrium processes, it is desired to consider the effect of a temperature gradient established by the surroundings across the system of interest when there is no physical barrier or wall between system and surroundings, that is to say, when they are open with respect to one another.", "The impossibility of a mechanical definition in terms of work for this circumstance does not alter the physical fact that a temperature gradient causes a diffusive flux of internal energy, a process that, in the thermodynamic view, might be proposed as a candidate concept for transfer of energy as heat.", "In this circumstance, it may be expected that there may also be active other drivers of diffusive flux of internal energy, such as gradient of chemical potential which drives transfer of matter, and gradient of electric potential which drives electric current and iontophoresis; such effects usually interact with diffusive flux of internal energy driven by temperature gradient, and such interactions are known as cross-effects.", "If cross-effects that result in diffusive transfer of internal energy were also labeled as heat transfers, they would sometimes violate the rule that pure heat transfer occurs only down a temperature gradient, never up one.", "They would also contradict the principle that all heat transfer is of one and the same kind, a principle founded on the idea of heat conduction between closed systems.", "One might to try to think narrowly of heat flux driven purely by temperature gradient as a conceptual component of diffusive internal energy flux, in the thermodynamic view, the concept resting specifically on careful calculations based on detailed knowledge of the processes and being indirectly assessed.", "In these circumstances, if perchance it happens that no transfer of matter is actualized, and there are no cross-effects, then the thermodynamic concept and the mechanical concept coincide, as if one were dealing with closed systems.", "But when there is transfer of matter, the exact laws by which temperature gradient drives diffusive flux of internal energy, rather than being exactly knowable, mostly need to be assumed, and in many cases are practically unverifiable.", "Consequently, when there is transfer of matter, the calculation of the pure 'heat flux' component of the diffusive flux of internal energy rests on practically unverifiable assumptions.", "This is a reason to think of heat as a specialized concept that relates primarily and precisely to closed systems, and applicable only in a very restricted way to open systems.", "In many writings in this context, the term \"heat flux\" is used when what is meant is therefore more accurately called diffusive flux of internal energy; such usage of the term \"heat flux\" is a residue of older and now obsolete language usage that allowed that a body may have a \"heat content\".", "In the kinetic theory, heat is explained in terms of the microscopic motions and interactions of constituent particles, such as electrons, atoms, and molecules.", "The immediate meaning of the kinetic energy of the constituent particles is not as heat.", "It is as a component of internal energy.", "In microscopic terms, heat is a transfer quantity, and is described by a transport theory, not as steadily localized kinetic energy of particles.", "Heat transfer arises from temperature gradients or differences, through the diffuse exchange of microscopic kinetic and potential particle energy, by particle collisions and other interactions.", "An early and vague expression of this was made by Francis Bacon.", "Precise and detailed versions of it were developed in the nineteenth century.", "In statistical mechanics, for a closed system (no transfer of matter), heat is the energy transfer associated with a disordered, microscopic action on the system, associated with jumps in occupation numbers of the energy levels of the system, without change in the values of the energy levels themselves.", "It is possible for macroscopic thermodynamic work to alter the occupation numbers without change in the values of the system energy levels themselves, but what distinguishes transfer as heat is that the transfer is entirely due to disordered, microscopic action, including radiative transfer.", "A mathematical definition can be formulated for small increments of quasi-static adiabatic work in terms of the statistical distribution of an ensemble of microstates.", "Quantity of heat transferred can be measured by calorimetry, or determined through calculations based on other quantities.", "Calorimetry is the empirical basis of the idea of quantity of heat transferred in a process.", "The transferred heat is measured by changes in a body of known properties, for example, temperature rise, change in volume or length, or phase change, such as melting of ice.", "A calculation of quantity of heat transferred can rely on a hypothetical quantity of energy transferred as adiabatic work and on the first law of thermodynamics.", "Such calculation is the primary approach of many theoretical studies of quantity of heat transferred.", "The discipline of heat transfer, typically considered an aspect of mechanical engineering and chemical engineering, deals with specific applied methods by which thermal energy in a system is generated, or converted, or transferred to another system.", "Although the definition of heat implicitly means the transfer of energy, the term \"heat transfer\" encompasses this traditional usage in many engineering disciplines and laymen language.", "\"Heat transfer\" is generally described as including the mechanisms of heat conduction, heat convection, thermal radiation, but may include mass transfer and heat in processes of phase changes.", "Convection may be described as the combined effects of conduction and fluid flow.", "From the thermodynamic point of view, heat flows into a fluid by diffusion to increase its energy, the fluid then transfers (advects) this increased internal energy (not heat) from one location to another, and this is then followed by a second thermal interaction which transfers heat to a second body or system, again by diffusion.", "This entire process is often regarded as an additional mechanism of heat transfer, although technically, \"heat transfer\" and thus heating and cooling occurs only on either end of such a conductive flow, but not as a result of flow.", "Thus, conduction can be said to \"transfer\" heat only as a net result of the process, but may not do so at every time within the complicated convective process.", "In an 1847 lecture entitled \"On Matter, Living Force, and Heat\", James Prescott Joule characterized the terms latent heat and sensible heat as components of heat each affecting distinct physical phenomena, namely the potential and kinetic energy of particles, respectively.", "He described latent energy as the energy possessed via a distancing of particles where attraction was over a greater distance, i.e. a form of potential energy, and the sensible heat as an energy involving the motion of particles, i.e. kinetic energy.", "Latent heat is the heat released or absorbed by a chemical substance or a thermodynamic system during a change of state that occurs without a change in temperature.", "Such a process may be a phase transition, such as the melting of ice or the boiling of water.", "Heat capacity is a measurable physical quantity equal to the ratio of the heat added to an object to the resulting temperature change.", "The \"molar heat capacity\" is the heat capacity per unit amount (SI unit: mole) of a pure substance, and the \"specific heat capacity\", often called simply \"specific heat\", is the heat capacity per unit mass of a material.", "Heat capacity is a physical property of a substance, which means that it depends on the state and properties of the substance under consideration.", "The specific heats of monatomic gases, such as helium, are nearly constant with temperature.", "Diatomic gases such as hydrogen display some temperature dependence, and triatomic gases (e.g., carbon dioxide) still more.", "Before the development of the laws of thermodynamics, heat was measured by changes in the states of the participating bodies.", "Some general rules, with important exceptions, can be stated as follows.", "In general, most bodies expand on heating.", "In this circumstance, heating a body at a constant volume increases the pressure it exerts on its constraining walls, while heating at a constant pressure increases its volume.", "Beyond this, most substances have three ordinarily recognized states of matter, solid, liquid, and gas.", "Some can also exist in a plasma.", "Many have further, more finely differentiated, states of matter, such as glass and liquid crystal.", "In many cases, at fixed temperature and pressure, a substance can exist in several distinct states of matter in what might be viewed as the same 'body'.", "For example, ice may float in a glass of water.", "Then the ice and the water are said to constitute two phases within the 'body'.", "Definite rules are known, telling how distinct phases may coexist in a 'body'.", "Mostly, at a fixed pressure, there is a definite temperature at which heating causes a solid to melt or evaporate, and a definite temperature at which heating causes a liquid to evaporate.", "In such cases, cooling has the reverse effects.", "All of these, the commonest cases, fit with a rule that heating can be measured by changes of state of a body.", "Such cases supply what are called \"thermometric bodies\", that allow the definition of empirical temperatures.", "Before 1848, all temperatures were defined in this way.", "There was thus a tight link, apparently logically determined, between heat and temperature, though they were recognized as conceptually thoroughly distinct, especially by Joseph Black in the later eighteenth century.", "There are important exceptions.", "They break the obviously apparent link between heat and temperature.", "They make it clear that empirical definitions of temperature are contingent on the peculiar properties of particular thermometric substances, and are thus precluded from the title 'absolute'.", "For example, water contracts on being heated near 277 K. It cannot be used as a thermometric substance near that temperature.", "Also, over a certain temperature range, ice contracts on heating.", "Moreover, many substances can exist in metastable states, such as with negative pressure, that survive only transiently and in very special conditions.", "Such facts, sometimes called 'anomalous', are some of the reasons for the thermodynamic definition of absolute temperature.", "In the early days of measurement of high temperatures, another factor was important, and used by Josiah Wedgwood in his pyrometer.", "The temperature reached in a process was estimated by the shrinkage of a sample of clay.", "The higher the temperature, the more the shrinkage.", "This was the only available more or less reliable method of measurement of temperatures above 1000 °C (1,832 °F).", "But such shrinkage is irreversible.", "The clay does not expand again on cooling.", "That is why it could be used for the measurement.", "But only once.", "It is not a thermometric material in the usual sense of the word.", "Nevertheless, the thermodynamic definition of absolute temperature does make essential use of the concept of heat, with proper circumspection.", "According to Denbigh (1981), the property of hotness is a concern of thermodynamics that should be defined without reference to the concept of heat.", "Consideration of hotness leads to the concept of empirical temperature.", "All physical systems are capable of heating or cooling others.", "With reference to hotness, the comparative terms hotter and colder are defined by the rule that heat flows from the hotter body to the colder.", "If a physical system is inhomogeneous or very rapidly or irregularly changing, for example by turbulence, it may be impossible to characterize it by a temperature, but still there can be transfer of energy as heat between it and another system.", "If a system has a physical state that is regular enough, and persists long enough to allow it to reach thermal equilibrium with a specified thermometer, then it has a temperature according to that thermometer.", "An empirical thermometer registers degree of hotness for such a system.", "Such a temperature is called empirical.", "For example, Truesdell writes about classical thermodynamics: \"At each time, the body is assigned a real number called the \"temperature\".", "This number is a measure of how hot the body is.", "\"\nPhysical systems that are too turbulent to have temperatures may still differ in hotness.", "A physical system that passes heat to another physical system is said to be the hotter of the two.", "More is required for the system to have a thermodynamic temperature.", "Its behavior must be so regular that its empirical temperature is the same for all suitably calibrated and scaled thermometers, and then its hotness is said to lie on the one-dimensional hotness manifold.", "This is part of the reason why heat is defined following Carathéodory and Born, solely as occurring other than by work or transfer of matter; temperature is advisedly and deliberately not mentioned in this now widely accepted definition.", "This is also the reason that the zeroth law of thermodynamics is stated explicitly.", "If three physical systems, \"A\", \"B\", and \"C\" are each not in their own states of internal thermodynamic equilibrium, it is possible that, with suitable physical connections being made between them, \"A\" can heat \"B\" and \"B\" can heat \"C\" and \"C\" can heat \"A\".", "In non-equilibrium situations, cycles of flow are possible.", "It is the special and uniquely distinguishing characteristic of internal thermodynamic equilibrium that this possibility is not open to thermodynamic systems (as distinguished amongst physical systems) which are in their own states of internal thermodynamic equilibrium; this is the reason why the zeroth law of thermodynamics needs explicit statement.", "That is to say, the relation 'is not colder than' between general non-equilibrium physical systems is not transitive, whereas, in contrast, the relation 'has no lower a temperature than' between thermodynamic systems in their own states of internal thermodynamic equilibrium is transitive.", "It follows from this that the relation 'is in thermal equilibrium with' is transitive, which is one way of stating the zeroth law.", "Just as temperature may be undefined for a sufficiently inhomogeneous system, so also may entropy be undefined for a system not in its own state of internal thermodynamic equilibrium.", "For example, 'the temperature of the solar system' is not a defined quantity.", "Likewise, 'the entropy of the solar system' is not defined in classical thermodynamics.", "It has not been possible to define non-equilibrium entropy, as a simple number for a whole system, in a clearly satisfactory way." ]

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[ "For the precise definition of heat, it is necessary that it occur by a path that does not include transfer of matter." ]

[ "A bid bond of amount not above 10% of the contract order total amount is deposited when a contractor, also known as the “supplier\" or \"principal\", is bidding on a tendered contract.", "The bid bond prequalifies the principal and provides the necessary security to the owner (or general contractor), also known as the “obligee”.", "This helps to avoid frivolous bids and guarantees that the principal will enter into the contract if it is awarded.", "A bid bond guarantees that the “obligee” will be paid the difference between the principal's tender price and the next closest tender price.", "This action is only triggered should the principal be awarded the contract but fails to enter into the contract, as agreed, with the obligee.", "The bid bond penalty is generally ten percent of the bidder's tender price.", "Contractors prefer the use of bid bonds because they are a less expensive option and they do not tie up cash or bank credit lines during the bidding process.", "Owners and general contractors also use bid bonds because they establish and confirm that the bidding contractor or supplier is qualified to undertake the project." ]

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[ "A bid bond is issued as part of a supply bidding process by the contractor to the project owner, to provide guarantee, that the winning bidder will undertake the contract under the terms at which they bid.", "The bid bond assures and guarantees that should the bidder be successful, the bidder will execute the contract and provide the required surety bonds." ]

[ "He was born in Kosovska Mitrovica, SR Serbia, SFR Yugoslavia.", "In season 1995/96 as 17-year-old Delibašić played for the junior team of Red Star Belgrade, but he never played for the first team.", "In 2003 Delibašić played with FK Leotar in the Champions League qualifying rounds after winning the 2002–03 Premier League of Bosnia and Herzegovina.", "In July 2003 he scored a goal in the 2nd qualifying round in a match against Slavia Praha, but the result of the match was a 1:2 loss for Leotar.", "The forward played 26 matches in 2003–04 and scored 11 goals.", "In summer 2004 he returned to Serbia and signed with FK Čukarički.", "One year later gone in Chinese Chongqing Lifan.", "In season 2007/08 Delibašić played for Greek Kallithea F.C.\nDelibašić signed a 2-year deal with Lokomotiv Plovdiv after being released from Kallithea in 2008.", "He was given the №9 shirt.", "Delibašić made his official debut for Lokomotiv in a match against Slavia Sofia on 27 September 2008.", "He played for 33 minutes.", "The result of the match was a 0:2 loss for Loko.", "On 2 October 2008 he scored his first goals for Lokomotiv Plovdiv against Lokomotiv Sofia.", "He scored two goals in the 32nd and 34th minute.", "The result of the match was a 3:2 win for Loko.", "Club\nLeotar\nPersonal" ]

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[ "He had previously played for Spartak Subotica, Bosnian FK Leotar, FK Čukarički, Chinese Chongqing Lifan and Greek Kallithea F.C., back in Serbia with FK Zemun and with Bulgarian Minyor Pernik and FK Banat Zrenjanin." ]

[ "The Sierra Reserve beginnings, like the San Gabriel Reserve, were by petitions sent to the US Congress from Tulare County officials wanting to stop the damage in the Sierra Nevada by timber and livestock commercial interests.", "The General Land Office which was responsible for management of public lands, sent Benjamin Allen to investigate and report back, which he did, recommending a set aside of land called Tulare Reserve.", "He originally had five million acres (20,000 km²) to six million acres (24,000 km²) for this reserve in his report.", "The majority of local citizens were supportive, any protests heard were coming from the sheepmen.", "Conservationist and later Venice, California founder Abbot Kinney and \"Century\" magazine editor Robert Underwood Johnson gave their support of the proposed set aside.", "Benjamin Allen, in his final report, reduced the size and changed the name to Sierra Forest Reserve.", "The new reserve bordered most of Yosemite National Park with its western boundary almost surrounding General Grant and Sequoia national parks.", "Its lands are now primarily part of the Sierra National Forest.", "Godfrey, Anthony \"The Ever-Changing View-A History of the National Forests in California\" USDA Forest Service Publishers, 2005" ]

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[ "The Sierra Forest Reserve was a federal reserve in the Sierra Nevada, in eastern California.", "The first was the San Gabriel Timberland Reserve." ]

[ "The Jacksonville Beaches communities are all located on an unnamed barrier island defined by the Atlantic Ocean to the east, the St. Johns River to the north, and the Intracoastal Waterway to the west.", "The island was actually originally a peninsula until 1912, when a 10-mile channel was dug connecting the San Pablo and Tolomato Rivers, facilitating the Intracoastal Waterway and separating the land from the mainland.", "The island has no official name; beginning in the 21st century there has been a push to name it San Pablo Island.", "The northernmost of the beach communities is Mayport, in Duval County.", "Since the consolidation of the Jacksonville and Duval County governments in 1968, Mayport has been within the city limits of Jacksonville.", "Most of Mayport is currently occupied by Naval Station Mayport, a major U.S. Navy base, itself also entirely located within the city of Jacksonville.", "Moving south along the coastline are three incorporated towns, also within Duval County: Atlantic Beach, Neptune Beach, and Jacksonville Beach.", "All three maintain their own municipal governments, however, residents receive county-level services from Jacksonville and vote for Jacksonville's mayor and City Council.", "Continuing south into St. Johns County is Ponte Vedra Beach.", "Typically, only the communities on the northern part of the island are considered the Beaches; areas to the south such as Vilano Beach are usually not included.", "The Palm Valley area of St. Johns County, much of which is also located on the island, is sometimes considered part of the Beaches.", "The parts of Duval County on the other side of the Intracoastal are sometimes known as the West Beaches.", "Further inland are Jacksonville's Arlington and Southside areas.", "The first inhabitants of the Jacksonville Beaches area were Native Americans.", "Like most of the Jacksonville area, the region was inhabited by the Timucua people at the time of European contact.", "Mayport was the first part of the beaches to see any concentrated population growth, when a small community of fishermen and river pilots grew up there, especially following the U.S. purchase of Florida in 1821.", "However, the entire Beaches area remained very sparsely populated until the end of the 19th century, when they were developed as resorts.", "Jacksonville Beach, originally known as Ruby and then as Pablo Beach, grew around the series of luxury hotels built in the area.", "Further growth was facilitated by a railroad connecting the town to Jacksonville.", "Atlantic Beach also grew as a resort community around a large hotel, and smaller hotels were built at Mayport.", "Neptune Beach seceded from Jacksonville Beach in 1931 and incorporated as its own town.", "Ponte Vedra Beach and Palm Valley remained much more rustic into the 20th century.", "Palm Valley, especially, mostly consisted of farmland.", "In 1914 mineral deposits were discovered at Ponte Vedra, after which point it grew as the town of Mineral City.", "Following World War I real estate development began in the area and the name was changed to Ponte Vedra Beach.", "Relations between the Beaches and the Jacksonville city government have at times been tense.", "The three incorporated towns in Duval County have fought with the city over the ways taxes and government services are shared; this led to a lawsuit in 1979, which established an interlocal agreement.", "The Beaches governments took up a second lawsuit in 1993 alleging a breach of the agreement, and members of the Jacksonville City Council sought to review the charter in 2006, angering locals.", "During much of this time the Beaches threatened forming their own county, \"Ocean County\", though this was resolved following the election of Neptune Beach resident John Delaney as Mayor of Jacksonville in 1995." ]

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[ "The Jacksonville Beaches, known locally as \"The Beaches\", are a group of towns and communities on the northern half of an unnamed barrier island on the US state of Florida's First Coast, all of which are excluded cities or parts of the city of Jacksonville itself.", "These communities are separated from the main body of the city of Jacksonville by the Intracoastal Waterway.", "The Jacksonville Beaches are located in Duval and northern St. Johns County counties, and make up part of the Jacksonville metropolitan area.", "The main communities generally identified as part of the Beaches are Mayport, Atlantic Beach, Neptune Beach, Jacksonville Beach, and Ponte Vedra Beach." ]

[ "Crowney was born in London, United Kingdom, to English parents Karin and Phil Crowney.", "she has two younger sisters (one named Robyn).", "Crowney grew up in Grosvenor Park, Chester, England; she completed her schooling at Bennett Memorial School in Tunbridge Wells, and later studied fashion and textiles at West Kent College.", "Crowney's entry into Bollywood came by chance in 2004 when she was backpacking in Thailand and stumbled upon an Indian film being shot there.", "So it came that her first appearance in a Bollywood film was in the item song \"Leke Pehla Pehla Pyaar\".", "She was an extra in the film \"Janasheen\".", "With little prior knowledge of the sub-continent, she was attracted by the music and dance, and decided to try her luck in Mumbai.", "She went on to do advertisements for Pond's, Nokia, HSBC and Samsung before landing her first proper role in the film \"MP3: Mera Pehla Pehla Pyaar\" in 2007.", "She also worked in shows, for which she was highly paid.", "In 2010, Crowney along with other non-Indian actresses such as Alice Patten were asked to leave Bollywood by Raj Thackeray's Maharashtra Navnirman Sena (MNS), a Mumbai-based political party.", "They campaigned for a ban on the estimated 1,000 British and other foreign actors who regularly appear in Bollywood films accusing them of stealing jobs from local girls.", "Crowney is performed in an item song named 'Reshma Ki Jawani' for the film \"Kaash Tum Hote\" which was released in 2014.", "She also appeared in an item song in the Telugu action-drama \"Shankara\", which was released in 2016." ]

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[ "Hazel Crowney, also spelt as Hazel Croney, is a British model and film actress who has appeared in many ad campaigns and some Bollywood films." ]

[ "Reimer’s book \"A Philosophy of Music Education\", first published in 1970, a second edition in 1989, and a third edition, \"A Philosophy of Music Education: Advancing the Vision\", in 2003, (Prentice Hall) has been translated into French, Japanese, and Chinese, with a Greek edition in preparation.", "He was the author and editor of some two dozen other books and has written over 145 articles and chapters on a variety of topics in music and arts education.", "Reimer’s textbooks on music for grades one through eight, Silver Burdett Music, were the most widely used throughout the United States and the world for two decades.", "As a participant in the professional life of his field, Reimer served on the editorial boards of all the major journals; was National Chairman of the National Association for Music Education (MENC) Committee on Aesthetic Education; was MENC liaison for Arts Education Initiatives: represented MENC as a member of the Alliance for Curriculum Reform and the Aesthetic Education Curriculum Program sponsored by the U.S. Office of Education; was a member of the six-person task force that wrote the National Standards for Music Education; and was one of six Commission Authors of position papers for the MENC Vision 2020 Project (the Housewright Symposium/Vision 2020).", "He was Director of a three-year research project on the general music curriculum sponsored by the U.S. Office of Education; was a research exchange scholar studying music education practices from Kindergarten through Conservatory in China for a three-month period in 1986, sponsored by the Chinese government and Harvard Project Zero; was for six years Co-Director and Principal Consultant for the teacher education project “Education for Aesthetic Awareness:", "The Cleveland Area Project for the Arts in the Schools”; and for five years was a member of the Rockefeller Brothers Fund Awards Committee for Exemplary School Arts Programs.", "Reimer presented many keynote addresses and lectures each year throughout the United States and the world, including appearances in England, Japan, Saudi Arabia, New Zealand, the Netherlands, Canada, Hong Kong, Ireland, South Africa, China, and Australia.", "He was awarded an Honorary Doctorate from DePaul University, Chicago, in 1997.", "Also in 1997 he was designated the third “Legend of Teaching” in the history of the Northwestern University School of Music.", "A special double issue of \"The Journal of Aesthetic Education\", \"Musings: Essays in Honor of Bennett Reimer,\" was published in Winter 2000.", "In 2002, Reimer was inducted into the Music Educators Hall of Fame.", "In 2008 he was the recipient of the MENC Senior Researcher Award.", "Reimer died in Wilmette, Illinois on November 18, 2013, aged 81.", "State University of New York, College at Fredonia.", "B.S. 1954.", "University of Illinois at Urbana-Champaign.", "M.S. 1955.", "University of Illinois at Urbana-Champaign.", "Ed.D. 1963.", "1955–1957 Richmond Professional Institute of the College of William and Mary, Richmond, VA.", "Instructor.", "Band Director; woodwinds; theory; conducting; music appreciation.", "1958–1960 Madison College, Harrisonburg, VA.", "Assistant Professor.", "Wind Ensembles; woodwinds; theory; conducting; music appreciation.", "Director of Music, Campus Laboratory School.", "1960–1965 University of Illinois at Urbana-Champaign.", "Instructor, Assistant Professor.", "Foundations of Music Education.", "Music and College Placement Consultant, University of Illinois Educational Placement Office.", "1965–1978 Case Western Reserve University, Cleveland, OH.", "Kulas Professor of Music, 1971–78; Director of Music Education.", "1978–1997 Northwestern University, Evanston, IL.", "John W. Beattie Professor of Music; Chairman of Music Education; Founder and Director, Center for the Study of Education and the Musical Experience.", "Reimer's viewpoint was that only \"good music\" (music evoking a feeling) should be taught.", "Teachers will have a firm pedagogical base and sensitivity, all will learn music because it helps us develop self-knowledge." ]

[ 3, 4, 5, 6, 7, 8, 9, 10, 11 ]

[ "Reimer then became a specialist in the philosophy of music education, curriculum development, theory of research, and comprehensive arts education programs." ]

[ "Reimer’s book \"A Philosophy of Music Education\", first published in 1970, a second edition in 1989, and a third edition, \"A Philosophy of Music Education: Advancing the Vision\", in 2003, (Prentice Hall) has been translated into French, Japanese, and Chinese, with a Greek edition in preparation.", "He was the author and editor of some two dozen other books and has written over 145 articles and chapters on a variety of topics in music and arts education.", "Reimer’s textbooks on music for grades one through eight, Silver Burdett Music, were the most widely used throughout the United States and the world for two decades.", "As a participant in the professional life of his field, Reimer served on the editorial boards of all the major journals; was National Chairman of the National Association for Music Education (MENC) Committee on Aesthetic Education; was MENC liaison for Arts Education Initiatives: represented MENC as a member of the Alliance for Curriculum Reform and the Aesthetic Education Curriculum Program sponsored by the U.S. Office of Education; was a member of the six-person task force that wrote the National Standards for Music Education; and was one of six Commission Authors of position papers for the MENC Vision 2020 Project (the Housewright Symposium/Vision 2020).", "He was Director of a three-year research project on the general music curriculum sponsored by the U.S. Office of Education; was a research exchange scholar studying music education practices from Kindergarten through Conservatory in China for a three-month period in 1986, sponsored by the Chinese government and Harvard Project Zero; was for six years Co-Director and Principal Consultant for the teacher education project “Education for Aesthetic Awareness:", "The Cleveland Area Project for the Arts in the Schools”; and for five years was a member of the Rockefeller Brothers Fund Awards Committee for Exemplary School Arts Programs.", "Reimer presented many keynote addresses and lectures each year throughout the United States and the world, including appearances in England, Japan, Saudi Arabia, New Zealand, the Netherlands, Canada, Hong Kong, Ireland, South Africa, China, and Australia.", "He was awarded an Honorary Doctorate from DePaul University, Chicago, in 1997.", "Also in 1997 he was designated the third “Legend of Teaching” in the history of the Northwestern University School of Music.", "A special double issue of \"The Journal of Aesthetic Education\", \"Musings: Essays in Honor of Bennett Reimer,\" was published in Winter 2000.", "In 2002, Reimer was inducted into the Music Educators Hall of Fame.", "In 2008 he was the recipient of the MENC Senior Researcher Award.", "Reimer died in Wilmette, Illinois on November 18, 2013, aged 81.", "State University of New York, College at Fredonia.", "B.S. 1954.", "University of Illinois at Urbana-Champaign.", "M.S. 1955.", "University of Illinois at Urbana-Champaign.", "Ed.D. 1963.", "1955–1957 Richmond Professional Institute of the College of William and Mary, Richmond, VA.", "Instructor.", "Band Director; woodwinds; theory; conducting; music appreciation.", "1958–1960 Madison College, Harrisonburg, VA.", "Assistant Professor.", "Wind Ensembles; woodwinds; theory; conducting; music appreciation.", "Director of Music, Campus Laboratory School.", "1960–1965 University of Illinois at Urbana-Champaign.", "Instructor, Assistant Professor.", "Foundations of Music Education.", "Music and College Placement Consultant, University of Illinois Educational Placement Office.", "1965–1978 Case Western Reserve University, Cleveland, OH.", "Kulas Professor of Music, 1971–78; Director of Music Education.", "1978–1997 Northwestern University, Evanston, IL.", "John W. Beattie Professor of Music; Chairman of Music Education; Founder and Director, Center for the Study of Education and the Musical Experience.", "Reimer's viewpoint was that only \"good music\" (music evoking a feeling) should be taught.", "Teachers will have a firm pedagogical base and sensitivity, all will learn music because it helps us develop self-knowledge." ]

[ 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33 ]

[ "A native of New York City, where he was born in 1932, he was on the faculties of Case Western Reserve University, Cleveland, Ohio (1965–1978) where he held the Kulas Endowed Chair in Music and was chair of the Music Education Department; the University of Illinois at Urbana-Champaign (1960–1965); Madison College, Harrisonburg, Virginia (1958–1960); and the Richmond Professional Institute of the College of William and Mary, (1955–1957)." ]

[ "The F2W was ordered by the US Navy to enter in the 1923 Pulitzer Trophy.", "Wright built the aircraft primarily of wood, covered in fabric, and was powered by the Wright T-3 Tornado engine.", "The first F2W flew for the first time on 2 August 1923.", "During the Pulitzer Race, the first F2W ran out of fuel and crashed.", "The second F2W, which carried twice as much fuel, finished third at 230.06 mph (370.25 km/h).", "It was later converted into a floatplane as the F2W-2 to take part in the 1924 Schneider Trophy race.", "During testing it was very unstable, and on its only flight, on 11 October 1924, crashed into the Delaware River at Philadelphia, Pennsylvania, when the tremendous torque of the Tornado engine flipped it onto its back while attempting to land.", "The pilot, badly injured, extricated himself from the wreckage.", "Notes\nBibliography" ]

[ 0, 1, 2 ]

[ "The Wright F2W was an American racing aircraft built by Wright Aeronautical Corporation for the US Navy." ]

[ "In 1997, Lafayette's KRXZ now KHXT switched frequencies from 107.7 to 107.9, opening up the door for a new station in Lake Charles to be operated at 107.5 MHz without any interference.", "Progressive Communications, Inc. filed for a full power station at 107.5 and was granted one by the Federal Communications Commission (FCC) within weeks.", "After months of construction, the station finally signed on the air on October 10, 1997, as \"Krawfish 107\" with the callsigns KRAW.", "Sometime in 2000, Krawfish 107, along with sister stations LA99 (now Gator 99.5), KJEF 92.9 (now 92-9 The Lake) and KJEF 1290 AM were sold to Apex Broadcasting, Inc., a small radio station company based in South Carolina.", "On August 1, 2000, Apex Broadcasting flipped 107.5 from Country to Urban Contemporary as \"V107.5\" with the callsigns changed to KVEE.", "There are many reasons why the format was switched.", "Krawfish 107 was likely put on the air only to cut into Kicks 96's ratings.", "It was basically all just to cover for LA99; Krawfish 107's sister station.", "LA99 was always the popular AC station in Lake Charles, beating out B104 (now Rhythmic Top 40 Hot 103.3) but never Kicks 96.", "And for Progressive Communications, Inc. to put Country on 107.5 would be a win-win situation to keep those ratings going to LA99.", "On February 26, 2004, the format was changed again, as \"107 Jamz\" with the callsigns changed to KJMH and expanding the format to include Hip Hop.", "In 2008, Apex Broadcasting sold the station, along with sister stations KHLA, KJEF, KLCL, KNGT, and KTSR to Gap Broadcasting, LLC.", "What eventually became Gap Central Broadcasting (following the formation of GapWest Broadcasting) was folded into Townsquare Media on August 13, 2010." ]

[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ]

[ "KJMH (107.5 FM, branded as \"107 Jamz\") is a radio station broadcasting an urban contemporary format.", "The station is currently owned by Townsquare Media and licensed to Townsquare Media Lake Charles License, LLC." ]

[ "All in the golden afternoon \nFull leisurely we glide;\nFor both our oars, with little skill,\nBy little arms are plied,\nWhile little hands make vain pretence\nOur wanderings to guide.", "Ah, cruel Three!", "In such an hour,\nBeneath such dreamy weather,\nTo beg a tale of breath too weak\nTo stir the tiniest feather!", "Yet what can one poor voice avail\nAgainst three tongues together?", "Imperious Prima flashes forth\nHer edict \"to begin it\"— \nIn gentler tones Secunda hopes\n\"There will be nonsense in it!\"— \nWhile Tertia interrupts the tale\nNot more than once a minute.", "Anon, to sudden silence won,\nIn fancy they pursue\nThe dream-child moving through a land\nOf wonders wild and new,\nIn friendly chat with bird or beast—\nAnd half believe it true.", "And ever, as the story drained\nThe wells of fancy dry,\nAnd faintly strove that weary one\nTo put the subject by,\n\"The rest next time—\" \"It is next time!\"", "The happy voices cry.", "Thus grew the tale of Wonderland:\nThus slowly, one by one,\nIts quaint events were hammered out—\nAnd now the tale is done,\nAnd home we steer, a merry crew,\nBeneath the setting sun.", "Alice!", "A childish story take,\nAnd with a gentle hand,\nLay it where Childhood's dreams are twined", "In Memory's mystic band,\nLike pilgrim's withered wreath of flowers\nPlucked in far-off land.", "\"All in the golden afternoon\" is a poem made up of seven 6-line stanzas.", "Each of the stanzas follows the same general rhyme scheme as well: ABCBDB - every second, fourth, and sixth line rhymes.", "Additionally, it would do well to note that the 'B' lines are typically in iambic trimeter and thus have fewer syllables than their preceding and succeeding lines.", "The lines that do not rhyme are mostly in iambic tetrameter; the only exceptions to both of these lie in the second, third and seventh stanzas.", "The first stanza also introduces the pun involving the three sisters' last name: Liddell.", "It thrice mentions the word little and plays off the fact that the pronunciation of both was quite similar.", "This poem depicts the story of how, during the summer of 1862 and in the company of the three Liddell sisters and Reverend Robinson Duckworth, Lewis Carroll composed \"Alice's Adventures in Wonderland\".", "It is from the first-hand accounts of those summer days that the background for this poem becomes clearer.", "Alice Pleasance Liddell was age 10 at the time that Charles Lutwidge Dodgson (Lewis Carroll) first described life in Wonderland.", "Alice and her two sisters spent much of their free time with Carroll and Duckworth.", "During the summer, the group would often take expeditions up the Isis branch of the Thames river, complete with picnic baskets and lessons in the art of rowing.", "During one of these excursions the first telling of Alice's adventures takes place.", "The story would have faded away had not Alice insisted that the tales be written down especially for her.", "The first copy of \"Alice's Adventures in Wonderland\" (then titled \"Alice's Adventures Under Ground\") was a handwritten volume given personally to Alice Liddell, who inspired the main character in the fantastical tales.", "When the story was about to be published as a book Carroll added the poem as a preface.", "He felt that his tale was a bit frightening for sensitive, young children, and he hoped that the poem would soften the fearfulness of the story and present a gateway into Wonderland.", "In doing so, Carroll dropped the original dedication to Alice Liddell which had read: \"A Christmas Gift to a Dear Child in Memory of a Summer Day.\"", "Carroll did, however, insert the last stanza of the poem as a special message to her, a nod to their shared experience in the creation of Wonderland.", "This poem closely follows what actually happened during those summer outings, according to Alice Liddell.", "In the fifth stanza, the \"weary one\" refers to Carroll himself, whom Alice recalls saying, \"And that's all till next time\" to which she and her sisters would respond with, \"Ah but it is next time.\"", "These snippets also help corroborate the rest of the history behind the poem.", "Additionally, Carroll and Alice cite that the day of the excursion described by the poem was \"burning\" hot; ironically, however, the day that they mention was cloudy, rainy and not particularly \"golden.", "\"", "The style of Carroll’s poems, including “All in the Golden Afternoon,” were considered to emulate a more traditional and, as some considered even in his own time, outdated form of poetry.", "Readers at this time would have been looking for poetry full of wit, irony, and the expression of conflict, but in accordance with the poets that he most admired, such as Tennyson and the Rossettis, Carroll's poetry embodied the principles of beauty and wisdom.", "This poem in particular contains many of the standard themes of this older, romantic form of poetry—including a dreamy, picturesque landscape and a presupposed listener.", "William Madden suggests that Carroll chose this outdated form of poetry for a purpose—the poems were not meant to stand alone, but to be a framework for the main piece of literature, \"Alice’s Adventures in Wonderland\".", "The poem puts the reader in the right frame of mind to interpret the themes in the novel—it is a compliment to his “work of nonsense.”", "Without the context of \"Alice's Adventures in Wonderland\", the poem lacks meaning." ]

[ 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34 ]

[ "\"All in the golden afternoon\" is the preface poem in Lewis Carroll's 1865 book \"Alice's Adventures in Wonderland\".", "Alice gave her name to Carroll's main character." ]

[ "Clark Hulings was born in 1922 in Florida, where his father, Courtland Marcus Hulings, was the manager of a plant which produced a gas for fumigating orange trees.", "His mother died of tuberculosis when he was an infant, and he and his sister, Susan, were sent to live with their maternal grandparents in Potsdam, New York, for the next three years, while his father worked in Valencia, Spain.", "In Valencia, Hulings’ father, while representing American Cyanamid, courted and married Elena Harker, the 21-year-old daughter of Herbert Edward Harker, the British Consul in Valencia, and his wife, Julia Howard Harker.", "Courtland Hulings and Elena Harker were married in London, England, in 1925.", "The two children joined them abroad.", "In 1928, the Hulings family returned to the United States, settling in Westfield, New Jersey, where Clark's younger sister, Elena, was born.", "At the age of twelve, his father arranged art lessons with Sigismund Ivanowski, a portrait and landscape painter who had served as Court Painter to Tsar Nicholas II.", "In his 1986 book \"A Gallery of Paintings,\" Hulings credits his father with conveying to him his \"great love of paintings.\"", "By the time Hulings graduated from school in 1940, the tuberculosis which had killed his mother left him in fragile health.", "He was unable to enter college.", "However, he did continue a limited schedule with Ivanowski, as well as with George Bridgman, the celebrated drawing teacher, at the Art Students League of New York.", "In the fall of 1941, Hulings was well enough to enroll at Haverford College.", "After graduating in 1944 with a degree in Physics, he was appointed to work on the Manhattan Project in Los Alamos, New Mexico.", "Yet his recurring ill health prevented his acceptance into the program.", "Instead, he remained in Santa Fe to recuperate, supporting himself by painting pastel portraits of children.", "In the spring of 1945 he was given a one-man show of landscapes at the New Mexico Museum of Fine Art.", "In 1946 Hulings moved to Baton Rouge, Louisiana where his parents lived at the time, and he had a one-man show of his work at the galleries of the Louisiana Art Commission.", "He included several portraits of family members and the show launched him on his successful career as a portrait painter.", "Hulings continued to paint landscapes and also became interested in design and illustration work, which led him back to The Art Students League for three years beginning in 1948 - this time as a student of Frank Reilly, a noted teacher and artist himself.", "In 1951 he gained employment doing wash drawings for a newspaper mat agency that specializing in supermarket ads.", "He gradually moved up to paperback book covers and magazine illustrations, by 1955, his illustration career was firmly established.", "But the lure of landscape painting sent him to Europe, first for four months, and later for almost three years.", "Over the course of his travels he studied figure painting in Florence, abstract design in Düsseldorf and roamed from the Arctic Circle to Southern Egypt.", "Hulings returned to New York City in the fall of 1960 and resumed his illustration career to recoup finances.", "But he planned his work schedule to include serious easel painting.", "By 1962 Hulings was earning enough with his easel painting to devote all of his attention to his lifelong path.", "He was admitted to the Grand Central Art Galleries, which represented him for the next eight years and held one-man shows of his work in 1965 and 1967.", "Hulings also began placing paintings in competitive shows of realistic art, winning several prizes, including The Council of American Artists’ award at the Hudson Valley Art Association for Restaurante Vicente, and the gold medal given by the Allied Artists of America for Ontinyent.", "He moved back to the artistic and cultural magnet of Santa Fe, New Mexico after a doctor suggested that it would be good for his health, due to dormant tuberculosis that was being aggravated by New York City pollution.", "In 1973 he garnered the first ever Prix de West award at the National Academy of Western Art (NAWA) in Oklahoma City for his painting \"Grand Canyon - Kaibab Trail\".", "This is an enormous oil that portrays a mule team barely navigating the Grand Canyon in deep winter snow.", "He went on to win three silver and two gold medals for both oil and watercolor at subsequent competitions at NAWA, part of the National Cowboy & Western Heritage Museum.", "In 1976 A Collection of Oil Paintings by Clark Hulings was published by The Lowell Press as a catalog to accompany a one-man show at the Cowboy Hall of Fame under the auspices of NAWA.", "He was presented with the Hall’s Trustees Gold Medal for his \"distinguished contribution to American art\".", "Two years later he was honored with a comprehensive retrospective of his work in Midland, Texas.", "In 1980, Hulings’s painting The Pink Parasol won wide acclaim at the annual Western Heritage Sale in Houston, Texas.", "His market scene, Kaleidescope, submitted in the 1981 sale, brought another record sale price.", "In 1999 he mounted a new one-man show at Nedra Matteucci Galleries in Santa Fe, New Mexico.", "It included thirty-five paintings, ten field sketches and twelve drawings.", "Everything sold on opening night.", "In 2007 he topped this success with another one-man show, this time in two venues.", "Timeless Beauty: Pursuing Life’s Textures included 36 paintings, 21 of which were sold at Bartfield Galleries in New York, and 15 of which were auctioned on Hilton Head, South Carolina through Morris & Whiteside Galleries.", "Once again, everything sold immediately.", "In conjunction with the show a revised edition of his book, A Gallery of Paintings, was also released.", "Hulings married Mary Belfi in 1966 and their daughter Elizabeth was born two years later.", "When they were not traveling, they lived in Santa Fe, New Mexico." ]

[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ]

[ "He was born in Florida and raised in New Jersey.", "Clark also lived in Spain, New York, Louisiana, and throughout Europe before settling in Santa Fe, New Mexico, in the early 1970s.", "His training as an artist began as a teenager with Sigismund Ivanowsky and George Bridgman, and concluded at the Art Students League of New York with Frank Reilly." ]

[ "Aberbargoed Buds was founded in 1957 after the previous team in the area, Aberbargoed Town, folded in 1949.", "The Buds, believed to be an abbreviation of \"Bedwellty Urban District sides\", began playing in the West Monmouthshire League before there was a reorganisation of the league structure and moved to the Gwent County League.", "The Buds won the Gwent Cup in 1984 and their first Gwent Championship in 1985–86.", "In 1999, Aberbargoed Town who had reformed in 1986 approached the Buds' committee to amalgamate the Town with the current Buds who were on the verge of folding leading up to the 1999–2000 season.", "The Town committee agreed to this arrangement which kept the Buds in the Gwent County League and the Town, now known as the seconds, in the North Gwent League.", "In 2001–02 the Buds won the Gwent Cup defeating Llanhilleth 3–0 and then retained the trophy the following year by defeating Blaenavon Blues 6–0.", "The Buds won the Gwent County League to complete a double but were not promoted to the Welsh League Division Three due to a lack of facilities.", "Having finished runners up in the following season (2003–04) and then third the season after (2004–05) managers Graham Owen and John Randall stood down.", "Former player Neil Thomas became manager.", "The club once again won the league during the 2005–06 season, which was decided in the last game of the season with the Buds defeating the reigning champions Clydach Wasps 4–1 to take the league title and gain promotion to Welsh League Football for the 2006–07 season.", "The Buds have twice reached Division One of the Welsh Football League but suffered relegation after a single season on both occasions, the most recent campaign being the 2015–16 season.", "At the end of the 2021–22 Ardal SE season the club initially finished in 12th places but were deducted 30 points by the Football Association of Wales and relegated, after finishing bottom of the revised divisional table." ]

[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ]

[ "Aberbargoed Buds Football Club is a football club based in Aberbargoed, Wales.", "The team play in the Ardal Leagues South East, tier 3 of the Welsh football pyramid." ]

[ "The term \"Seven Sisters\" was originally coined by John Alexander Black, founder of Lexpert magazine (now owned by Thomson Reuters).", "At the time, the Seven Sisters dominated the Canadian M&A legal advisory rankings.", "However, by 2006, Black stated \"the moniker may have run its course and that some people argue the Seven have shrunk to two or possibly three.\"", "Later that year, The Globe and Mail reported the Seven Sisters term was no longer valid, explaining that \"as the Canadian pool of major companies boils down to a thin concentrate, the upper legal tier has also shrunk.\"", "It noted that \"most observers agree the reigning top players are McCarthy Tetrault LLP, Stikeman Elliott LLP, Osler Hoskin & Harcourt LLP and Blake Cassels & Graydon LLP.\"", "As of 2017, only five of the original seven have become national law firms in Canada – the aforementioned four plus Torys LLP.", "In 2015, The Globe and Mail reported that the market had changed markedly from the early 2000s: \"Elite U.S. legal shops blanket the top 25 firms for M&A, taking 13 of the top spots on the chart.\"", "According to Bloomberg (FY 2015), the top 10 legal advisors by M&A transactions with any Canadian involvement were Simpson Thacher (NY), Sullivan & Cromwell (NY), Osler (TO), Skadden (NY), Torys (TO), Bennett Jones (TO), Shearman (NY), Davis Polk (NY), McCarthy (TO), and Morrison & Foerster (SF), signalling the integration of Canada into the larger North American market.", "The 'club of nine' was a similar term used in the UK until it was replaced by the Magic Circle.", "In alphabetical order the Seven Sisters included: Blakes, Davies, Goodmans, McCarthy, Osler, Stikeman, and Torys.", "The American Lawyer Global 200, first published in 2018, included a total of six Canadian law firms, excluding Gowling WLG which operates as two separate partnerships across the Atlantic.", "The Bank of Canada reported the 2017 CAD/USD exchange rate at 0.770.", "Separately, The Toronto Star reported that Torys had estimated revenues of CAD 275 million in 2006, prior to the opening of its Montreal and Calgary offices.", "In 2007, Lexpert also reported that since Torys' merger with New York-based Haythe & Curley, Torys \"has consistently ranked among the four most profitable large law firms in the Toronto market, during which time it has made up more than half the gap between itself and the top-ranked firm.", "This is significant because, accordingly, the four most profitable firms have for the last few years been in a group by themselves: there is a considerable drop-off in profitability between the fourth-ranked firm and the fifth-ranked firm, and between the fifth-ranked firm and the sixth-ranked firm.", "\"" ]

[ 0, 1, 2, 3, 4, 5, 6, 7, 8 ]

[ "The Seven Sisters refers to a historical collection of seven law firms with offices in Toronto, Ontario, Canada." ]

[ "The codex contains a complete text of the four Gospels.", "It contains also liturgical books with hagiographies: synaxarion and Menologion.", "The biblical text is written in one column per page, 23-24 lines per page.", "It was written in neat, and regular letters.", "The first three pages are written in gold, with exquisite miniatures, four on page 2, four on page 3.\nIt has iota adscriptum.", "The text is divided according to the (\"chapters\"), whose numbers are given at the margin, with the (\"titles of chapters\") at the top of the pages.", "There is also a division according to the Ammonian Sections, with references to the Eusebian Canons (written below Ammonian Section numbers).", "It contains Prolegomena, Epistula ad Carpianum, Eusebian Canon tables, tables of the (\"tables of contents\") before each Gospel, lectionary equipment at the margin (for liturgical use), and pictures.", "The Greek text of the codex is a representative of the Byzantine text-type.", "Hermann von Soden classified it to Ak (the Byzantine commentated text).", "Aland placed it in Category V.\nAccording to the Claremont Profile Method it belongs to the textual family Kx in Luke 1 and Luke 20.", "In Luke 10 no profile was made.", "At the margin of Mark 16:8 it has questionable scholion: εν τισι των αντιγραφων, εως ωδε πληρουται ο ευαγγελιστης εν πολλοις δε, και ταυτα φερεται.", "The text of the pericope John 7:53-8:11 is omitted.", "Scholz dated it to the 10th-century, Gregory to the 12th-century.", "Currently it is dated by the INTF to the 12th-century.", "The manuscript was brought to Paris by Catherine de' Medici.", "It was in private hands, and became one of the manuscripts used by Kuster's in his revised reprint of Mill's \"Novum Testamentum Graecum\" (Paris 8).", "Scholz examined a bigger part of Matthew, Mark and John in the codex.", "It was examined and described by Burgon and Paulin Martin.", "C. R. Gregory saw the manuscript in 1884.", "The codex is located now at the Bibliothèque nationale de France (Gr. 64) in Paris." ]

[ 0, 1, 2, 3, 4, 5, 6, 7 ]

[ "It has liturgical books and full marginalia." ]

[ "Shnaan, a Druze, was born and raised in Hurfeish.", "In his military service with the Israel Defense Forces, he was a fighter in the Herev Battalion.", "Afterwards he completed his academic studies at Tel Aviv University in general studies, Middle East studies and pre-law studies.", "Shnaan then returned to his home town, working between 1989-1995 as a teacher and acting principal of the local six-years secondary school.", "Throughout the years Shnaan was active with the Histadrut Labor Federation.", "He was appointed as an advisor to Deputy Minister of Internal Affairs Saleh Tarif.", "Following the elections to the 14th Knesset he was a senior advisor to the Minister responsible for Minorities Affairs within the Prime Minister's Office.", "He held this position between 1997 and 2001, and was later appointed as the administrator of the Northern District for the Ministry of Labor and Welfare.", "Shnaan was also director of the district's branch of the Ministry of Welfare.", "In 2005 he was appointed by Minister of Internal Affairs Ophir Pines-Paz as his senior advisor, maintaining the post for one year.", "In 2006, Shnaan nominated himself for the Labor Party's list of candidates for the 2006 elections.", "He was elected to the slot reserved for a Druze representative, 20th on the party's list, and entered the Knesset on 28 May 2008, following the resignation of Efraim Sneh.", "He was a member of the Education, Culture and Sports Committee.", "Prior to his entry to the Knesset, Shnaan was considered by party chairman Amir Peretz as his candidate for the post of minister, eventually given to Raleb Majadele.", "Placed 16th on the party's list for the 2009 elections, Shnaan lost his seat as Labor was reduced to 13 seats.", "He subsequently joined the breakaway Independence party, and returned to the Knesset on 14 February 2012 as a replacement for Matan Vilnai, who had been appointed as ambassador to China.", "Shnaan lost his Knesset seat in 2013 after Independence chose not to contend in the elections.", "In October 2017, Shnaan addressed a convention of the Arab-Jewish coexistence organization \"Women Wage Peace\" in Jerusalem.", "In late July 2018, Shachiv Shnaan took part in a delegation of Druze politicians and community leaders in a meeting with Prime Minister Benjamin Netanyahu and several cabinet ministers.", "They presented the community's opposition to clauses in Israel's newly enacted \"Nationality law\", impacting minority populations' status regarding self-definition and removing Arabic as an official language of the state.", "Shnaan resides in Hurfeish, is married and a father of five.", "His youngest son, border policeman Kamil Shinan, was killed during a terror attack on the Temple Mount on 14 July 2017." ]

[ 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 ]

[ "Shachiv Shnaan (, ; born 20 June 1960) is an Israeli-Druze politician who served as a member of the Knesset for Independence." ]

[ "Sackmann obtained his MSc (1961) and PhD (1964) degrees from the University of Stuttgart in the group of Theodor Förster.", "He then spent two years at Bell Telephone Laboratories in Murray Hill, New Jersey, and six years at Max Planck Institute for Biophysical Chemistry in Göttingen, Germany.", "Between 1974 and 1980 he was professor of physics and head of the biophysics department at Universität Ulm, and from 1980 until retirement in 2003 he held the same positions at the Physics Department of the Technical University of Munich.\nSackmann dedicated a lifetime of research towards probing the living cell with tools of physics, long before biophysics was the mode of the day.", "Considered as a father of biophysics in Europe, he pioneered, along with others, the idea of a “bottom up” approach towards understanding the cell – starting from relatively simple systems like lipid bilayers, giant vesicles and actin in solution and going towards more and more complex systems to reach eventually an understanding at the level of the entire cell.", "More than 200 publications and several books Literatur von und über", "Erich Sackmann testify to his contributions to soft matter and biophysics.", "His early work was mainly on lyotropic liquid crystals and lipid membranes.", "Later, along with his students he laid the foundations of our current understanding of membrane adhesion.", "Over the years, his team developed and improved the technique of reflection interference contrast microscopy – RICM (which is quantitative interference reflection microscopy – IRM) – a powerful tool to probe adhesion of membranes and thin films.", "Collaborations with theoreticians like Reinhard Lipowsky, Udo Seifert and Robijn Bruinsma have led to seminal works on adhesion of cell mimetic giant vesicles (also called liposomes).", "Another of his interests is the cytoskeleton and its dynamics.", "To study cytoskeletal dynamics, his team developed magnetic tweezers capable of exerting very small pulling forces.", "He has contributed to our understanding of the dynamics of single actin filaments, actin networks as well as intact living cells.", "His research interests include: physics of self assembly and function of artificial and biological membranes, viscoelastic microscopy of cells, physics of the actin based cytoskeleton: micro-rheology of macromolecular networks, applications of solid-supported lipid-protein membranes, ultrathin hydrated polymer layers and polymer/membrane composite films and neutron Reflectivity as a new tool to study the self assembly of membrane associated proteins.", "Along with Reinhard Lipowsky, he has authored \"the Structure and Dynamics of Membranes\".", "Recently, along with Rudolf Merkel, he has published \"Lehrbuch der Biophysik\" – a text book on biophysics aimed at students and researchers.", "He was elected a Fellow of the American Physical Society in 2002.", "In recognition of his research work, in 2006, he was awarded the Stern-Gerlach-Medal by the DPG, German Physical Society." ]

[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 ]

[ "Erich Sackmann (born 26 November 1934) is a German experimental physicist and a pioneer of biophysics in Europe." ]

[ "The word \"Dzüko\" is originally derived from the Viswema dialect of the Angamis \"Dzüko\" which loosely translated means \"Soulless and Dull\" referring to when some ancestors of Viswema who moved out to establish a new village in \"Dzüko\", due to the unfavorable weather conditions they were unable to harvest crops which led them to say \"the valley is very beautiful but is dull and soulless.", "\"\nA common misconception is that \"Dzüko\" derives its meaning from the Angami word which translates to \"Cold Water\" referring to the ice cold streams that flows through the valley.", "The main entry is from the foothills of Viswema where one can travel to the rest house above Teyozwü Hill by a Tata Sumo taxi.", "From here one has to climb forty minutes to the top of the mountain \"(Khiyoke)\".", "This is where Dzüko starts but the main valley is still another two hours' walk away.", "One can exit the valley from the same route but if one is planning to come back by foot, the Jakhama route is shorter.", "Also it can be reached in five hours of trek from Mount Tempü of Senapati district of Manipur.", "The new five-hour trek route was opened by MMTA (Manipur Mountaineering and Trekking Association).", "The Asian Highway 1 and also the NH-2 passes through its foothills.", "The nearest airport is Dimapur Airport at Chümoukedima–Dimapur about 96 kilometres (60 miles) away from Viswema while the Bir Tikendrajit International Airport is located about 120 kilometres (75 miles) south of Viswema.", "There is a Helipad just next to the Guest house however no service is seen in the last few years.", "The valley borders a region of old-growth forest, and is home to several rare and endangered species of flora and fauna, including the Dzüko Lily (\"Lilium mackliniae\") and the Blyth's tragopan, which is the state bird of Nagaland.", "A number of other rare species are also found here, including several rhododendron species, plants such as the \"aconita nagaram,\" and fauna including the Asian golden cat, the Hollock Gibbon, the Dzuko Valley horned toad (\"Megophrys dzukou\"), several species of leopard including the clouded leopard, the Asiatic black bear, the capped langur, the stump-tailed macaque, and the serow.", "It has periodically been threatened by forest fires, which tend to spread quickly due to prevalent wind conditions and are difficult to fight because of the inaccessible terrain around the valley.", "In 2006, a forest fire destroyed 20 kilometers of forest in the valley before it was contained.", "The 2020–21 Dzüko Valley wildfires destroyed an estimated 200 acres of forest land, as well as significant flora in the valley itself.", "There has been disputes for years between Manipur and Nagaland regarding the ownership of Dzüko Valley.", "Historically, the valley is an extent of the territory of Viswema under present-day Nagaland but today it is jointly preserved with the Southern Angami Public Organization which is also based in Nagaland.", "However, politically, the valley shares both Manipur and Nagaland state territories which the majority of the area falls under Manipur state boundary according to the map of the Survey of India." ]

[ 11, 12, 13, 14, 15 ]

[ "The Dzüko Valley is a valley located at the borders of the states of Nagaland and Manipur in Northeast India.", "The valley is famous for its wide range of flowers in every season but the most famous one is the Dzüko Lily and it is found only in this valley." ]

[ "The new name refers to the pupil of an eye, and to a legend of a painting of four dragons.", "The word Hitomi generally means \"eye\", and specifically the pupil, or entrance window of the eye - the aperture.", "There is also an ancient legend that inspires the name Hitomi.", "\"One day, many years ago, a painter was drawing four white dragons on a street.", "He finished drawing the dragons, but without \"Hitomi\".", "People who looked at the painting said \"why don't you paint Hitomi, it is not complete.", "The painter hesitated, but people pressured him.", "The painter then drew Hitomi on two of the four dragons.", "Immediately, these dragons came to life and flew up into the sky.", "The two dragons without Hitomi remained still\".", "The inspiration of this story is that Hitomi is regarded as the \"One last, but most important part\", and so we wish ASTRO-H to be the essential mission to solve mysteries of the universe in X-rays.", "Hitomi refers to the aperture of the eye, the part where incoming light is absorbed.", "From this, Hitomi reminds us of a black hole.", "We will observe Hitomi in the Universe using the Hitomi satellite.", "\"Hitomi\" objectives were to explore the large-scale structure and evolution of the universe, as well as the distribution of dark matter within galaxy clusters and how the galaxy clusters evolve over time; how matter behaves in strong gravitational fields (such as matter inspiraling into black holes), to explore the physical conditions in regions where cosmic rays are accelerated, as well as observing supernovae.", "In order to achieve this, it was designed to be capable of:\n\nIt was the sixth of a series of JAXA X-ray satellites, which started in 1979, and it was designed to observe sources that are an order of magnitude fainter than its predecessor, Suzaku.", "Its planned mission length was three years.", "At the time of launch, two other large X-ray satellites were carrying out observations in orbit: the Chandra X-ray Observatory and XMM-Newton, both of which were launched in 1999.", "The probe carried four instruments and six detectors to observe photons with energies ranging from soft X-rays to gamma rays, with a high energy resolution.", "\"Hitomi\" was built by an international collaboration led by JAXA with over 70 contributing institutions in Japan, the United States, Canada, and Europe, and over 160 scientists.", "With a mass of , At launch, \"Hitomi\" was the heaviest Japanese X-ray mission.", "The satellite is about in length.", "Two soft X-ray telescopes (SXT-S, SXT-I), with focal lengths of , focus light onto a soft X-ray Spectrometer (SXS), provided by NASA, with an energy range of 0.4-12 keV for high-resolution X-ray spectroscopy, and a soft X-ray imager (SXI), with an energy range of 0.3-12 keV.\nTwo hard X-ray telescopes (HXT), with a focus length of , focus light onto two hard X-ray imagers (HXI), with energy range 5-80 keV, which are mounted on a plate placed at the end of the extendable optical bench (EOB) that is deployed once the satellite is in orbit.", "The Canadian Space Agency (CSA) provided the Canadian ASTRO-H Metrology System (CAMS), which is a laser alignment system that will be used to measure the distortions in the extendible optical bench.", "Two soft Gamma-ray detectors (SGD), each containing three units, were mounted on two sides of the satellite, using non-focusing detectors to observe soft gamma-ray emission with energies from 60 to 600 KeV.\nThe Netherlands Institute for Space Research (SRON) in collaboration with the University of Geneva provided the filter-wheel and calibration source for the spectrometer.", "The launch of the satellite was planned for 2013 as of 2008, later revised to 2015 as of 2013.", "As of early February 2016, it was planned for 12 February, but was delayed due to poor weather forecasts.", "\"Hitomi\" launched on 17 February 2016 at 08:45 UTC into a low Earth orbit of approximately .", "The circular orbit had an orbital period of around 96 minutes, and an orbital inclination of 31.01°.", "It was launched from the Tanegashima Space Center on board an H-IIA launch vehicle.", "14 minutes after launch, the satellite separated from the launch vehicle.", "The solar arrays later deployed according to plan, and it began its on-orbit checkout.", "On 27 March 2016, JAXA reported that communication with \"Hitomi\" had \"failed from the start of its operation\" on 26 March 2016 at 07:40 UTC.", "On the same day, the U.S. Joint Space Operations Center (JSpOC) announced on Twitter that it had observed a breakup of the satellite into 5 pieces at 08:20 UTC on 26 March 2016, and its orbit also suddenly changed on the same day.", "Later analysis by the JSpOC found that the fragmentation likely took place around 01:42 UTC, but that there was no evidence the spacecraft had been struck by debris.", "Between 26 and 28 March 2016, JAXA reported receiving three brief signals from \"Hitomi\"; while the signals were offset by 200 kHz from what was expected from \"Hitomi\", their direction of origin and time of reception suggested they were legitimate.", "Later analysis, however, determined that the signals were not from \"Hitomi\" but from an unknown radio source not registered with the International Telecommunication Union.", "JAXA stated they were working to recover communication and control over the spacecraft, but that \"the recovery will require months, not days\".", "Initially suggested possibilities for the communication loss is that a helium gas leak, battery explosion, or stuck-open thruster caused the satellite to start rotating, rather than a catastrophic failure.", "JAXA announced on 1 April 2016 that \"Hitomi\" had lost attitude control at around 19:10 UTC on 25 March 2016.", "After analysing engineering data from just before the communication loss, however, no problems were noted with either the helium tank or batteries.", "The same day, JSpOC released orbital data for ten detected pieces of debris, five more than originally reported, including one piece that was large enough to initially be confused with the main body of the spacecraft.", "Amateur trackers observed what was believed to be \"Hitomi\" tumbling in orbit, with reports of the main spacecraft body (Object A) rotating once every 1.3 or 2.6 seconds, and the next largest piece (Object L) rotating every 10 seconds.", "JAXA ceased efforts to recover the satellite on 28 April 2016, switching focus to anomaly investigation.", "It was determined that the chain of events that led to the spacecraft's loss began with its inertial reference unit (IRU) reporting a rotation of 21.7° per hour at 19:10 UTC on 25 March 2016, though the vehicle was actually stable.", "The attitude control system attempted to use \"Hitomi\" reaction wheels to counteract the non-existent spin, which caused the spacecraft to rotate in the opposite direction.", "Because the IRU continued to report faulty data, the reaction wheels began to accumulate excessive momentum, tripping the spacecraft's computer into taking the vehicle into \"safe hold\" mode.", "Attitude control then tried to use its thrusters to stabilise the spacecraft; the Sun sensor was unable to lock on to the Sun's position, and continued thruster firings caused \"Hitomi\" to rotate even faster due to an incorrect software setting.", "Because of this excessive rotation rate, early on 26 March 2016 several parts of the spacecraft broke away, likely including both solar arrays and the extended optical bench.", "Reports of a \"Hitomi\" replacement mission first surfaced on 21 June 2016.", "According to an article from Kyodo News, JAXA was considering a launch of \"Hitomi 2\" in the early 2020s aboard Japan's new H3 launch vehicle.", "The spacecraft would be a near-copy of \"Hitomi\".", "However, a 27 June 2016 article from \"The Nikkei\" stated that some within the Ministry of Education, Culture, Sports, Science and Technology believed it was too early to grant funding for a \"Hitomi\" replacement.", "The article also noted that NASA had expressed support for a replacement mission led by Japan.", "On 14 July 2016, JAXA published a press release regarding the ongoing study of a successor.", "According to the press release, the spacecraft would be a remanufacture but with countermeasures reflecting \"Hitomi\" loss, and would be launched in 2020 on a H-IIA launch vehicle.", "The scientific mission of the \"ASTRO-H Successor\" would be based around the SXS instrument.", "The Minister of Education, Culture, Sports, Science and Technology, Hiroshi Hase, stated during a press conference on 15 July 2016 that funding for \"Hitomi\" successor will be allocated in the fiscal year 2017 budget request, and that he intends to accept the successor mission on the condition that the investigation of \"Hitomi\" destruction is completed and measures to prevent recurrence are done accordingly.", "The X-Ray Imaging and Spectroscopy Mission (XRISM) was approved by JAXA and NASA in April 2017, with launch planned after 2020." ]

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[ "The spacecraft was launched on 17 February 2016 and contact was lost on 26 March 2016, due to multiple incidents with the attitude control system leading to an uncontrolled spin rate and breakup of structurally weak elements." ]

[ "The original Manor of Foston and Scropton was held by the Agard family from the 14th to the 17th century.", "It was bought by John Bate in 1679.", "Richard Bate was High Sheriff of Derbyshire in 1705.", "Brownlow Bate sold the estate to John Broadhurst in 1784.", "The 17th century manor house was destroyed by fire in 1836, but many parts of that house survive.", "A new Jacobethan house was designed by T. C. Hine of Nottingham and built in 1863.", "Its main two storey front has eight bays and an off-centre three-storey tower.", "The house is now a Grade II listed building.", "HM Prison Service acquired the hall and grounds in 1953.", "During its Prison Service history Foston Hall has been a detention centre, an immigration centre, and finally before its closure during 1996 a satellite of Sudbury Prison.", "It was re-opened on 31 July 1997, following major refurbishment and building work, as a closed-category female prison.", "Foston Hall Prison is spread over seven wings that serve a variety of functions.", "The prison can accommodate 187 convicted prisoners, 80 remand prisoners and 16 juvenile prisoners.", "Foston Hall also has a Health Care Centre with three inpatient beds.", "The prison provides inmates with work in the prison gardens, the gym, the textile and craft workshop and the kitchens, all of which can lead to qualifications.", "In addition the prison's education department offers NVQs in Cleaning Services and hairdressing, as well as basic and key skills learning." ]

[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]

[ "The prison is operated by Her Majesty's Prison Service." ]

[ "The original Manor of Foston and Scropton was held by the Agard family from the 14th to the 17th century.", "It was bought by John Bate in 1679.", "Richard Bate was High Sheriff of Derbyshire in 1705.", "Brownlow Bate sold the estate to John Broadhurst in 1784.", "The 17th century manor house was destroyed by fire in 1836, but many parts of that house survive.", "A new Jacobethan house was designed by T. C. Hine of Nottingham and built in 1863.", "Its main two storey front has eight bays and an off-centre three-storey tower.", "The house is now a Grade II listed building.", "HM Prison Service acquired the hall and grounds in 1953.", "During its Prison Service history Foston Hall has been a detention centre, an immigration centre, and finally before its closure during 1996 a satellite of Sudbury Prison.", "It was re-opened on 31 July 1997, following major refurbishment and building work, as a closed-category female prison.", "Foston Hall Prison is spread over seven wings that serve a variety of functions.", "The prison can accommodate 187 convicted prisoners, 80 remand prisoners and 16 juvenile prisoners.", "Foston Hall also has a Health Care Centre with three inpatient beds.", "The prison provides inmates with work in the prison gardens, the gym, the textile and craft workshop and the kitchens, all of which can lead to qualifications.", "In addition the prison's education department offers NVQs in Cleaning Services and hairdressing, as well as basic and key skills learning." ]

[ 11, 12, 13, 14, 15 ]

[ "The prison is operated by Her Majesty's Prison Service." ]

[ "This film's music was composed by Tafoo and film song lyrics were by Altaf Bajwa.", "Film songs were sung by Naseebo Lal and Humaira Channa." ]

[ 0, 1 ]

[ "Film music was composed by the renowned composer Tafoo and the film song lyrics were by Altaf Bajwa." ]

[ "Kelly was born in Champaign, Illinois, to Edward Kelly (1940–1985), who taught at the State University of New York at Albany, and Linda (\"née\" DeMaio), a homemaker.", "She is of Italian and German descent on her mother's side and Irish descent on her father's.", "She was raised Catholic.", "Her father died of a heart attack when she was 15 years old.", "Kelly attended Tecumseh Elementary School in suburban Syracuse, New York.", "When she was 9, her family moved to Delmar, New York, a suburb of Albany, where she attended Bethlehem Central High School.", "She obtained an undergraduate degree in political science from the Maxwell School of Citizenship and Public Affairs at Syracuse University in 1992 and earned a J.D. from Albany Law School in 1995.", "Kelly was an associate attorney in the Chicago office of law firm Bickel & Brewer LLP.", "In fall 1996, she co-wrote an article, \"Litigation\", \"The Conflicting Roles of Lawyer as Director\", for the American Bar Association's journal.", "She later worked at Jones Day for nine years, where one of her clients was the credit bureau Experian.", "In 2003, Kelly moved to Washington, D.C., where she was hired by the ABC affiliate WJLA-TV as a general assignment reporter.", "She covered national and local events, including live coverage of the confirmation hearings for U.S. Supreme Court Justice Samuel Alito and Chief Justice John G. Roberts, the retirement of Justice Sandra Day O'Connor, the death of Chief Justice William Rehnquist, and the 2004 presidential election.", "CNN president Jonathan Klein later said he regretted not hiring Kelly as a reporter at the beginning of her career, as she was \"the one talent you'd want to have from somewhere else\".", "In 2004, Kelly applied for a job at Fox News.", "She contributed legal segments for \"Special Report with Brit Hume\" and hosted her own legal segment, \"Kelly's Court\", during \"Weekend Live\".", "She appeared in a weekly segment on \"The O'Reilly Factor\" and occasionally filled in for Greta Van Susteren on \"On the Record\", where most of her reporting focused on legal and political matters.", "She occasionally contributed as an anchor, but more often as a substitute anchor on weekends.", "On February 1, 2010, Kelly began hosting her own two-hour afternoon show, \"America Live\", which replaced \"The Live Desk\".", "She was a guest panelist on Fox News' late-night satire program \"Red Eye w/ Greg Gutfeld\".", "In 2010, viewership for \"America Live\" increased by 20%, averaging 1,293,000 viewers, and increased by 4% in the 25–54 age demographic, averaging 268,000 viewers.", "In December 2010, Kelly hosted a New Year's Eve special with Bill Hemmer.", "Kelly received media attention for her coverage of the results of the 2012 United States presidential election.", "On November 6, 2012 (the night of the election), Fox News' decision desk projected that Obama would win the state of Ohio along with a second term after part of the results had been released.", "In response to Karl Rove's opposition to this projection, Kelly walked backstage to the decision desk on camera and spoke with them; she also asked Rove, \"Is this just math that you do as a Republican to make yourself feel better?", "Or is this real?\"\nKelly left \"America Live\" in July 2013 and took maternity leave.", "On October 7, 2013, she began hosting a new nightly program, \"The Kelly File\".", "\"The Kelly File\" was occasionally the channel's ratings leader, topping \"The O'Reilly Factor\".", "In December 2013, Kelly commented on a \"Slate\" article on \"The Kelly File:\" \"For all you kids watching at home, Santa just is white, but this person is just arguing that maybe we should also have a black Santa,\" adding, \"But Santa is what he is, and just so you know, we're just debating this because someone wrote about it.\"", "Kelly also said that Jesus was a white man later in the segment.", "Soon after, Jon Stewart, Stephen Colbert, Rachel Maddow, Josh Barro, and others satirized her remarks.", "Two days later, she said on the air that her original comments were \"tongue-in-cheek\", and that the skin color of Jesus is \"far from settled\".", "In June 2015, Kelly interviewed Jim Bob Duggar and Michelle Duggar of \"19 Kids and Counting\" regarding their son Josh Duggar's alleged molestation of five girls in 2002.", "She later interviewed two of their daughters, Jill and Jessa.", "This show's Nielsen national estimates ratings of 3.09 million viewers, above its average 2.11 million, ranked with the 3.2 million for the Malaysia Airlines Flight 17 shootdown coverage and 7.3 million for the Ferguson riots coverage.", "In the Republican Party presidential debate on August 6, 2015, Kelly asked then-presidential candidate Donald Trump whether a man of his temperament ought to be elected president, noting that he has called various women insulting names in the past.", "Kelly's moderating generated a range of media and political reactions and her professionalism was criticized by Trump.", "Kelly responded to Trump's criticism by saying she would not \"apologize for doing good journalism\".", "Trump declined to attend the Iowa January 28 debate that she moderated.", "After the debate and off-camera, Ted Cruz said that Kelly had referred to Trump off-camera as \"Voldemort\", though Fox News denied it.", "Bill Maher complimented Kelly as being \"so much better\" than the candidates who attended the January 28 debate and argued that she was a more viable candidate for the Republican nomination.", "In an interview with CBS News Sunday Morning, Kelly reflected that she was disappointed with the lack of support she received from coworker Bill O'Reilly and CNN, the latter airing a Trump event the same time as the debate.", "In April, at her request, Kelly met with Trump at Trump Tower, having \"a chance to clear the air\".", "The following month, after interviewing Trump and being met with mixed reception, she expressed interest in doing another one with him.", "In June, she criticized Trump for his claims against Gonzalo P. Curiel's impartiality.", "In October, a contentious discussion between Kelly and Newt Gingrich on \"The Kelly File\" regarding Trump's sexual comments in a 2005 audio recording gained widespread social media reaction.", "In March 2016, it was announced that Kelly would host a one-hour prime time special on the Fox network wherein she would interview celebrities from the worlds of \"politics, entertainment, and other areas of human interest\".", "The special aired in May 2016, which was a sweeps month.", "It acquired 4.8 million viewers, but placed third in the ratings.", "Gabriel Sherman wrote of the stakes for Kelly as \"high\", elaborating that with Kelly being in the final year of her contract with Fox and having confirmed her ambitions, \"[t]he special was essentially a public interview for her next job.\"", "In July 2016, amid allegations of sexual harassment on the part of Fox News CEO Roger Ailes, Kelly was reported to have confirmed that she herself was also subjected to his harassment.", "Two days after the report, Ailes resigned from Fox News and his lawyer, Susan Estrich, publicly denied the charge.", "During her coverage of the 2016 Republican National Convention, her attire received criticism.", "In a defense of Kelly, Jenavieve Hatch of \"The Huffington Post\" commented, \"If you're a woman on national television reporting on a political event from hot, humid Cleveland, wearing a weather-appropriate outfit makes you the target of an endless stream of sexist commentary.\"", "In September, it was reported that Kelly would be collaborating with Michael De Luca to produce \"Embeds\", a scripted comedy about reporters covering politics, to be aired on a streaming service.", "Kelly appeared on the cover of the February 2016 issue of \"Vanity Fair\".", "In 2016, she was an honoree for \"Variety\"s \"Power of Women\" for her addressing child abuse.", "In late 2016, Kelly was alleged to be actively considering other news networks aside from Fox News, since her contract was a few months from expiring.", "In January 2017, \"The New York Times\" reported that she would leave Fox News for a \"triple role\" at NBC News, which would include a daytime talk show, a Sunday-night newsmagazine, and becoming a correspondent for major news events and political coverage.", "She departed Fox News on January 6, 2017, after the last episode of \"The Kelly File\" was aired.", "In January 2017, \"People\" quoted an unspecified source that Kelly remained under a non-compete clause with Fox until July 2017 which would prevent her from working for a competitor until the clause expires or is canceled.", "On June 2, 2017, Kelly interviewed Russian president Vladimir Putin, first in a panel discussion she moderated at the St. Petersburg International Economic Forum and later in a one-on-one interview for the premiere episode of NBC's \"Sunday Night with Megyn Kelly\", which aired June 4, 2017.", "Kelly's daytime talk show, \"Megyn Kelly Today\", premiered in September 2017.", "Kelly was being paid reportedly between $15 million and $20 million a year at NBC.", "After an initial run of eight episodes in the summer of 2017, NBC decided to bring her newsmagazine show \"Sunday Night with Megyn Kelly\" back for summer 2018 after a hiatus for football and the Winter Olympics, but only periodically.", "However, this return never materialized.", "Instead, Kelly continued to report stories for \"Dateline NBC\" during the summer of 2018, continuing her work for the show which she joined in 2017.", "On October 23, 2018, Kelly was criticized for on-air remarks she made on \"Megyn Kelly Today\" related to the appropriateness of blackface as part of Halloween costumes.", "She recollected that \"when I was a kid, that was okay as long as you were dressing up like a character\", and defended Luann de Lesseps's use of skin darkening spray to portray Diana Ross.", "After receiving backlash for her comments, Kelly issued an internal email apologizing for the remarks later that day.", "On October 26, 2018, NBC canceled \"Megyn Kelly Today\".", "It had been reported that Kelly was considering ending the program to focus on her role as a correspondent.", "Her contract was terminated January 11, 2019, with Kelly due the entire amount from the contract.", "She was reportedly not subject to any non-compete clause under her NBC contract.", "Kelly announced the launch of Devil May Care Media, her media production company, on September 10, 2020, with a podcast, \"The Megyn Kelly Show\".", "Its first episode premiered on September 28.", "On July 6, 2021, it was announced that the podcast would move to Sirius XM on September 7, 2021, to broadcast weekdays at 12 noon ET on the talk radio channel Triumph, along with a video simulcast available to Sirius XM subscribers.", "In February 2016, Kelly signed an agreement with HarperCollins to write an autobiography scheduled for release later that year, in a deal worth more than $10 million.", "The book, titled \"Settle for More\", was released on November 15, 2016.", "\"Bombshell\", a 2019 film portraying Kelly's career at Fox News, was released on December 13, 2019.", "Kelly is played by Charlize Theron, with other cast members including Margot Robbie as Kayla Pospisil (a composite character), Nicole Kidman as Gretchen Carlson, Nazanin Boniadi as Rudi Bakhtiar and John Lithgow as Roger Ailes.", "The film follows events at Fox News in the lead up to Ailes resigning from the organization.", "Kelly said she was not consulted for the film's content.", "Kelly married Daniel Kendall, an anesthesiologist, in 2001.", "The marriage ended in divorce in 2006.", "In 2008, she married Douglas Brunt, who was then president and CEO of the cybersecurity firm Authentium, and who became a full-time writer and novelist.", "They have three children, son Yates (b. 2009), daughter Yardley (b. 2011), and son Thatcher (b. 2013).", "Politically, Kelly identifies as an independent, and told \"Variety\" in 2015 that she had voted for both Democrats and Republicans.", "On October 12, 2016, Kelly stated in a segment on her show with Fox News commentator Julie Roginsky that she is a lifelong Catholic.", "Kelly has appeared at a fundraiser for parental rights organization Moms for Liberty." ]

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[ "Megyn Marie Kelly (; born November 18, 1970) is an American journalist, attorney, political commentator, talk show host, and television news anchor.", "She currently hosts a talk show and podcast, \"The Megyn Kelly Show\", that airs live daily on SiriusXM.", "She was a talk show host at Fox News from 2004 to 2017 and a host and correspondent with NBC News from 2017 to 2018.", "She is also active in posting to her Instagram page and YouTube channel.", "During her time at Fox News, Kelly hosted \"America Live\" and, before that, co-hosted \"America's Newsroom\" with Bill Hemmer.", "From 2007 to 2012, the two reporters hosted Fox News Channel's New Year's Eve specials.", "Kelly also hosted \"The Kelly File\" from October 2013 to January 2017.", "Kelly left Fox News in January 2017 and joined NBC News.", "She started hosting the third hour of the morning show \"Today\" with her program titled \"Megyn Kelly Today\" in September 2017.", "The show was cancelled in October 2018 after a segment discussing blackface, and she left the network in January 2019." ]

[ "Kelly was born in Champaign, Illinois, to Edward Kelly (1940–1985), who taught at the State University of New York at Albany, and Linda (\"née\" DeMaio), a homemaker.", "She is of Italian and German descent on her mother's side and Irish descent on her father's.", "She was raised Catholic.", "Her father died of a heart attack when she was 15 years old.", "Kelly attended Tecumseh Elementary School in suburban Syracuse, New York.", "When she was 9, her family moved to Delmar, New York, a suburb of Albany, where she attended Bethlehem Central High School.", "She obtained an undergraduate degree in political science from the Maxwell School of Citizenship and Public Affairs at Syracuse University in 1992 and earned a J.D. from Albany Law School in 1995.", "Kelly was an associate attorney in the Chicago office of law firm Bickel & Brewer LLP.", "In fall 1996, she co-wrote an article, \"Litigation\", \"The Conflicting Roles of Lawyer as Director\", for the American Bar Association's journal.", "She later worked at Jones Day for nine years, where one of her clients was the credit bureau Experian.", "In 2003, Kelly moved to Washington, D.C., where she was hired by the ABC affiliate WJLA-TV as a general assignment reporter.", "She covered national and local events, including live coverage of the confirmation hearings for U.S. Supreme Court Justice Samuel Alito and Chief Justice John G. Roberts, the retirement of Justice Sandra Day O'Connor, the death of Chief Justice William Rehnquist, and the 2004 presidential election.", "CNN president Jonathan Klein later said he regretted not hiring Kelly as a reporter at the beginning of her career, as she was \"the one talent you'd want to have from somewhere else\".", "In 2004, Kelly applied for a job at Fox News.", "She contributed legal segments for \"Special Report with Brit Hume\" and hosted her own legal segment, \"Kelly's Court\", during \"Weekend Live\".", "She appeared in a weekly segment on \"The O'Reilly Factor\" and occasionally filled in for Greta Van Susteren on \"On the Record\", where most of her reporting focused on legal and political matters.", "She occasionally contributed as an anchor, but more often as a substitute anchor on weekends.", "On February 1, 2010, Kelly began hosting her own two-hour afternoon show, \"America Live\", which replaced \"The Live Desk\".", "She was a guest panelist on Fox News' late-night satire program \"Red Eye w/ Greg Gutfeld\".", "In 2010, viewership for \"America Live\" increased by 20%, averaging 1,293,000 viewers, and increased by 4% in the 25–54 age demographic, averaging 268,000 viewers.", "In December 2010, Kelly hosted a New Year's Eve special with Bill Hemmer.", "Kelly received media attention for her coverage of the results of the 2012 United States presidential election.", "On November 6, 2012 (the night of the election), Fox News' decision desk projected that Obama would win the state of Ohio along with a second term after part of the results had been released.", "In response to Karl Rove's opposition to this projection, Kelly walked backstage to the decision desk on camera and spoke with them; she also asked Rove, \"Is this just math that you do as a Republican to make yourself feel better?", "Or is this real?\"\nKelly left \"America Live\" in July 2013 and took maternity leave.", "On October 7, 2013, she began hosting a new nightly program, \"The Kelly File\".", "\"The Kelly File\" was occasionally the channel's ratings leader, topping \"The O'Reilly Factor\".", "In December 2013, Kelly commented on a \"Slate\" article on \"The Kelly File:\" \"For all you kids watching at home, Santa just is white, but this person is just arguing that maybe we should also have a black Santa,\" adding, \"But Santa is what he is, and just so you know, we're just debating this because someone wrote about it.\"", "Kelly also said that Jesus was a white man later in the segment.", "Soon after, Jon Stewart, Stephen Colbert, Rachel Maddow, Josh Barro, and others satirized her remarks.", "Two days later, she said on the air that her original comments were \"tongue-in-cheek\", and that the skin color of Jesus is \"far from settled\".", "In June 2015, Kelly interviewed Jim Bob Duggar and Michelle Duggar of \"19 Kids and Counting\" regarding their son Josh Duggar's alleged molestation of five girls in 2002.", "She later interviewed two of their daughters, Jill and Jessa.", "This show's Nielsen national estimates ratings of 3.09 million viewers, above its average 2.11 million, ranked with the 3.2 million for the Malaysia Airlines Flight 17 shootdown coverage and 7.3 million for the Ferguson riots coverage.", "In the Republican Party presidential debate on August 6, 2015, Kelly asked then-presidential candidate Donald Trump whether a man of his temperament ought to be elected president, noting that he has called various women insulting names in the past.", "Kelly's moderating generated a range of media and political reactions and her professionalism was criticized by Trump.", "Kelly responded to Trump's criticism by saying she would not \"apologize for doing good journalism\".", "Trump declined to attend the Iowa January 28 debate that she moderated.", "After the debate and off-camera, Ted Cruz said that Kelly had referred to Trump off-camera as \"Voldemort\", though Fox News denied it.", "Bill Maher complimented Kelly as being \"so much better\" than the candidates who attended the January 28 debate and argued that she was a more viable candidate for the Republican nomination.", "In an interview with CBS News Sunday Morning, Kelly reflected that she was disappointed with the lack of support she received from coworker Bill O'Reilly and CNN, the latter airing a Trump event the same time as the debate.", "In April, at her request, Kelly met with Trump at Trump Tower, having \"a chance to clear the air\".", "The following month, after interviewing Trump and being met with mixed reception, she expressed interest in doing another one with him.", "In June, she criticized Trump for his claims against Gonzalo P. Curiel's impartiality.", "In October, a contentious discussion between Kelly and Newt Gingrich on \"The Kelly File\" regarding Trump's sexual comments in a 2005 audio recording gained widespread social media reaction.", "In March 2016, it was announced that Kelly would host a one-hour prime time special on the Fox network wherein she would interview celebrities from the worlds of \"politics, entertainment, and other areas of human interest\".", "The special aired in May 2016, which was a sweeps month.", "It acquired 4.8 million viewers, but placed third in the ratings.", "Gabriel Sherman wrote of the stakes for Kelly as \"high\", elaborating that with Kelly being in the final year of her contract with Fox and having confirmed her ambitions, \"[t]he special was essentially a public interview for her next job.\"", "In July 2016, amid allegations of sexual harassment on the part of Fox News CEO Roger Ailes, Kelly was reported to have confirmed that she herself was also subjected to his harassment.", "Two days after the report, Ailes resigned from Fox News and his lawyer, Susan Estrich, publicly denied the charge.", "During her coverage of the 2016 Republican National Convention, her attire received criticism.", "In a defense of Kelly, Jenavieve Hatch of \"The Huffington Post\" commented, \"If you're a woman on national television reporting on a political event from hot, humid Cleveland, wearing a weather-appropriate outfit makes you the target of an endless stream of sexist commentary.\"", "In September, it was reported that Kelly would be collaborating with Michael De Luca to produce \"Embeds\", a scripted comedy about reporters covering politics, to be aired on a streaming service.", "Kelly appeared on the cover of the February 2016 issue of \"Vanity Fair\".", "In 2016, she was an honoree for \"Variety\"s \"Power of Women\" for her addressing child abuse.", "In late 2016, Kelly was alleged to be actively considering other news networks aside from Fox News, since her contract was a few months from expiring.", "In January 2017, \"The New York Times\" reported that she would leave Fox News for a \"triple role\" at NBC News, which would include a daytime talk show, a Sunday-night newsmagazine, and becoming a correspondent for major news events and political coverage.", "She departed Fox News on January 6, 2017, after the last episode of \"The Kelly File\" was aired.", "In January 2017, \"People\" quoted an unspecified source that Kelly remained under a non-compete clause with Fox until July 2017 which would prevent her from working for a competitor until the clause expires or is canceled.", "On June 2, 2017, Kelly interviewed Russian president Vladimir Putin, first in a panel discussion she moderated at the St. Petersburg International Economic Forum and later in a one-on-one interview for the premiere episode of NBC's \"Sunday Night with Megyn Kelly\", which aired June 4, 2017.", "Kelly's daytime talk show, \"Megyn Kelly Today\", premiered in September 2017.", "Kelly was being paid reportedly between $15 million and $20 million a year at NBC.", "After an initial run of eight episodes in the summer of 2017, NBC decided to bring her newsmagazine show \"Sunday Night with Megyn Kelly\" back for summer 2018 after a hiatus for football and the Winter Olympics, but only periodically.", "However, this return never materialized.", "Instead, Kelly continued to report stories for \"Dateline NBC\" during the summer of 2018, continuing her work for the show which she joined in 2017.", "On October 23, 2018, Kelly was criticized for on-air remarks she made on \"Megyn Kelly Today\" related to the appropriateness of blackface as part of Halloween costumes.", "She recollected that \"when I was a kid, that was okay as long as you were dressing up like a character\", and defended Luann de Lesseps's use of skin darkening spray to portray Diana Ross.", "After receiving backlash for her comments, Kelly issued an internal email apologizing for the remarks later that day.", "On October 26, 2018, NBC canceled \"Megyn Kelly Today\".", "It had been reported that Kelly was considering ending the program to focus on her role as a correspondent.", "Her contract was terminated January 11, 2019, with Kelly due the entire amount from the contract.", "She was reportedly not subject to any non-compete clause under her NBC contract.", "Kelly announced the launch of Devil May Care Media, her media production company, on September 10, 2020, with a podcast, \"The Megyn Kelly Show\".", "Its first episode premiered on September 28.", "On July 6, 2021, it was announced that the podcast would move to Sirius XM on September 7, 2021, to broadcast weekdays at 12 noon ET on the talk radio channel Triumph, along with a video simulcast available to Sirius XM subscribers.", "In February 2016, Kelly signed an agreement with HarperCollins to write an autobiography scheduled for release later that year, in a deal worth more than $10 million.", "The book, titled \"Settle for More\", was released on November 15, 2016.", "\"Bombshell\", a 2019 film portraying Kelly's career at Fox News, was released on December 13, 2019.", "Kelly is played by Charlize Theron, with other cast members including Margot Robbie as Kayla Pospisil (a composite character), Nicole Kidman as Gretchen Carlson, Nazanin Boniadi as Rudi Bakhtiar and John Lithgow as Roger Ailes.", "The film follows events at Fox News in the lead up to Ailes resigning from the organization.", "Kelly said she was not consulted for the film's content.", "Kelly married Daniel Kendall, an anesthesiologist, in 2001.", "The marriage ended in divorce in 2006.", "In 2008, she married Douglas Brunt, who was then president and CEO of the cybersecurity firm Authentium, and who became a full-time writer and novelist.", "They have three children, son Yates (b. 2009), daughter Yardley (b. 2011), and son Thatcher (b. 2013).", "Politically, Kelly identifies as an independent, and told \"Variety\" in 2015 that she had voted for both Democrats and Republicans.", "On October 12, 2016, Kelly stated in a segment on her show with Fox News commentator Julie Roginsky that she is a lifelong Catholic.", "Kelly has appeared at a fundraiser for parental rights organization Moms for Liberty." ]

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[ "During her time at Fox News, Kelly hosted \"America Live\" and, before that, co-hosted \"America's Newsroom\" with Bill Hemmer.", "From 2007 to 2012, the two reporters hosted Fox News Channel's New Year's Eve specials.", "Kelly also hosted \"The Kelly File\" from October 2013 to January 2017.", "The show was cancelled in October 2018 after a segment discussing blackface, and she left the network in January 2019." ]

[ "Kelly was born in Champaign, Illinois, to Edward Kelly (1940–1985), who taught at the State University of New York at Albany, and Linda (\"née\" DeMaio), a homemaker.", "She is of Italian and German descent on her mother's side and Irish descent on her father's.", "She was raised Catholic.", "Her father died of a heart attack when she was 15 years old.", "Kelly attended Tecumseh Elementary School in suburban Syracuse, New York.", "When she was 9, her family moved to Delmar, New York, a suburb of Albany, where she attended Bethlehem Central High School.", "She obtained an undergraduate degree in political science from the Maxwell School of Citizenship and Public Affairs at Syracuse University in 1992 and earned a J.D. from Albany Law School in 1995.", "Kelly was an associate attorney in the Chicago office of law firm Bickel & Brewer LLP.", "In fall 1996, she co-wrote an article, \"Litigation\", \"The Conflicting Roles of Lawyer as Director\", for the American Bar Association's journal.", "She later worked at Jones Day for nine years, where one of her clients was the credit bureau Experian.", "In 2003, Kelly moved to Washington, D.C., where she was hired by the ABC affiliate WJLA-TV as a general assignment reporter.", "She covered national and local events, including live coverage of the confirmation hearings for U.S. Supreme Court Justice Samuel Alito and Chief Justice John G. Roberts, the retirement of Justice Sandra Day O'Connor, the death of Chief Justice William Rehnquist, and the 2004 presidential election.", "CNN president Jonathan Klein later said he regretted not hiring Kelly as a reporter at the beginning of her career, as she was \"the one talent you'd want to have from somewhere else\".", "In 2004, Kelly applied for a job at Fox News.", "She contributed legal segments for \"Special Report with Brit Hume\" and hosted her own legal segment, \"Kelly's Court\", during \"Weekend Live\".", "She appeared in a weekly segment on \"The O'Reilly Factor\" and occasionally filled in for Greta Van Susteren on \"On the Record\", where most of her reporting focused on legal and political matters.", "She occasionally contributed as an anchor, but more often as a substitute anchor on weekends.", "On February 1, 2010, Kelly began hosting her own two-hour afternoon show, \"America Live\", which replaced \"The Live Desk\".", "She was a guest panelist on Fox News' late-night satire program \"Red Eye w/ Greg Gutfeld\".", "In 2010, viewership for \"America Live\" increased by 20%, averaging 1,293,000 viewers, and increased by 4% in the 25–54 age demographic, averaging 268,000 viewers.", "In December 2010, Kelly hosted a New Year's Eve special with Bill Hemmer.", "Kelly received media attention for her coverage of the results of the 2012 United States presidential election.", "On November 6, 2012 (the night of the election), Fox News' decision desk projected that Obama would win the state of Ohio along with a second term after part of the results had been released.", "In response to Karl Rove's opposition to this projection, Kelly walked backstage to the decision desk on camera and spoke with them; she also asked Rove, \"Is this just math that you do as a Republican to make yourself feel better?", "Or is this real?\"\nKelly left \"America Live\" in July 2013 and took maternity leave.", "On October 7, 2013, she began hosting a new nightly program, \"The Kelly File\".", "\"The Kelly File\" was occasionally the channel's ratings leader, topping \"The O'Reilly Factor\".", "In December 2013, Kelly commented on a \"Slate\" article on \"The Kelly File:\" \"For all you kids watching at home, Santa just is white, but this person is just arguing that maybe we should also have a black Santa,\" adding, \"But Santa is what he is, and just so you know, we're just debating this because someone wrote about it.\"", "Kelly also said that Jesus was a white man later in the segment.", "Soon after, Jon Stewart, Stephen Colbert, Rachel Maddow, Josh Barro, and others satirized her remarks.", "Two days later, she said on the air that her original comments were \"tongue-in-cheek\", and that the skin color of Jesus is \"far from settled\".", "In June 2015, Kelly interviewed Jim Bob Duggar and Michelle Duggar of \"19 Kids and Counting\" regarding their son Josh Duggar's alleged molestation of five girls in 2002.", "She later interviewed two of their daughters, Jill and Jessa.", "This show's Nielsen national estimates ratings of 3.09 million viewers, above its average 2.11 million, ranked with the 3.2 million for the Malaysia Airlines Flight 17 shootdown coverage and 7.3 million for the Ferguson riots coverage.", "In the Republican Party presidential debate on August 6, 2015, Kelly asked then-presidential candidate Donald Trump whether a man of his temperament ought to be elected president, noting that he has called various women insulting names in the past.", "Kelly's moderating generated a range of media and political reactions and her professionalism was criticized by Trump.", "Kelly responded to Trump's criticism by saying she would not \"apologize for doing good journalism\".", "Trump declined to attend the Iowa January 28 debate that she moderated.", "After the debate and off-camera, Ted Cruz said that Kelly had referred to Trump off-camera as \"Voldemort\", though Fox News denied it.", "Bill Maher complimented Kelly as being \"so much better\" than the candidates who attended the January 28 debate and argued that she was a more viable candidate for the Republican nomination.", "In an interview with CBS News Sunday Morning, Kelly reflected that she was disappointed with the lack of support she received from coworker Bill O'Reilly and CNN, the latter airing a Trump event the same time as the debate.", "In April, at her request, Kelly met with Trump at Trump Tower, having \"a chance to clear the air\".", "The following month, after interviewing Trump and being met with mixed reception, she expressed interest in doing another one with him.", "In June, she criticized Trump for his claims against Gonzalo P. Curiel's impartiality.", "In October, a contentious discussion between Kelly and Newt Gingrich on \"The Kelly File\" regarding Trump's sexual comments in a 2005 audio recording gained widespread social media reaction.", "In March 2016, it was announced that Kelly would host a one-hour prime time special on the Fox network wherein she would interview celebrities from the worlds of \"politics, entertainment, and other areas of human interest\".", "The special aired in May 2016, which was a sweeps month.", "It acquired 4.8 million viewers, but placed third in the ratings.", "Gabriel Sherman wrote of the stakes for Kelly as \"high\", elaborating that with Kelly being in the final year of her contract with Fox and having confirmed her ambitions, \"[t]he special was essentially a public interview for her next job.\"", "In July 2016, amid allegations of sexual harassment on the part of Fox News CEO Roger Ailes, Kelly was reported to have confirmed that she herself was also subjected to his harassment.", "Two days after the report, Ailes resigned from Fox News and his lawyer, Susan Estrich, publicly denied the charge.", "During her coverage of the 2016 Republican National Convention, her attire received criticism.", "In a defense of Kelly, Jenavieve Hatch of \"The Huffington Post\" commented, \"If you're a woman on national television reporting on a political event from hot, humid Cleveland, wearing a weather-appropriate outfit makes you the target of an endless stream of sexist commentary.\"", "In September, it was reported that Kelly would be collaborating with Michael De Luca to produce \"Embeds\", a scripted comedy about reporters covering politics, to be aired on a streaming service.", "Kelly appeared on the cover of the February 2016 issue of \"Vanity Fair\".", "In 2016, she was an honoree for \"Variety\"s \"Power of Women\" for her addressing child abuse.", "In late 2016, Kelly was alleged to be actively considering other news networks aside from Fox News, since her contract was a few months from expiring.", "In January 2017, \"The New York Times\" reported that she would leave Fox News for a \"triple role\" at NBC News, which would include a daytime talk show, a Sunday-night newsmagazine, and becoming a correspondent for major news events and political coverage.", "She departed Fox News on January 6, 2017, after the last episode of \"The Kelly File\" was aired.", "In January 2017, \"People\" quoted an unspecified source that Kelly remained under a non-compete clause with Fox until July 2017 which would prevent her from working for a competitor until the clause expires or is canceled.", "On June 2, 2017, Kelly interviewed Russian president Vladimir Putin, first in a panel discussion she moderated at the St. Petersburg International Economic Forum and later in a one-on-one interview for the premiere episode of NBC's \"Sunday Night with Megyn Kelly\", which aired June 4, 2017.", "Kelly's daytime talk show, \"Megyn Kelly Today\", premiered in September 2017.", "Kelly was being paid reportedly between $15 million and $20 million a year at NBC.", "After an initial run of eight episodes in the summer of 2017, NBC decided to bring her newsmagazine show \"Sunday Night with Megyn Kelly\" back for summer 2018 after a hiatus for football and the Winter Olympics, but only periodically.", "However, this return never materialized.", "Instead, Kelly continued to report stories for \"Dateline NBC\" during the summer of 2018, continuing her work for the show which she joined in 2017.", "On October 23, 2018, Kelly was criticized for on-air remarks she made on \"Megyn Kelly Today\" related to the appropriateness of blackface as part of Halloween costumes.", "She recollected that \"when I was a kid, that was okay as long as you were dressing up like a character\", and defended Luann de Lesseps's use of skin darkening spray to portray Diana Ross.", "After receiving backlash for her comments, Kelly issued an internal email apologizing for the remarks later that day.", "On October 26, 2018, NBC canceled \"Megyn Kelly Today\".", "It had been reported that Kelly was considering ending the program to focus on her role as a correspondent.", "Her contract was terminated January 11, 2019, with Kelly due the entire amount from the contract.", "She was reportedly not subject to any non-compete clause under her NBC contract.", "Kelly announced the launch of Devil May Care Media, her media production company, on September 10, 2020, with a podcast, \"The Megyn Kelly Show\".", "Its first episode premiered on September 28.", "On July 6, 2021, it was announced that the podcast would move to Sirius XM on September 7, 2021, to broadcast weekdays at 12 noon ET on the talk radio channel Triumph, along with a video simulcast available to Sirius XM subscribers.", "In February 2016, Kelly signed an agreement with HarperCollins to write an autobiography scheduled for release later that year, in a deal worth more than $10 million.", "The book, titled \"Settle for More\", was released on November 15, 2016.", "\"Bombshell\", a 2019 film portraying Kelly's career at Fox News, was released on December 13, 2019.", "Kelly is played by Charlize Theron, with other cast members including Margot Robbie as Kayla Pospisil (a composite character), Nicole Kidman as Gretchen Carlson, Nazanin Boniadi as Rudi Bakhtiar and John Lithgow as Roger Ailes.", "The film follows events at Fox News in the lead up to Ailes resigning from the organization.", "Kelly said she was not consulted for the film's content.", "Kelly married Daniel Kendall, an anesthesiologist, in 2001.", "The marriage ended in divorce in 2006.", "In 2008, she married Douglas Brunt, who was then president and CEO of the cybersecurity firm Authentium, and who became a full-time writer and novelist.", "They have three children, son Yates (b. 2009), daughter Yardley (b. 2011), and son Thatcher (b. 2013).", "Politically, Kelly identifies as an independent, and told \"Variety\" in 2015 that she had voted for both Democrats and Republicans.", "On October 12, 2016, Kelly stated in a segment on her show with Fox News commentator Julie Roginsky that she is a lifelong Catholic.", "Kelly has appeared at a fundraiser for parental rights organization Moms for Liberty." ]

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[ "She was a talk show host at Fox News from 2004 to 2017 and a host and correspondent with NBC News from 2017 to 2018.", "Kelly left Fox News in January 2017 and joined NBC News.", "The show was cancelled in October 2018 after a segment discussing blackface, and she left the network in January 2019." ]

[ "The word comes from the Greek σαρκασμός (\"sarkasmós\") which is taken from σαρκάζειν (\"sarkázein\") meaning \"to tear flesh, bite the lip in rage, sneer\".", "It is first recorded in English in 1579, in an annotation to \"The Shepheardes Calender\" by Edmund Spenser:\nHowever, the word \"sarcastic\", meaning \"Characterized by or involving sarcasm; given to the use of sarcasm; bitterly cutting or caustic\", doesn't appear until 1695.", "In its entry on irony, Dictionary.com describes sarcasm thus:\nIn sarcasm, ridicule or mockery is used harshly, often crudely and contemptuously, for destructive purposes.", "It may be used in an indirect manner, and have the form of irony, as in \"What a fine musician you turned out to be!,\" \"It's like you're a whole different person now...,\" and \"Oh...", "Well then thanks for all the first aid over the years!\"", "or it may be used in the form of a direct statement, \"You couldn't play one piece correctly if you had two assistants.\"", "The distinctive quality of sarcasm is present in the spoken word and manifested chiefly by vocal inflection ...\nDistinguishing sarcasm from banter, and referring to the use of irony in sarcasm, Derek Bousfield writes that sarcasm is: The use of strategies which, \"on the surface\" appear to be appropriate to the situation, but are meant to be taken as meaning the opposite in terms of \"face management\".", "That is, the utterance which appears, on the surface, to maintain or enhance the face of the recipient actually attacks and damages the face of the recipient.", "... \"sarcasm\" is an insincere form of politeness which is used to offend one's interlocutor.", "17.'Never a truer word said in jest':", "A Pragmastylistic Analysis of Impoliteness as Banter in Henry IV, Part I, Derek Bousfield (University of Huddersfield, UK)\nJohn Haiman writes: \"There is an extremely close connection between sarcasm and irony, and literary theorists in particular often treat sarcasm as simply the crudest and least interesting form of irony.\"", "Also, he adds:\nFirst, situations may be ironic, but only people can be sarcastic.", "Second, people may be unintentionally ironic, but sarcasm requires intention.", "What is essential to sarcasm is that it is overt irony intentionally used by the speaker as a form of verbal aggression.", "While Henry Watson Fowler writes:\nSarcasm does not necessarily involve irony.", "But irony, or the use of expressions conveying different things according as they are interpreted, is so often made the vehicle of sarcasm ...", "The essence of sarcasm is the intention of giving pain by (ironical or other) bitter words.", "Sarcasm can be making uncertainty seem very certain, in fact, already done and that it was easy to determine.", "Professionals in psychology and related fields have long looked upon sarcasm negatively, particularly noting that sarcasm tends to be a maladaptive coping mechanism for those with unresolved anger or frustrations.", "Psychologist Clifford N. Lazarus describes sarcasm as \"hostility disguised as humor\".", "While an occasional sarcastic comment may enliven a conversation, Lazarus suggests that too frequent use of sarcasm tends to \"overwhelm the emotional flavor of any conversation\".", "Understanding the subtlety of this usage requires second-order interpretation of the speaker's or writer's intentions; different parts of the brain must work together to understand sarcasm.", "This sophisticated understanding can be lacking in some people with certain forms of brain damage, dementia and sometimes autism, and this perception has been located by MRI in the right parahippocampal gyrus.", "Research has shown that people with damage in the prefrontal cortex have difficulty understanding non-verbal aspects of language like tone, Richard Delmonico, a neuropsychologist at the University of California, Davis, told an interviewer.", "Such research could help doctors distinguish between different types of neurodegenerative diseases, such as frontotemporal dementia and Alzheimer's disease, according to David Salmon, a neuroscientist at the University of California, San Diego.", "In William Brant's \"Critique of Sarcastic Reason\", sarcasm is hypothesized to develop as a cognitive and emotional tool that adolescents use in order to test the borders of politeness and truth in conversation.", "Sarcasm recognition and expression both require the development of understanding forms of language, especially if sarcasm occurs without a cue or signal (e.g., a sarcastic tone or rolling the eyes).", "Sarcasm is argued to be more sophisticated than lying because lying is expressed as early as the age of three, but sarcastic expressions take place much later during development (Brant, 2012).", "According to Brant (2012, 145–6), sarcasm is\nCultural perspectives on sarcasm vary widely with more than a few cultures and linguistic groups finding it offensive to varying degrees.", "Thomas Carlyle despised it: \"Sarcasm I now see to be, in general, the language of the devil; for which reason I have long since as good as renounced it\".", "Fyodor Dostoevsky, on the other hand, recognized in it a cry of pain: Sarcasm, he said, was \"usually the last refuge of modest and chaste-souled people when the privacy of their soul is coarsely and intrusively invaded.\"", "RFC 1855, a collection of guidelines for Internet communications, includes a warning to be especially careful with it as it \"may not travel well.\"", "Another study of sarcasm over email verifies these claims.", "A professional translator has advised that international business executives \"should generally avoid sarcasm in intercultural business conversations and written communications\" because of the difficulties in translating sarcasm.", "A 2015 study by L. Huang, F. Gino and A.D. Galinsky of the Harvard Business School \"tests a novel theoretical model in which both the construction and interpretation of sarcasm lead to greater creativity because they activate abstract thinking.", "\"", "In English, sarcasm is often telegraphed with kinesic/prosodic cues by speaking more slowly and with a lower pitch.", "Similarly, Dutch uses a lowered pitch; sometimes to such an extent that the expression is reduced to a mere mumble.", "But other research shows that there are many ways that real speakers signal sarcastic intentions.", "One study found that in Cantonese, sarcasm is indicated by raising the fundamental frequency of one's voice.", "In Amharic, rising intonation is used to show sarcasm.", "Though in the English language there is no standard accepted method to denote irony or sarcasm in written conversation, several forms of punctuation have been proposed.", "Among the oldest and frequently attested are the percontation point—furthered by Henry Denham in the 1580s—and the irony mark—furthered by Alcanter de Brahm in the 19th century.", "Both of these marks were represented visually by a ⸮ backwards question mark (unicode U+2E2E).", "Each of these punctuation marks are primarily used to indicate that a sentence should be understood as ironic, but not necessarily designate sarcasm that is not ironic.", "By contrast, more recent proposals, such as the snark mark, or the use of a following tilde are specifically intended to denote sarcasm rather than irony.", "A bracketed exclamation point or question mark as well as scare quotes are also sometimes used to express irony or ironic sarcasm.", "In certain Ethiopic languages, sarcasm and unreal phrases are indicated at the end of a sentence with a sarcasm mark called temherte slaq, a character that looks like an inverted exclamation point ¡.", "The usage directly parallels John Wilkins' 1668 proposal to use the inverted exclamation point as an irony mark.", "A proposal by Asteraye Tsigie and Daniel Yacob in 1999 to include the \"temherte slaq\" in unicode was unsuccessful.", "While sarcasm (harsh ridicule or mockery) is often directly associated with verbal irony (meaning the opposite of what is said) and the two are frequently used together; sarcasm is not necessarily ironic by definition, and either element can be used without the other.", "Examples of sarcasm and irony used together:\n\"My you're early!\"", "(After one arrives extremely late).", "\"What a fine artist you've become!\"", "(When meaning to express displeasure).", "Example of sarcasm without irony: (frequently attributed to Winston Churchill)", "After an onlooker comments on one being drunk: \"My dear, tomorrow I will be sober, and you will still be ugly!\"\nExample of irony without sarcasm:\nAfter a popular teacher apologizes to the class for answering his phone in the other room: \"I don't know if we can forgive you!\"", "A French company has developed an analytics tool that claims to have up to 80% accuracy in identifying sarcastic comments posted online.", "In June 2014, the United States Secret Service requested bids for software that would identify sarcasm in tweets.", "The Buddhist monk Ṭhānissaro Bhikkhu has identified sarcasm as contrary to right speech, an aspect of the Noble Eightfold Path leading to the end of suffering.", "He opines that sarcasm is an unskillful and unwholesome method of humor, which he contrasts with an approach based on frankly highlighting the ironies inherent in life.", "In late August 2016, it was reported that North Korea banned sarcasm against the government.", "Reports claim that the government gave the warnings in mass meetings across the country." ]

[ 0, 1 ]

[ "Sarcasm is the caustic use of words, often in a humorous way, to mock someone or something." ]

[ "The word comes from the Greek σαρκασμός (\"sarkasmós\") which is taken from σαρκάζειν (\"sarkázein\") meaning \"to tear flesh, bite the lip in rage, sneer\".", "It is first recorded in English in 1579, in an annotation to \"The Shepheardes Calender\" by Edmund Spenser:\nHowever, the word \"sarcastic\", meaning \"Characterized by or involving sarcasm; given to the use of sarcasm; bitterly cutting or caustic\", doesn't appear until 1695.", "In its entry on irony, Dictionary.com describes sarcasm thus:\nIn sarcasm, ridicule or mockery is used harshly, often crudely and contemptuously, for destructive purposes.", "It may be used in an indirect manner, and have the form of irony, as in \"What a fine musician you turned out to be!,\" \"It's like you're a whole different person now...,\" and \"Oh...", "Well then thanks for all the first aid over the years!\"", "or it may be used in the form of a direct statement, \"You couldn't play one piece correctly if you had two assistants.\"", "The distinctive quality of sarcasm is present in the spoken word and manifested chiefly by vocal inflection ...\nDistinguishing sarcasm from banter, and referring to the use of irony in sarcasm, Derek Bousfield writes that sarcasm is: The use of strategies which, \"on the surface\" appear to be appropriate to the situation, but are meant to be taken as meaning the opposite in terms of \"face management\".", "That is, the utterance which appears, on the surface, to maintain or enhance the face of the recipient actually attacks and damages the face of the recipient.", "... \"sarcasm\" is an insincere form of politeness which is used to offend one's interlocutor.", "17.'Never a truer word said in jest':", "A Pragmastylistic Analysis of Impoliteness as Banter in Henry IV, Part I, Derek Bousfield (University of Huddersfield, UK)\nJohn Haiman writes: \"There is an extremely close connection between sarcasm and irony, and literary theorists in particular often treat sarcasm as simply the crudest and least interesting form of irony.\"", "Also, he adds:\nFirst, situations may be ironic, but only people can be sarcastic.", "Second, people may be unintentionally ironic, but sarcasm requires intention.", "What is essential to sarcasm is that it is overt irony intentionally used by the speaker as a form of verbal aggression.", "While Henry Watson Fowler writes:\nSarcasm does not necessarily involve irony.", "But irony, or the use of expressions conveying different things according as they are interpreted, is so often made the vehicle of sarcasm ...", "The essence of sarcasm is the intention of giving pain by (ironical or other) bitter words.", "Sarcasm can be making uncertainty seem very certain, in fact, already done and that it was easy to determine.", "Professionals in psychology and related fields have long looked upon sarcasm negatively, particularly noting that sarcasm tends to be a maladaptive coping mechanism for those with unresolved anger or frustrations.", "Psychologist Clifford N. Lazarus describes sarcasm as \"hostility disguised as humor\".", "While an occasional sarcastic comment may enliven a conversation, Lazarus suggests that too frequent use of sarcasm tends to \"overwhelm the emotional flavor of any conversation\".", "Understanding the subtlety of this usage requires second-order interpretation of the speaker's or writer's intentions; different parts of the brain must work together to understand sarcasm.", "This sophisticated understanding can be lacking in some people with certain forms of brain damage, dementia and sometimes autism, and this perception has been located by MRI in the right parahippocampal gyrus.", "Research has shown that people with damage in the prefrontal cortex have difficulty understanding non-verbal aspects of language like tone, Richard Delmonico, a neuropsychologist at the University of California, Davis, told an interviewer.", "Such research could help doctors distinguish between different types of neurodegenerative diseases, such as frontotemporal dementia and Alzheimer's disease, according to David Salmon, a neuroscientist at the University of California, San Diego.", "In William Brant's \"Critique of Sarcastic Reason\", sarcasm is hypothesized to develop as a cognitive and emotional tool that adolescents use in order to test the borders of politeness and truth in conversation.", "Sarcasm recognition and expression both require the development of understanding forms of language, especially if sarcasm occurs without a cue or signal (e.g., a sarcastic tone or rolling the eyes).", "Sarcasm is argued to be more sophisticated than lying because lying is expressed as early as the age of three, but sarcastic expressions take place much later during development (Brant, 2012).", "According to Brant (2012, 145–6), sarcasm is\nCultural perspectives on sarcasm vary widely with more than a few cultures and linguistic groups finding it offensive to varying degrees.", "Thomas Carlyle despised it: \"Sarcasm I now see to be, in general, the language of the devil; for which reason I have long since as good as renounced it\".", "Fyodor Dostoevsky, on the other hand, recognized in it a cry of pain: Sarcasm, he said, was \"usually the last refuge of modest and chaste-souled people when the privacy of their soul is coarsely and intrusively invaded.\"", "RFC 1855, a collection of guidelines for Internet communications, includes a warning to be especially careful with it as it \"may not travel well.\"", "Another study of sarcasm over email verifies these claims.", "A professional translator has advised that international business executives \"should generally avoid sarcasm in intercultural business conversations and written communications\" because of the difficulties in translating sarcasm.", "A 2015 study by L. Huang, F. Gino and A.D. Galinsky of the Harvard Business School \"tests a novel theoretical model in which both the construction and interpretation of sarcasm lead to greater creativity because they activate abstract thinking.", "\"", "In English, sarcasm is often telegraphed with kinesic/prosodic cues by speaking more slowly and with a lower pitch.", "Similarly, Dutch uses a lowered pitch; sometimes to such an extent that the expression is reduced to a mere mumble.", "But other research shows that there are many ways that real speakers signal sarcastic intentions.", "One study found that in Cantonese, sarcasm is indicated by raising the fundamental frequency of one's voice.", "In Amharic, rising intonation is used to show sarcasm.", "Though in the English language there is no standard accepted method to denote irony or sarcasm in written conversation, several forms of punctuation have been proposed.", "Among the oldest and frequently attested are the percontation point—furthered by Henry Denham in the 1580s—and the irony mark—furthered by Alcanter de Brahm in the 19th century.", "Both of these marks were represented visually by a ⸮ backwards question mark (unicode U+2E2E).", "Each of these punctuation marks are primarily used to indicate that a sentence should be understood as ironic, but not necessarily designate sarcasm that is not ironic.", "By contrast, more recent proposals, such as the snark mark, or the use of a following tilde are specifically intended to denote sarcasm rather than irony.", "A bracketed exclamation point or question mark as well as scare quotes are also sometimes used to express irony or ironic sarcasm.", "In certain Ethiopic languages, sarcasm and unreal phrases are indicated at the end of a sentence with a sarcasm mark called temherte slaq, a character that looks like an inverted exclamation point ¡.", "The usage directly parallels John Wilkins' 1668 proposal to use the inverted exclamation point as an irony mark.", "A proposal by Asteraye Tsigie and Daniel Yacob in 1999 to include the \"temherte slaq\" in unicode was unsuccessful.", "While sarcasm (harsh ridicule or mockery) is often directly associated with verbal irony (meaning the opposite of what is said) and the two are frequently used together; sarcasm is not necessarily ironic by definition, and either element can be used without the other.", "Examples of sarcasm and irony used together:\n\"My you're early!\"", "(After one arrives extremely late).", "\"What a fine artist you've become!\"", "(When meaning to express displeasure).", "Example of sarcasm without irony: (frequently attributed to Winston Churchill)", "After an onlooker comments on one being drunk: \"My dear, tomorrow I will be sober, and you will still be ugly!\"\nExample of irony without sarcasm:\nAfter a popular teacher apologizes to the class for answering his phone in the other room: \"I don't know if we can forgive you!\"", "A French company has developed an analytics tool that claims to have up to 80% accuracy in identifying sarcastic comments posted online.", "In June 2014, the United States Secret Service requested bids for software that would identify sarcasm in tweets.", "The Buddhist monk Ṭhānissaro Bhikkhu has identified sarcasm as contrary to right speech, an aspect of the Noble Eightfold Path leading to the end of suffering.", "He opines that sarcasm is an unskillful and unwholesome method of humor, which he contrasts with an approach based on frankly highlighting the ironies inherent in life.", "In late August 2016, it was reported that North Korea banned sarcasm against the government.", "Reports claim that the government gave the warnings in mass meetings across the country." ]

[ 41, 42, 43, 44, 45, 46, 47, 48, 49 ]

[ "Sarcasm may employ ambivalence, although it is not necessarily ironic." ]

[ "The codex is one of only two known purple minuscules (minuscule 1143 is the other), written with gold ink.", "It contains the text of the four Gospels on 405 purple parchment leaves (17.6 by 19.2 cm), with some lacunae (Matthew 20:18-26, 21:45-22:9, Luke 10:36-11:2, 18:25-37, 20:24-26, John 11:26-48, 13:2-23, 17:1-12).", "The text is written in one column per page, 17 lines per page.", "The text is divided according to the (\"chapters\"), whose number are given in the margin, and the (\"titles of chapters\") written at the top of the pages in silver uncials.", "There is also a division according to the Ammonian Sections.", "There are no references to the Eusebian Canons.", "It contains the Eusebian tables, which were added by later hand.", "Tables of the (\"tables of contents\") are placed before each of the four Gospels.", "It has the famous Jerusalem Colophon.", "The manuscript is similar to Beratinus 2 (Minuscule 1143).", "The Greek text of the codex has been considered a representative of the so-called Caesarean text-type.", "Aland placed it in Category III.", "In the Gospel of Mark, this manuscript is closely aligned to Codex Koridethi.", "According to Aland, the quality of the text is higher in the Gospel of Mark, however lower in Matthew and Luke.", "Minuscule 565 is considered a member of Family 1 in the Gospel of John.", "According to the Claremont Profile Method it represents the Alexandrian text in Luke 1 and Kx in Luke 10 and Luke 20.", "In it lacks , a reading supported by the manuscripts A B K M N S", "U Y Δ Θ Π Ψ Ω 047 0141 8 9 1192.", "The entire verse of is omitted, a reading supported by the manuscripts X \"f\"1 1009 1365 ℓ \"76\" ℓ \"253\" b vgmss syrs, pal arm geo Diatessaron.", "It lacks the Pericope Adulterae (John 7:53-8:1), with an explanatory note.", "The manuscript is dated by the INTF to the 9th century.", "The manuscript comes from the area of the Black Sea, in Pontus.", "In 1829 it was brought to Petersburg.", "The manuscript was examined and described by Eduard de Muralt, along with the codices 566, 568-572, 574, 575, and 1567.", "The text of Mark was edited in 1885 by Johannes Engebretsen Belsheim.", "The codex now is located at the Russian National Library (Gr. 53) at Saint Petersburg." ]

[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ]

[ "The manuscript is lacunose." ]

[ "A classic lava lamp contains a standard incandescent or halogen lamp which heats a tall (often tapered) glass bottle.", "A formula from a 1968 US patent consisted of water and a transparent, translucent, or opaque mix of mineral oil, paraffin wax, and carbon tetrachloride.p.", "2, line 30 The clear water or mineral oil can optionally be coloured with translucent dyes.", "Common wax has a density much lower than that of water and would float on top at any temperature.", "However, carbon tetrachloride is denser than water (also nonflammable and miscible with wax) and is added to the wax to make its density at room temperature slightly higher than that of the water.", "When heated, the wax mixture becomes less dense than the water, because it expands more than water when both are heated.p.", "1, lines 40 & 45 It also becomes fluid, causing blobs of it to ascend to the top of the lamp.", "There, they cool, increasing their density relative to that of the water, and descend.p.", "1, line 47 A metallic wire coil in the bottle's base breaks the cooled blobs' surface tension, allowing them to recombine.", "Since 1970, lava lamps made for the US market have not used carbon tetrachloride, whose use was banned that year due to toxicity.", "Haggerty, their current manufacturer, has stated that their current formulation is a trade secret.", "The underlying fluid mechanics phenomenon in lava lamps is a form of Rayleigh–Taylor instability.", "The bulb is normally 25 to 40 watts.", "It generally takes 45–60 minutes for the wax to warm up enough to form freely rising blobs, when operating the lamp at standard room temperature, and as long as 2 to 3 hours if the room is cooler.", "Once the wax is molten, the lamp should not be agitated, or the two fluids may emulsify, and the fluid surrounding the wax blobs will remain cloudy rather than clear.", "Some recombination will occur as part of the normal cycle of the wax in the container, but the only way to recombine all of the wax is to turn off the lamp and wait for a few hours.", "The wax then settles back to the bottom, forming one blob once again.", "Severe cases can require many heating-cooling cycles to clear.", "In 2015, a new design was introduced that uses ferrofluid in place of wax.", "British entrepreneur Edward Craven Walker had the idea for the lava lamp in 1963 after watching a homemade egg timer, made from a cocktail shaker filled with liquids, as it bubbled on a stovetop in a pub.", "He hired British inventor David George Smith to develop the device and the chemical formula it required.", "Smith is credited as the inventor on the original for a \"Display Device\" filed and assigned to Craven-Walker's company in 1965, and subsequently issued in 1968.", "Craven Walker's company, Crestworth, was based in Poole, Dorset, United Kingdom.", "He named the lamp \"Astro\" and had variations such as the \"Astro Mini\" and the \"Astro Coach\" lantern.", "In 1965, Adolph Wertheimer and Hy Spector were intrigued by Walker's product when they saw it at a German trade show.", "They bought the American rights and began the Lava Manufacturing Corporation in Chicago to sell what they called the Lava Lite Lamp.", "In the late 1970s, US rights were sold to Larry Haggerty, who created a subsidiary of his company, Haggerty Enterprises, called Lava World International, which produced American lava lamps for over 30 years.", "In 2003, American lava lamp maker Lava World International (formerly Lava-Simplex-Scribe Internationale) moved its production to China.", "In 2008, it was acquired by Talon Merchant Capital and its name was changed to Lava Lite LLC.", "As of 2016, lava lamps were being sold under Lifespan brands in North America.", "In 2018, the 'Lava Lamp' brand was acquired by toy and gift maker Schylling Inc. of North Andover, MA.", "who continue to hold the US trademark rights to both the shape and name of LAVA lamp.", "When the American rights were sold, Craven Walker retained the rights for the rest of the world, and took on two business partners in the late 1980s, Cressida Granger and David Mulley.", "They eventually took over the company and changed its name to Mathmos in 1992.", "Edward Craven Walker remained a consultant to them until his death in 2000.", "Mathmos continues to make Lava Lamps and related products.", "They have won two Queens Awards for Export, and the Best Multi-Media prize at the Design Week awards.", "Astro lava lamp was launched in 1963 and celebrated its 50th anniversary in 2013.", "Mathmos lava lamps are still made in the original factory in Poole, Dorset." ]

[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 ]

[ "It consists of a bolus of a special coloured wax mixture inside a glass vessel, the remainder of which contains clear or translucent liquid.", "The vessel is placed on a base containing an incandescent light bulb whose heat causes temporary reductions in the wax's density and the liquid's surface tension.", "The lamps are designed in a variety of styles and colours." ]

[ "A classic lava lamp contains a standard incandescent or halogen lamp which heats a tall (often tapered) glass bottle.", "A formula from a 1968 US patent consisted of water and a transparent, translucent, or opaque mix of mineral oil, paraffin wax, and carbon tetrachloride.p.", "2, line 30 The clear water or mineral oil can optionally be coloured with translucent dyes.", "Common wax has a density much lower than that of water and would float on top at any temperature.", "However, carbon tetrachloride is denser than water (also nonflammable and miscible with wax) and is added to the wax to make its density at room temperature slightly higher than that of the water.", "When heated, the wax mixture becomes less dense than the water, because it expands more than water when both are heated.p.", "1, lines 40 & 45 It also becomes fluid, causing blobs of it to ascend to the top of the lamp.", "There, they cool, increasing their density relative to that of the water, and descend.p.", "1, line 47 A metallic wire coil in the bottle's base breaks the cooled blobs' surface tension, allowing them to recombine.", "Since 1970, lava lamps made for the US market have not used carbon tetrachloride, whose use was banned that year due to toxicity.", "Haggerty, their current manufacturer, has stated that their current formulation is a trade secret.", "The underlying fluid mechanics phenomenon in lava lamps is a form of Rayleigh–Taylor instability.", "The bulb is normally 25 to 40 watts.", "It generally takes 45–60 minutes for the wax to warm up enough to form freely rising blobs, when operating the lamp at standard room temperature, and as long as 2 to 3 hours if the room is cooler.", "Once the wax is molten, the lamp should not be agitated, or the two fluids may emulsify, and the fluid surrounding the wax blobs will remain cloudy rather than clear.", "Some recombination will occur as part of the normal cycle of the wax in the container, but the only way to recombine all of the wax is to turn off the lamp and wait for a few hours.", "The wax then settles back to the bottom, forming one blob once again.", "Severe cases can require many heating-cooling cycles to clear.", "In 2015, a new design was introduced that uses ferrofluid in place of wax.", "British entrepreneur Edward Craven Walker had the idea for the lava lamp in 1963 after watching a homemade egg timer, made from a cocktail shaker filled with liquids, as it bubbled on a stovetop in a pub.", "He hired British inventor David George Smith to develop the device and the chemical formula it required.", "Smith is credited as the inventor on the original for a \"Display Device\" filed and assigned to Craven-Walker's company in 1965, and subsequently issued in 1968.", "Craven Walker's company, Crestworth, was based in Poole, Dorset, United Kingdom.", "He named the lamp \"Astro\" and had variations such as the \"Astro Mini\" and the \"Astro Coach\" lantern.", "In 1965, Adolph Wertheimer and Hy Spector were intrigued by Walker's product when they saw it at a German trade show.", "They bought the American rights and began the Lava Manufacturing Corporation in Chicago to sell what they called the Lava Lite Lamp.", "In the late 1970s, US rights were sold to Larry Haggerty, who created a subsidiary of his company, Haggerty Enterprises, called Lava World International, which produced American lava lamps for over 30 years.", "In 2003, American lava lamp maker Lava World International (formerly Lava-Simplex-Scribe Internationale) moved its production to China.", "In 2008, it was acquired by Talon Merchant Capital and its name was changed to Lava Lite LLC.", "As of 2016, lava lamps were being sold under Lifespan brands in North America.", "In 2018, the 'Lava Lamp' brand was acquired by toy and gift maker Schylling Inc. of North Andover, MA.", "who continue to hold the US trademark rights to both the shape and name of LAVA lamp.", "When the American rights were sold, Craven Walker retained the rights for the rest of the world, and took on two business partners in the late 1980s, Cressida Granger and David Mulley.", "They eventually took over the company and changed its name to Mathmos in 1992.", "Edward Craven Walker remained a consultant to them until his death in 2000.", "Mathmos continues to make Lava Lamps and related products.", "They have won two Queens Awards for Export, and the Best Multi-Media prize at the Design Week awards.", "Astro lava lamp was launched in 1963 and celebrated its 50th anniversary in 2013.", "Mathmos lava lamps are still made in the original factory in Poole, Dorset." ]

[ 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38 ]

[ "A lava lamp is a decorative lamp, invented in 1963 by British entrepreneur Edward Craven Walker, the founder of the lighting company Mathmos." ]

[ "A physical theory is a model of physical events.", "It is judged by the extent to which its predictions agree with empirical observations.", "The quality of a physical theory is also judged on its ability to make new predictions which can be verified by new observations.", "A physical theory differs from a mathematical theorem in that while both are based on some form of axioms, judgment of mathematical applicability is not based on agreement with any experimental results.", "A physical theory similarly differs from a mathematical theory, in the sense that the word \"theory\" has a different meaning in mathematical terms.", "A physical theory involves one or more relationships between various measurable quantities.", "Archimedes realized that a ship floats by displacing its mass of water, Pythagoras understood the relation between the length of a vibrating string and the musical tone it produces.", "Other examples include entropy as a measure of the uncertainty regarding the positions and motions of unseen particles and the quantum mechanical idea that (action and) energy are not continuously variable.", "Theoretical physics consists of several different approaches.", "In this regard, theoretical particle physics forms a good example.", "For instance: \"phenomenologists\" might employ (semi-) empirical formulas and heuristics to agree with experimental results, often without deep physical understanding.", "\"Modelers\" (also called \"model-builders\") often appear much like phenomenologists, but try to model speculative theories that have certain desirable features (rather than on experimental data), or apply the techniques of mathematical modeling to physics problems.", "Some attempt to create approximate theories, called \"effective theories\", because fully developed theories may be regarded as unsolvable or too complicated.", "Other theorists may try to unify, formalise, reinterpret or generalise extant theories, or create completely new ones altogether.", "Sometimes the vision provided by pure mathematical systems can provide clues to how a physical system might be modeled; e.g., the notion, due to Riemann and others, that space itself might be curved.", "Theoretical problems that need computational investigation are often the concern of computational physics.", "Theoretical advances may consist in setting aside old, incorrect paradigms (e.g., aether theory of light propagation, caloric theory of heat, burning consisting of evolving phlogiston, or astronomical bodies revolving around the Earth) or may be an alternative model that provides answers that are more accurate or that can be more widely applied.", "In the latter case, a correspondence principle will be required to recover the previously known result.", "Sometimes though, advances may proceed along different paths.", "For example, an essentially correct theory may need some conceptual or factual revisions; atomic theory, first postulated millennia ago (by several thinkers in Greece and India) and the two-fluid theory of electricity are two cases in this point.", "However, an exception to all the above is the wave–particle duality, a theory combining aspects of different, opposing models via the Bohr complementarity principle.", "Physical theories become accepted if they are able to make correct predictions and no (or few) incorrect ones.", "The theory should have, at least as a secondary objective, a certain economy and elegance (compare to mathematical beauty), a notion sometimes called \"Occam's razor\" after the 13th-century English philosopher William of Occam (or Ockham), in which the simpler of two theories that describe the same matter just as adequately is preferred (but conceptual simplicity may mean mathematical complexity).", "They are also more likely to be accepted if they connect a wide range of phenomena.", "Testing the consequences of a theory is part of the scientific method.", "Physical theories can be grouped into three categories: \"mainstream theories\", \"proposed theories\" and \"fringe theories\".", "Theoretical physics began at least 2,300 years ago, under the Pre-socratic philosophy, and continued by Plato and Aristotle, whose views held sway for a millennium.", "During the rise of medieval universities, the only acknowledged intellectual disciplines were the seven liberal arts of the \"Trivium\" like grammar, logic, and rhetoric and of the \"Quadrivium\" like arithmetic, geometry, music and astronomy.", "During the Middle Ages and Renaissance, the concept of experimental science, the counterpoint to theory, began with scholars such as Ibn al-Haytham and Francis Bacon.", "As the Scientific Revolution gathered pace, the concepts of matter, energy, space, time and causality slowly began to acquire the form we know today, and other sciences spun off from the rubric of natural philosophy.", "Thus began the modern era of theory with the Copernican paradigm shift in astronomy, soon followed by Johannes Kepler's expressions for planetary orbits, which summarized the meticulous observations of Tycho Brahe; the works of these men (alongside Galileo's) can perhaps be considered to constitute the Scientific Revolution.", "The great push toward the modern concept of explanation started with Galileo, one of the few physicists who was both a consummate theoretician and a great experimentalist.", "The analytic geometry and mechanics of Descartes were incorporated into the calculus and mechanics of Isaac Newton, another theoretician/experimentalist of the highest order, writing Principia Mathematica.", "In it contained a grand synthesis of the work of Copernicus, Galileo and Kepler; as well as Newton's theories of mechanics and gravitation, which held sway as worldviews until the early 20th century.", "Simultaneously, progress was also made in optics (in particular colour theory and the ancient science of geometrical optics), courtesy of Newton, Descartes and the Dutchmen Snell and Huygens.", "In the 18th and 19th centuries Joseph-Louis Lagrange, Leonhard Euler and William Rowan Hamilton would extend the theory of classical mechanics considerably.", "They picked up the interactive intertwining of mathematics and physics begun two millennia earlier by Pythagoras.", "Among the great conceptual achievements of the 19th and 20th centuries were the consolidation of the idea of energy (as well as its global conservation) by the inclusion of heat, electricity and magnetism, and then light.", "The laws of thermodynamics, and most importantly the introduction of the singular concept of entropy began to provide a macroscopic explanation for the properties of matter.", "Statistical mechanics (followed by statistical physics and Quantum statistical mechanics) emerged as an offshoot of thermodynamics late in the 19th century.", "Another important event in the 19th century was the discovery of electromagnetic theory, unifying the previously separate phenomena of electricity, magnetism and light.", "The pillars of modern physics, and perhaps the most revolutionary theories in the history of physics, have been relativity theory and quantum mechanics.", "Newtonian mechanics was subsumed under special relativity and Newton's gravity was given a kinematic explanation by general relativity.", "Quantum mechanics led to an understanding of blackbody radiation (which indeed, was an original motivation for the theory) and of anomalies in the specific heats of solids — and finally to an understanding of the internal structures of atoms and molecules.", "Quantum mechanics soon gave way to the formulation of quantum field theory (QFT), begun in the late 1920s.", "In the aftermath of World War 2, more progress brought much renewed interest in QFT, which had since the early efforts, stagnated.", "The same period also saw fresh attacks on the problems of superconductivity and phase transitions, as well as the first applications of QFT in the area of theoretical condensed matter.", "The 1960s and 70s saw the formulation of the Standard model of particle physics using QFT and progress in condensed matter physics (theoretical foundations of superconductivity and critical phenomena, among others), in parallel to the applications of relativity to problems in astronomy and cosmology respectively.", "All of these achievements depended on the theoretical physics as a moving force both to suggest experiments and to consolidate results — often by ingenious application of existing mathematics, or, as in the case of Descartes and Newton (with Leibniz), by inventing new mathematics.", "Fourier's studies of heat conduction led to a new branch of mathematics: infinite, orthogonal series.", "Modern theoretical physics attempts to unify theories and explain phenomena in further attempts to understand the Universe, from the cosmological to the elementary particle scale.", "Where experimentation cannot be done, theoretical physics still tries to advance through the use of mathematical models.", "Mainstream theories (sometimes referred to as \"central theories\") are the body of knowledge of both factual and scientific views and possess a usual scientific quality of the tests of repeatability, consistency with existing well-established science and experimentation.", "There do exist mainstream theories that are generally accepted theories based solely upon their effects explaining a wide variety of data, although the detection, explanation, and possible composition are subjects of debate.", "The proposed theories of physics are usually relatively new theories which deal with the study of physics which include scientific approaches, means for determining the validity of models and new types of reasoning used to arrive at the theory.", "However, some proposed theories include theories that have been around for decades and have eluded methods of discovery and testing.", "Proposed theories can include fringe theories in the process of becoming established (and, sometimes, gaining wider acceptance).", "Proposed theories usually have not been tested.", "In addition to the theories like those listed below, there are also different interpretations of quantum mechanics, which may or may not be considered different theories since it is debatable whether they yield different predictions for physical experiments, even in principle.", "Fringe theories include any new area of scientific endeavor in the process of becoming established and some proposed theories.", "It can include speculative sciences.", "This includes physics fields and physical theories presented in accordance with known evidence, and a body of associated predictions have been made according to that theory.", "Some fringe theories go on to become a widely accepted part of physics.", "Other fringe theories end up being disproven.", "Some fringe theories are a form of protoscience and others are a form of pseudoscience.", "The falsification of the original theory sometimes leads to reformulation of the theory.", "\"Thought\" experiments are situations created in one's mind, asking a question akin to \"suppose you are in this situation, assuming such is true, what would follow?\".", "They are usually created to investigate phenomena that are not readily experienced in every-day situations.", "Famous examples of such thought experiments are Schrödinger's cat, the EPR thought experiment, simple illustrations of time dilation, and so on.", "These usually lead to real experiments designed to verify that the conclusion (and therefore the assumptions) of the thought experiments are correct.", "The EPR thought experiment led to the Bell inequalities, which were then tested to various degrees of rigor, leading to the acceptance of the current formulation of quantum mechanics and probabilism as a working hypothesis." ]

[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25 ]

[ "Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena." ]

[ "A physical theory is a model of physical events.", "It is judged by the extent to which its predictions agree with empirical observations.", "The quality of a physical theory is also judged on its ability to make new predictions which can be verified by new observations.", "A physical theory differs from a mathematical theorem in that while both are based on some form of axioms, judgment of mathematical applicability is not based on agreement with any experimental results.", "A physical theory similarly differs from a mathematical theory, in the sense that the word \"theory\" has a different meaning in mathematical terms.", "A physical theory involves one or more relationships between various measurable quantities.", "Archimedes realized that a ship floats by displacing its mass of water, Pythagoras understood the relation between the length of a vibrating string and the musical tone it produces.", "Other examples include entropy as a measure of the uncertainty regarding the positions and motions of unseen particles and the quantum mechanical idea that (action and) energy are not continuously variable.", "Theoretical physics consists of several different approaches.", "In this regard, theoretical particle physics forms a good example.", "For instance: \"phenomenologists\" might employ (semi-) empirical formulas and heuristics to agree with experimental results, often without deep physical understanding.", "\"Modelers\" (also called \"model-builders\") often appear much like phenomenologists, but try to model speculative theories that have certain desirable features (rather than on experimental data), or apply the techniques of mathematical modeling to physics problems.", "Some attempt to create approximate theories, called \"effective theories\", because fully developed theories may be regarded as unsolvable or too complicated.", "Other theorists may try to unify, formalise, reinterpret or generalise extant theories, or create completely new ones altogether.", "Sometimes the vision provided by pure mathematical systems can provide clues to how a physical system might be modeled; e.g., the notion, due to Riemann and others, that space itself might be curved.", "Theoretical problems that need computational investigation are often the concern of computational physics.", "Theoretical advances may consist in setting aside old, incorrect paradigms (e.g., aether theory of light propagation, caloric theory of heat, burning consisting of evolving phlogiston, or astronomical bodies revolving around the Earth) or may be an alternative model that provides answers that are more accurate or that can be more widely applied.", "In the latter case, a correspondence principle will be required to recover the previously known result.", "Sometimes though, advances may proceed along different paths.", "For example, an essentially correct theory may need some conceptual or factual revisions; atomic theory, first postulated millennia ago (by several thinkers in Greece and India) and the two-fluid theory of electricity are two cases in this point.", "However, an exception to all the above is the wave–particle duality, a theory combining aspects of different, opposing models via the Bohr complementarity principle.", "Physical theories become accepted if they are able to make correct predictions and no (or few) incorrect ones.", "The theory should have, at least as a secondary objective, a certain economy and elegance (compare to mathematical beauty), a notion sometimes called \"Occam's razor\" after the 13th-century English philosopher William of Occam (or Ockham), in which the simpler of two theories that describe the same matter just as adequately is preferred (but conceptual simplicity may mean mathematical complexity).", "They are also more likely to be accepted if they connect a wide range of phenomena.", "Testing the consequences of a theory is part of the scientific method.", "Physical theories can be grouped into three categories: \"mainstream theories\", \"proposed theories\" and \"fringe theories\".", "Theoretical physics began at least 2,300 years ago, under the Pre-socratic philosophy, and continued by Plato and Aristotle, whose views held sway for a millennium.", "During the rise of medieval universities, the only acknowledged intellectual disciplines were the seven liberal arts of the \"Trivium\" like grammar, logic, and rhetoric and of the \"Quadrivium\" like arithmetic, geometry, music and astronomy.", "During the Middle Ages and Renaissance, the concept of experimental science, the counterpoint to theory, began with scholars such as Ibn al-Haytham and Francis Bacon.", "As the Scientific Revolution gathered pace, the concepts of matter, energy, space, time and causality slowly began to acquire the form we know today, and other sciences spun off from the rubric of natural philosophy.", "Thus began the modern era of theory with the Copernican paradigm shift in astronomy, soon followed by Johannes Kepler's expressions for planetary orbits, which summarized the meticulous observations of Tycho Brahe; the works of these men (alongside Galileo's) can perhaps be considered to constitute the Scientific Revolution.", "The great push toward the modern concept of explanation started with Galileo, one of the few physicists who was both a consummate theoretician and a great experimentalist.", "The analytic geometry and mechanics of Descartes were incorporated into the calculus and mechanics of Isaac Newton, another theoretician/experimentalist of the highest order, writing Principia Mathematica.", "In it contained a grand synthesis of the work of Copernicus, Galileo and Kepler; as well as Newton's theories of mechanics and gravitation, which held sway as worldviews until the early 20th century.", "Simultaneously, progress was also made in optics (in particular colour theory and the ancient science of geometrical optics), courtesy of Newton, Descartes and the Dutchmen Snell and Huygens.", "In the 18th and 19th centuries Joseph-Louis Lagrange, Leonhard Euler and William Rowan Hamilton would extend the theory of classical mechanics considerably.", "They picked up the interactive intertwining of mathematics and physics begun two millennia earlier by Pythagoras.", "Among the great conceptual achievements of the 19th and 20th centuries were the consolidation of the idea of energy (as well as its global conservation) by the inclusion of heat, electricity and magnetism, and then light.", "The laws of thermodynamics, and most importantly the introduction of the singular concept of entropy began to provide a macroscopic explanation for the properties of matter.", "Statistical mechanics (followed by statistical physics and Quantum statistical mechanics) emerged as an offshoot of thermodynamics late in the 19th century.", "Another important event in the 19th century was the discovery of electromagnetic theory, unifying the previously separate phenomena of electricity, magnetism and light.", "The pillars of modern physics, and perhaps the most revolutionary theories in the history of physics, have been relativity theory and quantum mechanics.", "Newtonian mechanics was subsumed under special relativity and Newton's gravity was given a kinematic explanation by general relativity.", "Quantum mechanics led to an understanding of blackbody radiation (which indeed, was an original motivation for the theory) and of anomalies in the specific heats of solids — and finally to an understanding of the internal structures of atoms and molecules.", "Quantum mechanics soon gave way to the formulation of quantum field theory (QFT), begun in the late 1920s.", "In the aftermath of World War 2, more progress brought much renewed interest in QFT, which had since the early efforts, stagnated.", "The same period also saw fresh attacks on the problems of superconductivity and phase transitions, as well as the first applications of QFT in the area of theoretical condensed matter.", "The 1960s and 70s saw the formulation of the Standard model of particle physics using QFT and progress in condensed matter physics (theoretical foundations of superconductivity and critical phenomena, among others), in parallel to the applications of relativity to problems in astronomy and cosmology respectively.", "All of these achievements depended on the theoretical physics as a moving force both to suggest experiments and to consolidate results — often by ingenious application of existing mathematics, or, as in the case of Descartes and Newton (with Leibniz), by inventing new mathematics.", "Fourier's studies of heat conduction led to a new branch of mathematics: infinite, orthogonal series.", "Modern theoretical physics attempts to unify theories and explain phenomena in further attempts to understand the Universe, from the cosmological to the elementary particle scale.", "Where experimentation cannot be done, theoretical physics still tries to advance through the use of mathematical models.", "Mainstream theories (sometimes referred to as \"central theories\") are the body of knowledge of both factual and scientific views and possess a usual scientific quality of the tests of repeatability, consistency with existing well-established science and experimentation.", "There do exist mainstream theories that are generally accepted theories based solely upon their effects explaining a wide variety of data, although the detection, explanation, and possible composition are subjects of debate.", "The proposed theories of physics are usually relatively new theories which deal with the study of physics which include scientific approaches, means for determining the validity of models and new types of reasoning used to arrive at the theory.", "However, some proposed theories include theories that have been around for decades and have eluded methods of discovery and testing.", "Proposed theories can include fringe theories in the process of becoming established (and, sometimes, gaining wider acceptance).", "Proposed theories usually have not been tested.", "In addition to the theories like those listed below, there are also different interpretations of quantum mechanics, which may or may not be considered different theories since it is debatable whether they yield different predictions for physical experiments, even in principle.", "Fringe theories include any new area of scientific endeavor in the process of becoming established and some proposed theories.", "It can include speculative sciences.", "This includes physics fields and physical theories presented in accordance with known evidence, and a body of associated predictions have been made according to that theory.", "Some fringe theories go on to become a widely accepted part of physics.", "Other fringe theories end up being disproven.", "Some fringe theories are a form of protoscience and others are a form of pseudoscience.", "The falsification of the original theory sometimes leads to reformulation of the theory.", "\"Thought\" experiments are situations created in one's mind, asking a question akin to \"suppose you are in this situation, assuming such is true, what would follow?\".", "They are usually created to investigate phenomena that are not readily experienced in every-day situations.", "Famous examples of such thought experiments are Schrödinger's cat, the EPR thought experiment, simple illustrations of time dilation, and so on.", "These usually lead to real experiments designed to verify that the conclusion (and therefore the assumptions) of the thought experiments are correct.", "The EPR thought experiment led to the Bell inequalities, which were then tested to various degrees of rigor, leading to the acceptance of the current formulation of quantum mechanics and probabilism as a working hypothesis." ]

[ 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51 ]

[ "Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena.", "The advancement of science generally depends on the interplay between experimental studies and theory.", "In some cases, theoretical physics adheres to standards of mathematical rigour while giving little weight to experiments and observations." ]

[ "By convention, the Heptarchy period lasted from the end of Roman rule in Britain in the 5th century, until most of the Anglo-Saxon kingdoms came under the overlordship of Egbert of Wessex in 829.", "This approximately 400-year period of European history is often referred to as the Early Middle Ages or, more controversially, as the Dark Ages.", "Although \"heptarchy\" suggests the existence of seven kingdoms, the term is just used as a label of convenience and does not imply the existence of a clear-cut or stable group of seven kingdoms.", "The number of kingdoms and sub-kingdoms fluctuated rapidly during this period as competing kings contended for supremacy.", "In the late 6th century, the king of Kent was a prominent lord in the south.", "In the 7th century, the rulers of Northumbria and Wessex were powerful.", "In the 8th century, Mercia achieved hegemony over the other surviving kingdoms, particularly with \"Offa the Great\".", "Yet, as late as the reigns of Eadwig and Edgar (955–75), it was still possible to speak of separate kingdoms within the English population.", "Alongside the seven kingdoms, a number of other political divisions also existed, such as the kingdoms (or sub-kingdoms) of: Bernicia and Deira within Northumbria; Lindsey in present-day Lincolnshire; the Hwicce in the southwest Midlands; the Magonsæte or Magonset, a sub-kingdom of Mercia in what is now Herefordshire; the Wihtwara, a Jutish kingdom on the Isle of Wight, originally as important as the Cantwara of Kent; the Middle Angles, a group of tribes based around modern Leicestershire, later conquered by the Mercians; the Hæstingas (around the town of Hastings in Sussex); and the Gewisse, a Saxon tribe in what is now southern Hampshire that later developed into the kingdom of Wessex.", "The decline of the Heptarchy and the eventual emergence of the kingdom of England was a drawn-out process, taking place over the course of the 9th to 10th centuries.", "Over the course of the 9th century, the Danish enclave at York expanded into the Danelaw, with about half of England under Danish rule.", "The English unification under Alfred the Great was a reaction to the threat by the common enemy.", "In 886, Alfred retook London, and the \"Anglo-Saxon Chronicle\" says that \"all of the English people (\"all Angelcyn\") not subject to the Danes submitted themselves to King Alfred.\"", "The unification of the kingdom of England was complete only in the 10th century, following the expulsion of Eric Bloodaxe as king of Northumbria.", "Æthelstan was the first to be King of all England.", "The four main kingdoms in Anglo-Saxon England were:\n\n\nThe other main kingdoms, which were conquered by others entirely at some point in their history, before the unification of England, are:\n\nOther minor kingdoms and territories:", "Whilst heraldry did not exist in its modern form at the time, arms were attributed to the kingdoms of the Anglo-Saxon heptarchy from the 12th or 13th century onward.", "Some of these were based on existing description, for example with the attributed arms of Northumbria deriving from a description in the 8th century Historia Ecclesiastica Gentis Anglorum, which describes a flag flown over the tomb of King Oswald of Northumbria as \"made of gold and purple\", which eventually came to be gold and red.", "The Kingdom of Essex, for instance, was assigned a red shield with three notched swords (or \"seaxes\").", "This coat was used by the counties of Essex and Middlesex until 1910, when the Middlesex County Council applied for a formal grant from the College of Arms (\"The Times\", 1910).", "Middlesex was granted a red shield with three notched swords and a \"Saxon Crown\".", "Essex County Council was granted the arms without the crown in 1932.", "Similarly, the modern county of Kent uses the arms of the Kingdom of the same name, and the Mercian Cross of St Albans is still used in the arms of city of St Albans." ]

[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ]

[ "The Heptarchy is a collective name applied to the seven kingdoms of Anglo-Saxon England from the Anglo-Saxon settlement of Britain in the 5th century until the 8th century consolidation into the four kingdoms of Mercia, Northumbria, Wessex and East Anglia.", "The term 'Heptarchy' (from the Greek , ; from , : \"seven\"; , : \"reign, rule\" and the suffix , ) alludes to the tradition that there were seven Anglo-Saxon kingdoms, usually enumerated as: East Anglia, Essex, Kent, Mercia, Northumbria, Sussex, and Wessex." ]

[ "Planck's constant was formulated as part of Max Planck's successful effort to produce a mathematical expression that accurately predicted the observed spectral distribution of thermal radiation from a closed furnace (black-body radiation).", "This mathematical expression is now known as Planck's law.", "In the last years of the 19th century, Max Planck was investigating the problem of black-body radiation first posed by Kirchhoff some 40 years earlier.", "Every physical body spontaneously and continuously emits electromagnetic radiation.", "There was no expression or explanation for the overall shape of the observed emission spectrum.", "At the time, Wien's law fit the data for short wavelengths and high temperatures, but failed for long wavelengths.", "Also around this time, but unknown to Planck, Lord Rayleigh had derived theoretically a formula, now known as the Rayleigh–Jeans law, that could reasonably predict long wavelengths but failed dramatically at short wavelengths.", "Approaching this problem, Planck hypothesized that the equations of motion for light describe a set of harmonic oscillators, one for each possible frequency.", "He examined how the entropy of the oscillators varied with the temperature of the body, trying to match Wien's law, and was able to derive an approximate mathematical function for the black-body spectrum, which gave a simple empirical formula for long wavelengths.", "Planck tried to find a mathematical expression that could reproduce Wien's law (for short wavelengths) and the empirical formula (for long wavelengths).", "This expression included a constant, formula_3, which is thought to be for Hilfsgrösse (auxiliary variable), and subsequently became known as the Planck constant.", "The expression formulated by Planck showed that the spectral radiance of a body for frequency at absolute temperature is given by\nformula_4\nwhere formula_5 is the Boltzmann constant, formula_3 is the Planck constant, and formula_7 is the speed of light in the medium, whether material or vacuum.", "The spectral radiance of a body, formula_8, describes the amount of energy it emits at different radiation frequencies.", "It is the power emitted per unit area of the body, per unit solid angle of emission, per unit frequency.", "The spectral radiance can also be expressed per unit wavelength formula_9 instead of per unit frequency.", "In this case, it is given by\nformula_10\nshowing how radiated energy emitted at shorter wavelengths increases more rapidly with temperature than energy emitted at longer wavelengths.", "Planck's law may also be expressed in other terms, such as the number of photons emitted at a certain wavelength, or the energy density in a volume of radiation.", "The SI units of formula_8 are , while those of formula_12 are .", "Planck soon realized that his solution was not unique.", "There were several different solutions, each of which gave a different value for the entropy of the oscillators.", "To save his theory, Planck resorted to using the then-controversial theory of statistical mechanics, which he described as \"an act of despair …", "I was ready to sacrifice any of my previous convictions about physics.\"", "One of his new boundary conditions was\nWith this new condition, Planck had imposed the quantization of the energy of the oscillators, \"a purely formal assumption …", "actually I did not think much about it ...\" in his own words, but one that would revolutionize physics.", "Applying this new approach to Wien's displacement law showed that the \"energy element\" must be proportional to the frequency of the oscillator, the first version of what is now sometimes termed the \"Planck–Einstein relation\":\nformula_13\nPlanck was able to calculate the value of formula_1 from experimental data on black-body radiation: his result, , is within 1.2% of the currently accepted value.", "He also made the first determination of the Boltzmann constant formula_5 from the same data and theory.", "The black-body problem was revisited in 1905, when Lord Rayleigh and James Jeans (on the one hand) and Albert Einstein (on the other hand) independently proved that classical electromagnetism could \"never\" account for the observed spectrum.", "These proofs are commonly known as the \"ultraviolet catastrophe\", a name coined by Paul Ehrenfest in 1911.", "They contributed greatly (along with Einstein's work on the photoelectric effect) in convincing physicists that Planck's postulate of quantized energy levels was more than a mere mathematical formalism.", "The first Solvay Conference in 1911 was devoted to \"the theory of radiation and quanta\".", "The photoelectric effect is the emission of electrons (called \"photoelectrons\") from a surface when light is shone on it.", "It was first observed by Alexandre Edmond Becquerel in 1839, although credit is usually reserved for Heinrich Hertz, who published the first thorough investigation in 1887.", "Another particularly thorough investigation was published by Philipp Lenard (Lénárd Fülöp) in 1902.", "Einstein's 1905 paper discussing the effect in terms of light quanta would earn him the Nobel Prize in 1921, after his predictions had been confirmed by the experimental work of Robert Andrews Millikan.", "The Nobel committee awarded the prize for his work on the photo-electric effect, rather than relativity, both because of a bias against purely theoretical physics not grounded in discovery or experiment, and dissent amongst its members as to the actual proof that relativity was real.", "Before Einstein's paper, electromagnetic radiation such as visible light was considered to behave as a wave: hence the use of the terms \"frequency\" and \"wavelength\" to characterize different types of radiation.", "The energy transferred by a wave in a given time is called its intensity.", "The light from a theatre spotlight is more \"intense\" than the light from a domestic lightbulb; that is to say that the spotlight gives out more energy per unit time and per unit space (and hence consumes more electricity) than the ordinary bulb, even though the color of the light might be very similar.", "Other waves, such as sound or the waves crashing against a seafront, also have their intensity.", "However, the energy account of the photoelectric effect didn't seem to agree with the wave description of light.", "The \"photoelectrons\" emitted as a result of the photoelectric effect have a certain kinetic energy, which can be measured.", "This kinetic energy (for each photoelectron) is \"independent\" of the intensity of the light, but depends linearly on the frequency; and if the frequency is too low (corresponding to a photon energy that is less than the work function of the material), no photoelectrons are emitted at all, unless a plurality of photons, whose energetic sum is greater than the energy of the photoelectrons, acts virtually simultaneously (multiphoton effect).", "Assuming the frequency is high enough to cause the photoelectric effect, a rise in intensity of the light source causes more photoelectrons to be emitted with the same kinetic energy, rather than the same number of photoelectrons to be emitted with higher kinetic energy.", "Einstein's explanation for these observations was that light itself is quantized; that the energy of light is not transferred continuously as in a classical wave, but only in small \"packets\" or quanta.", "The size of these \"packets\" of energy, which would later be named photons, was to be the same as Planck's \"energy element\", giving the modern version of the Planck–Einstein relation:\nformula_16\nEinstein's postulate was later proven experimentally: the constant of proportionality between the frequency of incident light formula_17 and the kinetic energy of photoelectrons formula_18 was shown to be equal to the Planck constant formula_1.", "It was John William Nicholson in 1912 who introduced h-bar into the theory of the atom which was the first quantum and nuclear atom and the first to quantize angular momentum as \"h\"/2.", "Niels Bohr quoted him in his 1913 paper of the Bohr model of the atom.", "The influence of the work of Nicholson’s nuclear quantum atomic model on Bohr’s model has been written about by many historians.", "Niels Bohr introduced the third quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model.", "The first quantized model of the atom was introduced in 1910 by Arthur Erich Haas and much discussed at the 1911 Solvay conference.", "In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation.", "If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus.", "Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies formula_20\nformula_21\nwhere formula_22 is the speed of light in vacuum, formula_23 is an experimentally determined constant (the Rydberg constant) and formula_24.", "Once the electron reached the lowest energy level (formula_25), it could not get any closer to the nucleus (lower energy).", "This approach also allowed Bohr to account for the Rydberg formula, an empirical description of the atomic spectrum of hydrogen, and to account for the value of the Rydberg constant formula_23 in terms of other fundamental constants.", "Bohr also introduced the quantity formula_27, now known as the reduced Planck constant, as the quantum of angular momentum.", "At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model.", "The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum.", "In modern terms, if formula_28 is the total angular momentum of a system with rotational invariance, and formula_29 the angular momentum measured along any given direction, these quantities can only take on the values\nformula_30", "The Planck constant also occurs in statements of Werner Heisenberg's uncertainty principle.", "Given numerous particles prepared in the same state, the uncertainty in their position, formula_31, and the uncertainty in their momentum, formula_32, obey\nformula_33\nwhere the uncertainty is given as the standard deviation of the measured value from its expected value.", "There are several other such pairs of physically measurable conjugate variables which obey a similar rule.", "One example is time vs. energy.", "The inverse relationship between the uncertainty of the two conjugate variables forces a tradeoff in quantum experiments, as measuring one quantity more precisely results in the other quantity becoming imprecise.", "In addition to some assumptions underlying the interpretation of certain values in the quantum mechanical formulation, one of the fundamental cornerstones to the entire theory lies in the commutator relationship between the position operator formula_34 and the momentum operator formula_35:\nformula_36\nwhere formula_37 is the Kronecker delta.", "The Planck relation connects the particular photon energy with its associated wave frequency :\nformula_38\nThis energy is extremely small in terms of ordinarily perceived everyday objects.", "Since the frequency , wavelength , and speed of light are related by formula_39, the relation can also be expressed as\nformula_40", "In 1923, Louis de Broglie generalized the Planck–Einstein relation by postulating that the Planck constant represents the proportionality between the momentum and the quantum wavelength of not just the photon, but the quantum wavelength of any particle.", "This was confirmed by experiments soon afterward.", "This holds throughout the quantum theory, including electrodynamics.", "The de Broglie wavelength of the particle is given by\nformula_41\nwhere denotes the linear momentum of a particle, such as a photon, or any other elementary particle.", "The energy of a photon with angular frequency is given by\nformula_42\nwhile its linear momentum relates to\nformula_43\nwhere is an angular wavenumber.", "These two relations are the temporal and spatial parts of the special relativistic expression using 4-vectors.", "formula_44", "Classical statistical mechanics requires the existence of (but does not define its value).", "Eventually, following upon Planck's discovery, it was speculated that physical action could not take on an arbitrary value, but instead was restricted to integer multiples of a very small quantity, the \"[elementary] quantum of action\", now called the \"Planck constant\".", "This was a significant conceptual part of the so-called \"old quantum theory\" developed by physicists including Bohr, Sommerfeld, and Ishiwara, in which particle trajectories exist but are hidden, but quantum laws constrain them based on their action.", "This view has been replaced by fully modern quantum theory, in which definite trajectories of motion do not even exist; rather, the particle is represented by a wavefunction spread out in space and in time.", "Thus there is no value of the action as classically defined.", "Related to this is the concept of energy quantization which existed in old quantum theory and also exists in altered form in modern quantum physics.", "Classical physics cannot explain either quantization of energy or the lack of classical particle motion.", "In many cases, such as for monochromatic light or for atoms, quantization of energy also implies that only certain energy levels are allowed, and values in between are forbidden.", "Implicit in the dimensions of the Planck constant is the fact that the SI unit of frequency, the hertz, represents one complete cycle, 360 degrees or radians, per second.", "In applications where it is natural to use the angular frequency (i.e. where the frequency is expressed in terms of radians per second instead of cycles per second or hertz)", "it is often useful to absorb a factor of into the Planck constant.", "The resulting constant is called the reduced Planck constant.", "It is equal to the Planck constant divided by , and is denoted formula_45 (pronounced \"h-bar\"):\nformula_46", "The Planck constant has dimensions of angular momentum.", "In SI units, the Planck constant is expressed in joules per hertz (J⋅Hz or kg⋅m2⋅s−1).", "formula_47\nformula_48\nThe above values have been adopted as fixed in the 2019 redefinition of the SI base units.", "In the system of \"natural units\" used by theoretical physicists, formula_45, the reduced Planck constant, is defined to be exactly one.", "In these units, is then exactly formula_50", "Since 2019, the numerical value of the Planck constant has been fixed, with a finite decimal representation.", "Under the present definition of the kilogram, which states that \"The kilogram [...] is defined by taking the fixed numerical value of to be when expressed in the unit J⋅s, which is equal to kg⋅m2⋅s−1, where the metre and the second are defined in terms of speed of light and duration of hyperfine transition of the ground state of an unperturbed caesium-133 atom .\"", "This implies that mass metrology is now aimed to find the value of one kilogram, and thus it is kilogram which is \"compensating\".", "Every experiment aiming to measure the kilogram (such as the Kibble balance and the X-ray crystal density method), will essentially refine the value of a kilogram.", "As an illustration of this, suppose the decision of making to be exact was taken in 2010, when its measured value was , thus the present definition of kilogram was also enforced.", "In the future, the value of one kilogram must be refined to times the mass of the International Prototype of the Kilogram (IPK).", "The Planck constant is related to the quantization of light and matter.", "It can be seen as a subatomic-scale constant.", "In a unit system adapted to subatomic scales, the electronvolt is the appropriate unit of energy and the petahertz the appropriate unit of frequency.", "Atomic unit systems are based (in part) on the Planck constant.", "The physical meaning of the Planck constant could suggest some basic features of our physical world.", "The Planck constant is one of the smallest constants used in physics.", "This reflects the fact that on a scale adapted to humans, where energies are typical of the order of kilojoules and times are typical of the order of seconds or minutes, the Planck constant is very small.", "One can regard the Planck constant to be only relevant to the microscopic scale instead of the macroscopic scale in our everyday experience.", "Equivalently, the order of the Planck constant reflects the fact that everyday objects and systems are made of a \"large\" number of microscopic particles.", "For example, green light with a wavelength of 555 nanometres (a wavelength that can be perceived by the human eye to be green) has a frequency of ().", "Each photon has an energy .", "That is a very small amount of energy in terms of everyday experience, but everyday experience is not concerned with individual photons any more than with individual atoms or molecules.", "An amount of light more typical in everyday experience (though much larger than the smallest amount perceivable by the human eye) is the energy of one mole of photons; its energy can be computed by multiplying the photon energy by the Avogadro constant, , with the result of , about the food energy in three apples.", "In principle, the Planck constant can be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons, and this is how its value was first calculated in the early twentieth century.", "In practice, these are no longer the most accurate methods.", "Since the value of the Planck constant is fixed now, it is no longer determined or calculated in laboratories.", "Some of the practices given below to determine the Planck constant are now used to determine the mass of the kilogram.", "The below-given methods \"except\" the X-ray crystal density method rely on the theoretical basis of the Josephson effect and the quantum Hall effect.", "The Josephson constant \"K\"J relates the potential difference \"U\" generated by the Josephson effect at a \"Josephson junction\" with the frequency \"ν\" of the microwave radiation.", "The theoretical treatment of Josephson effect suggests very strongly that .", "formula_51\nThe Josephson constant may be measured by comparing the potential difference generated by an array of Josephson junctions with a potential difference which is known in SI volts.", "The measurement of the potential difference in SI units is done by allowing an electrostatic force to cancel out a measurable gravitational force, in a Kibble balance.", "Assuming the validity of the theoretical treatment of the Josephson effect, \"K\"J is related to the Planck constant by\nformula_52", "A Kibble balance (formerly known as a watt balance) is an instrument for comparing two powers, one of which is measured in SI watts and the other of which is measured in conventional electrical units.", "From the definition of the \"conventional\" watt \"W\"90, this gives a measure of the product \"K\"J2\"R\"K in SI units, where \"R\"K is the von Klitzing constant which appears in the quantum Hall effect.", "If the theoretical treatments of the Josephson effect and the quantum Hall effect are valid, and in particular assuming that , the measurement of \"K\"J2\"R\"K is a direct determination of the Planck constant.", "formula_53", "The gyromagnetic ratio \"γ\" is the constant of proportionality between the frequency \"ν\" of nuclear magnetic resonance (or electron paramagnetic resonance for electrons) and the applied magnetic field .", "It is difficult to measure gyromagnetic ratios precisely because of the difficulties in precisely measuring \"B\", but the value for protons in water at is known to better than one part per million.", "The protons are said to be \"shielded\" from the applied magnetic field by the electrons in the water molecule, the same effect that gives rise to chemical shift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, \"γ\"′p.", "The gyromagnetic ratio is related to the shielded proton magnetic moment \"μ\"′p, the spin number \"I\" ( for protons) and the reduced Planck constant.", "formula_54\nThe ratio of the shielded proton magnetic moment \"μ\"′p to the electron magnetic moment \"μ\"e can be measured separately and to high precision, as the imprecisely known value of the applied magnetic field cancels itself out in taking the ratio.", "The value of \"μ\"e in Bohr magnetons is also known: it is half the electron g-factor \"g\"e.", "Hence\nformula_55\nformula_56\nA further complication is that the measurement of \"γ\"′p involves the measurement of an electric current: this is invariably measured in \"conventional\" amperes rather than in SI amperes, so a conversion factor is required.", "The symbol \"Γ\"′p-90 is used for the measured gyromagnetic ratio using conventional electrical units.", "In addition, there are two methods of measuring the value, a \"low-field\" method and a \"high-field\" method, and the conversion factors are different in the two cases.", "Only the high-field value \"Γ\"′p-90(hi) is of interest in determining the Planck constant.", "formula_57\nSubstitution gives the expression for the Planck constant in terms of \"Γ\"′p-90(hi):\nformula_58", "The Faraday constant \"F\" is the charge of one mole of electrons, equal to the Avogadro constant \"N\"A multiplied by the elementary charge \"e\".", "It can be determined by careful electrolysis experiments, measuring the amount of silver dissolved from an electrode in a given time and for a given electric current.", "Substituting the definitions of \"N\"A and \"e\" gives the relation to the Planck constant.", "formula_59", "The X-ray crystal density method is primarily a method for determining the Avogadro constant \"N\"A but as the Avogadro constant is related to the Planck constant it also determines a value for \"h\".", "The principle behind the method is to determine \"N\"A as the ratio between the volume of the unit cell of a crystal, measured by X-ray crystallography, and the molar volume of the substance.", "Crystals of silicon are used, as they are available in high quality and purity by the technology developed for the semiconductor industry.", "The unit cell volume is calculated from the spacing between two crystal planes referred to as \"d\"220.", "The molar volume \"V\"m(Si) requires a knowledge of the density of the crystal and the atomic weight of the silicon used.", "The Planck constant is given by\nformula_60", "The experimental measurement of the Planck constant in the Large Hadron Collider laboratory was carried out in 2011.", "The study called PCC using a giant particle accelerator helped to better understand the relationships between the Planck constant and measuring distances in space." ]

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[ "In 1900, Max Planck empirically derived a formula for the observed spectrum." ]

[ "Planck's constant was formulated as part of Max Planck's successful effort to produce a mathematical expression that accurately predicted the observed spectral distribution of thermal radiation from a closed furnace (black-body radiation).", "This mathematical expression is now known as Planck's law.", "In the last years of the 19th century, Max Planck was investigating the problem of black-body radiation first posed by Kirchhoff some 40 years earlier.", "Every physical body spontaneously and continuously emits electromagnetic radiation.", "There was no expression or explanation for the overall shape of the observed emission spectrum.", "At the time, Wien's law fit the data for short wavelengths and high temperatures, but failed for long wavelengths.", "Also around this time, but unknown to Planck, Lord Rayleigh had derived theoretically a formula, now known as the Rayleigh–Jeans law, that could reasonably predict long wavelengths but failed dramatically at short wavelengths.", "Approaching this problem, Planck hypothesized that the equations of motion for light describe a set of harmonic oscillators, one for each possible frequency.", "He examined how the entropy of the oscillators varied with the temperature of the body, trying to match Wien's law, and was able to derive an approximate mathematical function for the black-body spectrum, which gave a simple empirical formula for long wavelengths.", "Planck tried to find a mathematical expression that could reproduce Wien's law (for short wavelengths) and the empirical formula (for long wavelengths).", "This expression included a constant, formula_3, which is thought to be for Hilfsgrösse (auxiliary variable), and subsequently became known as the Planck constant.", "The expression formulated by Planck showed that the spectral radiance of a body for frequency at absolute temperature is given by\nformula_4\nwhere formula_5 is the Boltzmann constant, formula_3 is the Planck constant, and formula_7 is the speed of light in the medium, whether material or vacuum.", "The spectral radiance of a body, formula_8, describes the amount of energy it emits at different radiation frequencies.", "It is the power emitted per unit area of the body, per unit solid angle of emission, per unit frequency.", "The spectral radiance can also be expressed per unit wavelength formula_9 instead of per unit frequency.", "In this case, it is given by\nformula_10\nshowing how radiated energy emitted at shorter wavelengths increases more rapidly with temperature than energy emitted at longer wavelengths.", "Planck's law may also be expressed in other terms, such as the number of photons emitted at a certain wavelength, or the energy density in a volume of radiation.", "The SI units of formula_8 are , while those of formula_12 are .", "Planck soon realized that his solution was not unique.", "There were several different solutions, each of which gave a different value for the entropy of the oscillators.", "To save his theory, Planck resorted to using the then-controversial theory of statistical mechanics, which he described as \"an act of despair …", "I was ready to sacrifice any of my previous convictions about physics.\"", "One of his new boundary conditions was\nWith this new condition, Planck had imposed the quantization of the energy of the oscillators, \"a purely formal assumption …", "actually I did not think much about it ...\" in his own words, but one that would revolutionize physics.", "Applying this new approach to Wien's displacement law showed that the \"energy element\" must be proportional to the frequency of the oscillator, the first version of what is now sometimes termed the \"Planck–Einstein relation\":\nformula_13\nPlanck was able to calculate the value of formula_1 from experimental data on black-body radiation: his result, , is within 1.2% of the currently accepted value.", "He also made the first determination of the Boltzmann constant formula_5 from the same data and theory.", "The black-body problem was revisited in 1905, when Lord Rayleigh and James Jeans (on the one hand) and Albert Einstein (on the other hand) independently proved that classical electromagnetism could \"never\" account for the observed spectrum.", "These proofs are commonly known as the \"ultraviolet catastrophe\", a name coined by Paul Ehrenfest in 1911.", "They contributed greatly (along with Einstein's work on the photoelectric effect) in convincing physicists that Planck's postulate of quantized energy levels was more than a mere mathematical formalism.", "The first Solvay Conference in 1911 was devoted to \"the theory of radiation and quanta\".", "The photoelectric effect is the emission of electrons (called \"photoelectrons\") from a surface when light is shone on it.", "It was first observed by Alexandre Edmond Becquerel in 1839, although credit is usually reserved for Heinrich Hertz, who published the first thorough investigation in 1887.", "Another particularly thorough investigation was published by Philipp Lenard (Lénárd Fülöp) in 1902.", "Einstein's 1905 paper discussing the effect in terms of light quanta would earn him the Nobel Prize in 1921, after his predictions had been confirmed by the experimental work of Robert Andrews Millikan.", "The Nobel committee awarded the prize for his work on the photo-electric effect, rather than relativity, both because of a bias against purely theoretical physics not grounded in discovery or experiment, and dissent amongst its members as to the actual proof that relativity was real.", "Before Einstein's paper, electromagnetic radiation such as visible light was considered to behave as a wave: hence the use of the terms \"frequency\" and \"wavelength\" to characterize different types of radiation.", "The energy transferred by a wave in a given time is called its intensity.", "The light from a theatre spotlight is more \"intense\" than the light from a domestic lightbulb; that is to say that the spotlight gives out more energy per unit time and per unit space (and hence consumes more electricity) than the ordinary bulb, even though the color of the light might be very similar.", "Other waves, such as sound or the waves crashing against a seafront, also have their intensity.", "However, the energy account of the photoelectric effect didn't seem to agree with the wave description of light.", "The \"photoelectrons\" emitted as a result of the photoelectric effect have a certain kinetic energy, which can be measured.", "This kinetic energy (for each photoelectron) is \"independent\" of the intensity of the light, but depends linearly on the frequency; and if the frequency is too low (corresponding to a photon energy that is less than the work function of the material), no photoelectrons are emitted at all, unless a plurality of photons, whose energetic sum is greater than the energy of the photoelectrons, acts virtually simultaneously (multiphoton effect).", "Assuming the frequency is high enough to cause the photoelectric effect, a rise in intensity of the light source causes more photoelectrons to be emitted with the same kinetic energy, rather than the same number of photoelectrons to be emitted with higher kinetic energy.", "Einstein's explanation for these observations was that light itself is quantized; that the energy of light is not transferred continuously as in a classical wave, but only in small \"packets\" or quanta.", "The size of these \"packets\" of energy, which would later be named photons, was to be the same as Planck's \"energy element\", giving the modern version of the Planck–Einstein relation:\nformula_16\nEinstein's postulate was later proven experimentally: the constant of proportionality between the frequency of incident light formula_17 and the kinetic energy of photoelectrons formula_18 was shown to be equal to the Planck constant formula_1.", "It was John William Nicholson in 1912 who introduced h-bar into the theory of the atom which was the first quantum and nuclear atom and the first to quantize angular momentum as \"h\"/2.", "Niels Bohr quoted him in his 1913 paper of the Bohr model of the atom.", "The influence of the work of Nicholson’s nuclear quantum atomic model on Bohr’s model has been written about by many historians.", "Niels Bohr introduced the third quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model.", "The first quantized model of the atom was introduced in 1910 by Arthur Erich Haas and much discussed at the 1911 Solvay conference.", "In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation.", "If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus.", "Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies formula_20\nformula_21\nwhere formula_22 is the speed of light in vacuum, formula_23 is an experimentally determined constant (the Rydberg constant) and formula_24.", "Once the electron reached the lowest energy level (formula_25), it could not get any closer to the nucleus (lower energy).", "This approach also allowed Bohr to account for the Rydberg formula, an empirical description of the atomic spectrum of hydrogen, and to account for the value of the Rydberg constant formula_23 in terms of other fundamental constants.", "Bohr also introduced the quantity formula_27, now known as the reduced Planck constant, as the quantum of angular momentum.", "At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model.", "The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum.", "In modern terms, if formula_28 is the total angular momentum of a system with rotational invariance, and formula_29 the angular momentum measured along any given direction, these quantities can only take on the values\nformula_30", "The Planck constant also occurs in statements of Werner Heisenberg's uncertainty principle.", "Given numerous particles prepared in the same state, the uncertainty in their position, formula_31, and the uncertainty in their momentum, formula_32, obey\nformula_33\nwhere the uncertainty is given as the standard deviation of the measured value from its expected value.", "There are several other such pairs of physically measurable conjugate variables which obey a similar rule.", "One example is time vs. energy.", "The inverse relationship between the uncertainty of the two conjugate variables forces a tradeoff in quantum experiments, as measuring one quantity more precisely results in the other quantity becoming imprecise.", "In addition to some assumptions underlying the interpretation of certain values in the quantum mechanical formulation, one of the fundamental cornerstones to the entire theory lies in the commutator relationship between the position operator formula_34 and the momentum operator formula_35:\nformula_36\nwhere formula_37 is the Kronecker delta.", "The Planck relation connects the particular photon energy with its associated wave frequency :\nformula_38\nThis energy is extremely small in terms of ordinarily perceived everyday objects.", "Since the frequency , wavelength , and speed of light are related by formula_39, the relation can also be expressed as\nformula_40", "In 1923, Louis de Broglie generalized the Planck–Einstein relation by postulating that the Planck constant represents the proportionality between the momentum and the quantum wavelength of not just the photon, but the quantum wavelength of any particle.", "This was confirmed by experiments soon afterward.", "This holds throughout the quantum theory, including electrodynamics.", "The de Broglie wavelength of the particle is given by\nformula_41\nwhere denotes the linear momentum of a particle, such as a photon, or any other elementary particle.", "The energy of a photon with angular frequency is given by\nformula_42\nwhile its linear momentum relates to\nformula_43\nwhere is an angular wavenumber.", "These two relations are the temporal and spatial parts of the special relativistic expression using 4-vectors.", "formula_44", "Classical statistical mechanics requires the existence of (but does not define its value).", "Eventually, following upon Planck's discovery, it was speculated that physical action could not take on an arbitrary value, but instead was restricted to integer multiples of a very small quantity, the \"[elementary] quantum of action\", now called the \"Planck constant\".", "This was a significant conceptual part of the so-called \"old quantum theory\" developed by physicists including Bohr, Sommerfeld, and Ishiwara, in which particle trajectories exist but are hidden, but quantum laws constrain them based on their action.", "This view has been replaced by fully modern quantum theory, in which definite trajectories of motion do not even exist; rather, the particle is represented by a wavefunction spread out in space and in time.", "Thus there is no value of the action as classically defined.", "Related to this is the concept of energy quantization which existed in old quantum theory and also exists in altered form in modern quantum physics.", "Classical physics cannot explain either quantization of energy or the lack of classical particle motion.", "In many cases, such as for monochromatic light or for atoms, quantization of energy also implies that only certain energy levels are allowed, and values in between are forbidden.", "Implicit in the dimensions of the Planck constant is the fact that the SI unit of frequency, the hertz, represents one complete cycle, 360 degrees or radians, per second.", "In applications where it is natural to use the angular frequency (i.e. where the frequency is expressed in terms of radians per second instead of cycles per second or hertz)", "it is often useful to absorb a factor of into the Planck constant.", "The resulting constant is called the reduced Planck constant.", "It is equal to the Planck constant divided by , and is denoted formula_45 (pronounced \"h-bar\"):\nformula_46", "The Planck constant has dimensions of angular momentum.", "In SI units, the Planck constant is expressed in joules per hertz (J⋅Hz or kg⋅m2⋅s−1).", "formula_47\nformula_48\nThe above values have been adopted as fixed in the 2019 redefinition of the SI base units.", "In the system of \"natural units\" used by theoretical physicists, formula_45, the reduced Planck constant, is defined to be exactly one.", "In these units, is then exactly formula_50", "Since 2019, the numerical value of the Planck constant has been fixed, with a finite decimal representation.", "Under the present definition of the kilogram, which states that \"The kilogram [...] is defined by taking the fixed numerical value of to be when expressed in the unit J⋅s, which is equal to kg⋅m2⋅s−1, where the metre and the second are defined in terms of speed of light and duration of hyperfine transition of the ground state of an unperturbed caesium-133 atom .\"", "This implies that mass metrology is now aimed to find the value of one kilogram, and thus it is kilogram which is \"compensating\".", "Every experiment aiming to measure the kilogram (such as the Kibble balance and the X-ray crystal density method), will essentially refine the value of a kilogram.", "As an illustration of this, suppose the decision of making to be exact was taken in 2010, when its measured value was , thus the present definition of kilogram was also enforced.", "In the future, the value of one kilogram must be refined to times the mass of the International Prototype of the Kilogram (IPK).", "The Planck constant is related to the quantization of light and matter.", "It can be seen as a subatomic-scale constant.", "In a unit system adapted to subatomic scales, the electronvolt is the appropriate unit of energy and the petahertz the appropriate unit of frequency.", "Atomic unit systems are based (in part) on the Planck constant.", "The physical meaning of the Planck constant could suggest some basic features of our physical world.", "The Planck constant is one of the smallest constants used in physics.", "This reflects the fact that on a scale adapted to humans, where energies are typical of the order of kilojoules and times are typical of the order of seconds or minutes, the Planck constant is very small.", "One can regard the Planck constant to be only relevant to the microscopic scale instead of the macroscopic scale in our everyday experience.", "Equivalently, the order of the Planck constant reflects the fact that everyday objects and systems are made of a \"large\" number of microscopic particles.", "For example, green light with a wavelength of 555 nanometres (a wavelength that can be perceived by the human eye to be green) has a frequency of ().", "Each photon has an energy .", "That is a very small amount of energy in terms of everyday experience, but everyday experience is not concerned with individual photons any more than with individual atoms or molecules.", "An amount of light more typical in everyday experience (though much larger than the smallest amount perceivable by the human eye) is the energy of one mole of photons; its energy can be computed by multiplying the photon energy by the Avogadro constant, , with the result of , about the food energy in three apples.", "In principle, the Planck constant can be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons, and this is how its value was first calculated in the early twentieth century.", "In practice, these are no longer the most accurate methods.", "Since the value of the Planck constant is fixed now, it is no longer determined or calculated in laboratories.", "Some of the practices given below to determine the Planck constant are now used to determine the mass of the kilogram.", "The below-given methods \"except\" the X-ray crystal density method rely on the theoretical basis of the Josephson effect and the quantum Hall effect.", "The Josephson constant \"K\"J relates the potential difference \"U\" generated by the Josephson effect at a \"Josephson junction\" with the frequency \"ν\" of the microwave radiation.", "The theoretical treatment of Josephson effect suggests very strongly that .", "formula_51\nThe Josephson constant may be measured by comparing the potential difference generated by an array of Josephson junctions with a potential difference which is known in SI volts.", "The measurement of the potential difference in SI units is done by allowing an electrostatic force to cancel out a measurable gravitational force, in a Kibble balance.", "Assuming the validity of the theoretical treatment of the Josephson effect, \"K\"J is related to the Planck constant by\nformula_52", "A Kibble balance (formerly known as a watt balance) is an instrument for comparing two powers, one of which is measured in SI watts and the other of which is measured in conventional electrical units.", "From the definition of the \"conventional\" watt \"W\"90, this gives a measure of the product \"K\"J2\"R\"K in SI units, where \"R\"K is the von Klitzing constant which appears in the quantum Hall effect.", "If the theoretical treatments of the Josephson effect and the quantum Hall effect are valid, and in particular assuming that , the measurement of \"K\"J2\"R\"K is a direct determination of the Planck constant.", "formula_53", "The gyromagnetic ratio \"γ\" is the constant of proportionality between the frequency \"ν\" of nuclear magnetic resonance (or electron paramagnetic resonance for electrons) and the applied magnetic field .", "It is difficult to measure gyromagnetic ratios precisely because of the difficulties in precisely measuring \"B\", but the value for protons in water at is known to better than one part per million.", "The protons are said to be \"shielded\" from the applied magnetic field by the electrons in the water molecule, the same effect that gives rise to chemical shift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, \"γ\"′p.", "The gyromagnetic ratio is related to the shielded proton magnetic moment \"μ\"′p, the spin number \"I\" ( for protons) and the reduced Planck constant.", "formula_54\nThe ratio of the shielded proton magnetic moment \"μ\"′p to the electron magnetic moment \"μ\"e can be measured separately and to high precision, as the imprecisely known value of the applied magnetic field cancels itself out in taking the ratio.", "The value of \"μ\"e in Bohr magnetons is also known: it is half the electron g-factor \"g\"e.", "Hence\nformula_55\nformula_56\nA further complication is that the measurement of \"γ\"′p involves the measurement of an electric current: this is invariably measured in \"conventional\" amperes rather than in SI amperes, so a conversion factor is required.", "The symbol \"Γ\"′p-90 is used for the measured gyromagnetic ratio using conventional electrical units.", "In addition, there are two methods of measuring the value, a \"low-field\" method and a \"high-field\" method, and the conversion factors are different in the two cases.", "Only the high-field value \"Γ\"′p-90(hi) is of interest in determining the Planck constant.", "formula_57\nSubstitution gives the expression for the Planck constant in terms of \"Γ\"′p-90(hi):\nformula_58", "The Faraday constant \"F\" is the charge of one mole of electrons, equal to the Avogadro constant \"N\"A multiplied by the elementary charge \"e\".", "It can be determined by careful electrolysis experiments, measuring the amount of silver dissolved from an electrode in a given time and for a given electric current.", "Substituting the definitions of \"N\"A and \"e\" gives the relation to the Planck constant.", "formula_59", "The X-ray crystal density method is primarily a method for determining the Avogadro constant \"N\"A but as the Avogadro constant is related to the Planck constant it also determines a value for \"h\".", "The principle behind the method is to determine \"N\"A as the ratio between the volume of the unit cell of a crystal, measured by X-ray crystallography, and the molar volume of the substance.", "Crystals of silicon are used, as they are available in high quality and purity by the technology developed for the semiconductor industry.", "The unit cell volume is calculated from the spacing between two crystal planes referred to as \"d\"220.", "The molar volume \"V\"m(Si) requires a knowledge of the density of the crystal and the atomic weight of the silicon used.", "The Planck constant is given by\nformula_60", "The experimental measurement of the Planck constant in the Large Hadron Collider laboratory was carried out in 2011.", "The study called PCC using a giant particle accelerator helped to better understand the relationships between the Planck constant and measuring distances in space." ]

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[ "The Planck constant, or Planck's constant, is a fundamental physical constant denoted formula_1, and is of fundamental importance in quantum mechanics.", "A photon's energy is equal to its frequency multiplied by the Planck constant.", "Due to mass–energy equivalence, the Planck constant also relates mass to frequency.", "He was able to calculate the proportionality constant from the experimental measurements, and that constant is named in his honor.", "In 1905, Albert Einstein determined a \"quantum\" or minimal element of the energy of the electromagnetic wave itself." ]

[ "Planck's constant was formulated as part of Max Planck's successful effort to produce a mathematical expression that accurately predicted the observed spectral distribution of thermal radiation from a closed furnace (black-body radiation).", "This mathematical expression is now known as Planck's law.", "In the last years of the 19th century, Max Planck was investigating the problem of black-body radiation first posed by Kirchhoff some 40 years earlier.", "Every physical body spontaneously and continuously emits electromagnetic radiation.", "There was no expression or explanation for the overall shape of the observed emission spectrum.", "At the time, Wien's law fit the data for short wavelengths and high temperatures, but failed for long wavelengths.", "Also around this time, but unknown to Planck, Lord Rayleigh had derived theoretically a formula, now known as the Rayleigh–Jeans law, that could reasonably predict long wavelengths but failed dramatically at short wavelengths.", "Approaching this problem, Planck hypothesized that the equations of motion for light describe a set of harmonic oscillators, one for each possible frequency.", "He examined how the entropy of the oscillators varied with the temperature of the body, trying to match Wien's law, and was able to derive an approximate mathematical function for the black-body spectrum, which gave a simple empirical formula for long wavelengths.", "Planck tried to find a mathematical expression that could reproduce Wien's law (for short wavelengths) and the empirical formula (for long wavelengths).", "This expression included a constant, formula_3, which is thought to be for Hilfsgrösse (auxiliary variable), and subsequently became known as the Planck constant.", "The expression formulated by Planck showed that the spectral radiance of a body for frequency at absolute temperature is given by\nformula_4\nwhere formula_5 is the Boltzmann constant, formula_3 is the Planck constant, and formula_7 is the speed of light in the medium, whether material or vacuum.", "The spectral radiance of a body, formula_8, describes the amount of energy it emits at different radiation frequencies.", "It is the power emitted per unit area of the body, per unit solid angle of emission, per unit frequency.", "The spectral radiance can also be expressed per unit wavelength formula_9 instead of per unit frequency.", "In this case, it is given by\nformula_10\nshowing how radiated energy emitted at shorter wavelengths increases more rapidly with temperature than energy emitted at longer wavelengths.", "Planck's law may also be expressed in other terms, such as the number of photons emitted at a certain wavelength, or the energy density in a volume of radiation.", "The SI units of formula_8 are , while those of formula_12 are .", "Planck soon realized that his solution was not unique.", "There were several different solutions, each of which gave a different value for the entropy of the oscillators.", "To save his theory, Planck resorted to using the then-controversial theory of statistical mechanics, which he described as \"an act of despair …", "I was ready to sacrifice any of my previous convictions about physics.\"", "One of his new boundary conditions was\nWith this new condition, Planck had imposed the quantization of the energy of the oscillators, \"a purely formal assumption …", "actually I did not think much about it ...\" in his own words, but one that would revolutionize physics.", "Applying this new approach to Wien's displacement law showed that the \"energy element\" must be proportional to the frequency of the oscillator, the first version of what is now sometimes termed the \"Planck–Einstein relation\":\nformula_13\nPlanck was able to calculate the value of formula_1 from experimental data on black-body radiation: his result, , is within 1.2% of the currently accepted value.", "He also made the first determination of the Boltzmann constant formula_5 from the same data and theory.", "The black-body problem was revisited in 1905, when Lord Rayleigh and James Jeans (on the one hand) and Albert Einstein (on the other hand) independently proved that classical electromagnetism could \"never\" account for the observed spectrum.", "These proofs are commonly known as the \"ultraviolet catastrophe\", a name coined by Paul Ehrenfest in 1911.", "They contributed greatly (along with Einstein's work on the photoelectric effect) in convincing physicists that Planck's postulate of quantized energy levels was more than a mere mathematical formalism.", "The first Solvay Conference in 1911 was devoted to \"the theory of radiation and quanta\".", "The photoelectric effect is the emission of electrons (called \"photoelectrons\") from a surface when light is shone on it.", "It was first observed by Alexandre Edmond Becquerel in 1839, although credit is usually reserved for Heinrich Hertz, who published the first thorough investigation in 1887.", "Another particularly thorough investigation was published by Philipp Lenard (Lénárd Fülöp) in 1902.", "Einstein's 1905 paper discussing the effect in terms of light quanta would earn him the Nobel Prize in 1921, after his predictions had been confirmed by the experimental work of Robert Andrews Millikan.", "The Nobel committee awarded the prize for his work on the photo-electric effect, rather than relativity, both because of a bias against purely theoretical physics not grounded in discovery or experiment, and dissent amongst its members as to the actual proof that relativity was real.", "Before Einstein's paper, electromagnetic radiation such as visible light was considered to behave as a wave: hence the use of the terms \"frequency\" and \"wavelength\" to characterize different types of radiation.", "The energy transferred by a wave in a given time is called its intensity.", "The light from a theatre spotlight is more \"intense\" than the light from a domestic lightbulb; that is to say that the spotlight gives out more energy per unit time and per unit space (and hence consumes more electricity) than the ordinary bulb, even though the color of the light might be very similar.", "Other waves, such as sound or the waves crashing against a seafront, also have their intensity.", "However, the energy account of the photoelectric effect didn't seem to agree with the wave description of light.", "The \"photoelectrons\" emitted as a result of the photoelectric effect have a certain kinetic energy, which can be measured.", "This kinetic energy (for each photoelectron) is \"independent\" of the intensity of the light, but depends linearly on the frequency; and if the frequency is too low (corresponding to a photon energy that is less than the work function of the material), no photoelectrons are emitted at all, unless a plurality of photons, whose energetic sum is greater than the energy of the photoelectrons, acts virtually simultaneously (multiphoton effect).", "Assuming the frequency is high enough to cause the photoelectric effect, a rise in intensity of the light source causes more photoelectrons to be emitted with the same kinetic energy, rather than the same number of photoelectrons to be emitted with higher kinetic energy.", "Einstein's explanation for these observations was that light itself is quantized; that the energy of light is not transferred continuously as in a classical wave, but only in small \"packets\" or quanta.", "The size of these \"packets\" of energy, which would later be named photons, was to be the same as Planck's \"energy element\", giving the modern version of the Planck–Einstein relation:\nformula_16\nEinstein's postulate was later proven experimentally: the constant of proportionality between the frequency of incident light formula_17 and the kinetic energy of photoelectrons formula_18 was shown to be equal to the Planck constant formula_1.", "It was John William Nicholson in 1912 who introduced h-bar into the theory of the atom which was the first quantum and nuclear atom and the first to quantize angular momentum as \"h\"/2.", "Niels Bohr quoted him in his 1913 paper of the Bohr model of the atom.", "The influence of the work of Nicholson’s nuclear quantum atomic model on Bohr’s model has been written about by many historians.", "Niels Bohr introduced the third quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model.", "The first quantized model of the atom was introduced in 1910 by Arthur Erich Haas and much discussed at the 1911 Solvay conference.", "In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation.", "If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus.", "Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies formula_20\nformula_21\nwhere formula_22 is the speed of light in vacuum, formula_23 is an experimentally determined constant (the Rydberg constant) and formula_24.", "Once the electron reached the lowest energy level (formula_25), it could not get any closer to the nucleus (lower energy).", "This approach also allowed Bohr to account for the Rydberg formula, an empirical description of the atomic spectrum of hydrogen, and to account for the value of the Rydberg constant formula_23 in terms of other fundamental constants.", "Bohr also introduced the quantity formula_27, now known as the reduced Planck constant, as the quantum of angular momentum.", "At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model.", "The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum.", "In modern terms, if formula_28 is the total angular momentum of a system with rotational invariance, and formula_29 the angular momentum measured along any given direction, these quantities can only take on the values\nformula_30", "The Planck constant also occurs in statements of Werner Heisenberg's uncertainty principle.", "Given numerous particles prepared in the same state, the uncertainty in their position, formula_31, and the uncertainty in their momentum, formula_32, obey\nformula_33\nwhere the uncertainty is given as the standard deviation of the measured value from its expected value.", "There are several other such pairs of physically measurable conjugate variables which obey a similar rule.", "One example is time vs. energy.", "The inverse relationship between the uncertainty of the two conjugate variables forces a tradeoff in quantum experiments, as measuring one quantity more precisely results in the other quantity becoming imprecise.", "In addition to some assumptions underlying the interpretation of certain values in the quantum mechanical formulation, one of the fundamental cornerstones to the entire theory lies in the commutator relationship between the position operator formula_34 and the momentum operator formula_35:\nformula_36\nwhere formula_37 is the Kronecker delta.", "The Planck relation connects the particular photon energy with its associated wave frequency :\nformula_38\nThis energy is extremely small in terms of ordinarily perceived everyday objects.", "Since the frequency , wavelength , and speed of light are related by formula_39, the relation can also be expressed as\nformula_40", "In 1923, Louis de Broglie generalized the Planck–Einstein relation by postulating that the Planck constant represents the proportionality between the momentum and the quantum wavelength of not just the photon, but the quantum wavelength of any particle.", "This was confirmed by experiments soon afterward.", "This holds throughout the quantum theory, including electrodynamics.", "The de Broglie wavelength of the particle is given by\nformula_41\nwhere denotes the linear momentum of a particle, such as a photon, or any other elementary particle.", "The energy of a photon with angular frequency is given by\nformula_42\nwhile its linear momentum relates to\nformula_43\nwhere is an angular wavenumber.", "These two relations are the temporal and spatial parts of the special relativistic expression using 4-vectors.", "formula_44", "Classical statistical mechanics requires the existence of (but does not define its value).", "Eventually, following upon Planck's discovery, it was speculated that physical action could not take on an arbitrary value, but instead was restricted to integer multiples of a very small quantity, the \"[elementary] quantum of action\", now called the \"Planck constant\".", "This was a significant conceptual part of the so-called \"old quantum theory\" developed by physicists including Bohr, Sommerfeld, and Ishiwara, in which particle trajectories exist but are hidden, but quantum laws constrain them based on their action.", "This view has been replaced by fully modern quantum theory, in which definite trajectories of motion do not even exist; rather, the particle is represented by a wavefunction spread out in space and in time.", "Thus there is no value of the action as classically defined.", "Related to this is the concept of energy quantization which existed in old quantum theory and also exists in altered form in modern quantum physics.", "Classical physics cannot explain either quantization of energy or the lack of classical particle motion.", "In many cases, such as for monochromatic light or for atoms, quantization of energy also implies that only certain energy levels are allowed, and values in between are forbidden.", "Implicit in the dimensions of the Planck constant is the fact that the SI unit of frequency, the hertz, represents one complete cycle, 360 degrees or radians, per second.", "In applications where it is natural to use the angular frequency (i.e. where the frequency is expressed in terms of radians per second instead of cycles per second or hertz)", "it is often useful to absorb a factor of into the Planck constant.", "The resulting constant is called the reduced Planck constant.", "It is equal to the Planck constant divided by , and is denoted formula_45 (pronounced \"h-bar\"):\nformula_46", "The Planck constant has dimensions of angular momentum.", "In SI units, the Planck constant is expressed in joules per hertz (J⋅Hz or kg⋅m2⋅s−1).", "formula_47\nformula_48\nThe above values have been adopted as fixed in the 2019 redefinition of the SI base units.", "In the system of \"natural units\" used by theoretical physicists, formula_45, the reduced Planck constant, is defined to be exactly one.", "In these units, is then exactly formula_50", "Since 2019, the numerical value of the Planck constant has been fixed, with a finite decimal representation.", "Under the present definition of the kilogram, which states that \"The kilogram [...] is defined by taking the fixed numerical value of to be when expressed in the unit J⋅s, which is equal to kg⋅m2⋅s−1, where the metre and the second are defined in terms of speed of light and duration of hyperfine transition of the ground state of an unperturbed caesium-133 atom .\"", "This implies that mass metrology is now aimed to find the value of one kilogram, and thus it is kilogram which is \"compensating\".", "Every experiment aiming to measure the kilogram (such as the Kibble balance and the X-ray crystal density method), will essentially refine the value of a kilogram.", "As an illustration of this, suppose the decision of making to be exact was taken in 2010, when its measured value was , thus the present definition of kilogram was also enforced.", "In the future, the value of one kilogram must be refined to times the mass of the International Prototype of the Kilogram (IPK).", "The Planck constant is related to the quantization of light and matter.", "It can be seen as a subatomic-scale constant.", "In a unit system adapted to subatomic scales, the electronvolt is the appropriate unit of energy and the petahertz the appropriate unit of frequency.", "Atomic unit systems are based (in part) on the Planck constant.", "The physical meaning of the Planck constant could suggest some basic features of our physical world.", "The Planck constant is one of the smallest constants used in physics.", "This reflects the fact that on a scale adapted to humans, where energies are typical of the order of kilojoules and times are typical of the order of seconds or minutes, the Planck constant is very small.", "One can regard the Planck constant to be only relevant to the microscopic scale instead of the macroscopic scale in our everyday experience.", "Equivalently, the order of the Planck constant reflects the fact that everyday objects and systems are made of a \"large\" number of microscopic particles.", "For example, green light with a wavelength of 555 nanometres (a wavelength that can be perceived by the human eye to be green) has a frequency of ().", "Each photon has an energy .", "That is a very small amount of energy in terms of everyday experience, but everyday experience is not concerned with individual photons any more than with individual atoms or molecules.", "An amount of light more typical in everyday experience (though much larger than the smallest amount perceivable by the human eye) is the energy of one mole of photons; its energy can be computed by multiplying the photon energy by the Avogadro constant, , with the result of , about the food energy in three apples.", "In principle, the Planck constant can be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons, and this is how its value was first calculated in the early twentieth century.", "In practice, these are no longer the most accurate methods.", "Since the value of the Planck constant is fixed now, it is no longer determined or calculated in laboratories.", "Some of the practices given below to determine the Planck constant are now used to determine the mass of the kilogram.", "The below-given methods \"except\" the X-ray crystal density method rely on the theoretical basis of the Josephson effect and the quantum Hall effect.", "The Josephson constant \"K\"J relates the potential difference \"U\" generated by the Josephson effect at a \"Josephson junction\" with the frequency \"ν\" of the microwave radiation.", "The theoretical treatment of Josephson effect suggests very strongly that .", "formula_51\nThe Josephson constant may be measured by comparing the potential difference generated by an array of Josephson junctions with a potential difference which is known in SI volts.", "The measurement of the potential difference in SI units is done by allowing an electrostatic force to cancel out a measurable gravitational force, in a Kibble balance.", "Assuming the validity of the theoretical treatment of the Josephson effect, \"K\"J is related to the Planck constant by\nformula_52", "A Kibble balance (formerly known as a watt balance) is an instrument for comparing two powers, one of which is measured in SI watts and the other of which is measured in conventional electrical units.", "From the definition of the \"conventional\" watt \"W\"90, this gives a measure of the product \"K\"J2\"R\"K in SI units, where \"R\"K is the von Klitzing constant which appears in the quantum Hall effect.", "If the theoretical treatments of the Josephson effect and the quantum Hall effect are valid, and in particular assuming that , the measurement of \"K\"J2\"R\"K is a direct determination of the Planck constant.", "formula_53", "The gyromagnetic ratio \"γ\" is the constant of proportionality between the frequency \"ν\" of nuclear magnetic resonance (or electron paramagnetic resonance for electrons) and the applied magnetic field .", "It is difficult to measure gyromagnetic ratios precisely because of the difficulties in precisely measuring \"B\", but the value for protons in water at is known to better than one part per million.", "The protons are said to be \"shielded\" from the applied magnetic field by the electrons in the water molecule, the same effect that gives rise to chemical shift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, \"γ\"′p.", "The gyromagnetic ratio is related to the shielded proton magnetic moment \"μ\"′p, the spin number \"I\" ( for protons) and the reduced Planck constant.", "formula_54\nThe ratio of the shielded proton magnetic moment \"μ\"′p to the electron magnetic moment \"μ\"e can be measured separately and to high precision, as the imprecisely known value of the applied magnetic field cancels itself out in taking the ratio.", "The value of \"μ\"e in Bohr magnetons is also known: it is half the electron g-factor \"g\"e.", "Hence\nformula_55\nformula_56\nA further complication is that the measurement of \"γ\"′p involves the measurement of an electric current: this is invariably measured in \"conventional\" amperes rather than in SI amperes, so a conversion factor is required.", "The symbol \"Γ\"′p-90 is used for the measured gyromagnetic ratio using conventional electrical units.", "In addition, there are two methods of measuring the value, a \"low-field\" method and a \"high-field\" method, and the conversion factors are different in the two cases.", "Only the high-field value \"Γ\"′p-90(hi) is of interest in determining the Planck constant.", "formula_57\nSubstitution gives the expression for the Planck constant in terms of \"Γ\"′p-90(hi):\nformula_58", "The Faraday constant \"F\" is the charge of one mole of electrons, equal to the Avogadro constant \"N\"A multiplied by the elementary charge \"e\".", "It can be determined by careful electrolysis experiments, measuring the amount of silver dissolved from an electrode in a given time and for a given electric current.", "Substituting the definitions of \"N\"A and \"e\" gives the relation to the Planck constant.", "formula_59", "The X-ray crystal density method is primarily a method for determining the Avogadro constant \"N\"A but as the Avogadro constant is related to the Planck constant it also determines a value for \"h\".", "The principle behind the method is to determine \"N\"A as the ratio between the volume of the unit cell of a crystal, measured by X-ray crystallography, and the molar volume of the substance.", "Crystals of silicon are used, as they are available in high quality and purity by the technology developed for the semiconductor industry.", "The unit cell volume is calculated from the spacing between two crystal planes referred to as \"d\"220.", "The molar volume \"V\"m(Si) requires a knowledge of the density of the crystal and the atomic weight of the silicon used.", "The Planck constant is given by\nformula_60", "The experimental measurement of the Planck constant in the Large Hadron Collider laboratory was carried out in 2011.", "The study called PCC using a giant particle accelerator helped to better understand the relationships between the Planck constant and measuring distances in space." ]

[ 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44 ]

[ "A photon's energy is equal to its frequency multiplied by the Planck constant.", "Due to mass–energy equivalence, the Planck constant also relates mass to frequency.", "He was able to calculate the proportionality constant from the experimental measurements, and that constant is named in his honor." ]

[ "Planck's constant was formulated as part of Max Planck's successful effort to produce a mathematical expression that accurately predicted the observed spectral distribution of thermal radiation from a closed furnace (black-body radiation).", "This mathematical expression is now known as Planck's law.", "In the last years of the 19th century, Max Planck was investigating the problem of black-body radiation first posed by Kirchhoff some 40 years earlier.", "Every physical body spontaneously and continuously emits electromagnetic radiation.", "There was no expression or explanation for the overall shape of the observed emission spectrum.", "At the time, Wien's law fit the data for short wavelengths and high temperatures, but failed for long wavelengths.", "Also around this time, but unknown to Planck, Lord Rayleigh had derived theoretically a formula, now known as the Rayleigh–Jeans law, that could reasonably predict long wavelengths but failed dramatically at short wavelengths.", "Approaching this problem, Planck hypothesized that the equations of motion for light describe a set of harmonic oscillators, one for each possible frequency.", "He examined how the entropy of the oscillators varied with the temperature of the body, trying to match Wien's law, and was able to derive an approximate mathematical function for the black-body spectrum, which gave a simple empirical formula for long wavelengths.", "Planck tried to find a mathematical expression that could reproduce Wien's law (for short wavelengths) and the empirical formula (for long wavelengths).", "This expression included a constant, formula_3, which is thought to be for Hilfsgrösse (auxiliary variable), and subsequently became known as the Planck constant.", "The expression formulated by Planck showed that the spectral radiance of a body for frequency at absolute temperature is given by\nformula_4\nwhere formula_5 is the Boltzmann constant, formula_3 is the Planck constant, and formula_7 is the speed of light in the medium, whether material or vacuum.", "The spectral radiance of a body, formula_8, describes the amount of energy it emits at different radiation frequencies.", "It is the power emitted per unit area of the body, per unit solid angle of emission, per unit frequency.", "The spectral radiance can also be expressed per unit wavelength formula_9 instead of per unit frequency.", "In this case, it is given by\nformula_10\nshowing how radiated energy emitted at shorter wavelengths increases more rapidly with temperature than energy emitted at longer wavelengths.", "Planck's law may also be expressed in other terms, such as the number of photons emitted at a certain wavelength, or the energy density in a volume of radiation.", "The SI units of formula_8 are , while those of formula_12 are .", "Planck soon realized that his solution was not unique.", "There were several different solutions, each of which gave a different value for the entropy of the oscillators.", "To save his theory, Planck resorted to using the then-controversial theory of statistical mechanics, which he described as \"an act of despair …", "I was ready to sacrifice any of my previous convictions about physics.\"", "One of his new boundary conditions was\nWith this new condition, Planck had imposed the quantization of the energy of the oscillators, \"a purely formal assumption …", "actually I did not think much about it ...\" in his own words, but one that would revolutionize physics.", "Applying this new approach to Wien's displacement law showed that the \"energy element\" must be proportional to the frequency of the oscillator, the first version of what is now sometimes termed the \"Planck–Einstein relation\":\nformula_13\nPlanck was able to calculate the value of formula_1 from experimental data on black-body radiation: his result, , is within 1.2% of the currently accepted value.", "He also made the first determination of the Boltzmann constant formula_5 from the same data and theory.", "The black-body problem was revisited in 1905, when Lord Rayleigh and James Jeans (on the one hand) and Albert Einstein (on the other hand) independently proved that classical electromagnetism could \"never\" account for the observed spectrum.", "These proofs are commonly known as the \"ultraviolet catastrophe\", a name coined by Paul Ehrenfest in 1911.", "They contributed greatly (along with Einstein's work on the photoelectric effect) in convincing physicists that Planck's postulate of quantized energy levels was more than a mere mathematical formalism.", "The first Solvay Conference in 1911 was devoted to \"the theory of radiation and quanta\".", "The photoelectric effect is the emission of electrons (called \"photoelectrons\") from a surface when light is shone on it.", "It was first observed by Alexandre Edmond Becquerel in 1839, although credit is usually reserved for Heinrich Hertz, who published the first thorough investigation in 1887.", "Another particularly thorough investigation was published by Philipp Lenard (Lénárd Fülöp) in 1902.", "Einstein's 1905 paper discussing the effect in terms of light quanta would earn him the Nobel Prize in 1921, after his predictions had been confirmed by the experimental work of Robert Andrews Millikan.", "The Nobel committee awarded the prize for his work on the photo-electric effect, rather than relativity, both because of a bias against purely theoretical physics not grounded in discovery or experiment, and dissent amongst its members as to the actual proof that relativity was real.", "Before Einstein's paper, electromagnetic radiation such as visible light was considered to behave as a wave: hence the use of the terms \"frequency\" and \"wavelength\" to characterize different types of radiation.", "The energy transferred by a wave in a given time is called its intensity.", "The light from a theatre spotlight is more \"intense\" than the light from a domestic lightbulb; that is to say that the spotlight gives out more energy per unit time and per unit space (and hence consumes more electricity) than the ordinary bulb, even though the color of the light might be very similar.", "Other waves, such as sound or the waves crashing against a seafront, also have their intensity.", "However, the energy account of the photoelectric effect didn't seem to agree with the wave description of light.", "The \"photoelectrons\" emitted as a result of the photoelectric effect have a certain kinetic energy, which can be measured.", "This kinetic energy (for each photoelectron) is \"independent\" of the intensity of the light, but depends linearly on the frequency; and if the frequency is too low (corresponding to a photon energy that is less than the work function of the material), no photoelectrons are emitted at all, unless a plurality of photons, whose energetic sum is greater than the energy of the photoelectrons, acts virtually simultaneously (multiphoton effect).", "Assuming the frequency is high enough to cause the photoelectric effect, a rise in intensity of the light source causes more photoelectrons to be emitted with the same kinetic energy, rather than the same number of photoelectrons to be emitted with higher kinetic energy.", "Einstein's explanation for these observations was that light itself is quantized; that the energy of light is not transferred continuously as in a classical wave, but only in small \"packets\" or quanta.", "The size of these \"packets\" of energy, which would later be named photons, was to be the same as Planck's \"energy element\", giving the modern version of the Planck–Einstein relation:\nformula_16\nEinstein's postulate was later proven experimentally: the constant of proportionality between the frequency of incident light formula_17 and the kinetic energy of photoelectrons formula_18 was shown to be equal to the Planck constant formula_1.", "It was John William Nicholson in 1912 who introduced h-bar into the theory of the atom which was the first quantum and nuclear atom and the first to quantize angular momentum as \"h\"/2.", "Niels Bohr quoted him in his 1913 paper of the Bohr model of the atom.", "The influence of the work of Nicholson’s nuclear quantum atomic model on Bohr’s model has been written about by many historians.", "Niels Bohr introduced the third quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model.", "The first quantized model of the atom was introduced in 1910 by Arthur Erich Haas and much discussed at the 1911 Solvay conference.", "In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation.", "If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus.", "Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies formula_20\nformula_21\nwhere formula_22 is the speed of light in vacuum, formula_23 is an experimentally determined constant (the Rydberg constant) and formula_24.", "Once the electron reached the lowest energy level (formula_25), it could not get any closer to the nucleus (lower energy).", "This approach also allowed Bohr to account for the Rydberg formula, an empirical description of the atomic spectrum of hydrogen, and to account for the value of the Rydberg constant formula_23 in terms of other fundamental constants.", "Bohr also introduced the quantity formula_27, now known as the reduced Planck constant, as the quantum of angular momentum.", "At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model.", "The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum.", "In modern terms, if formula_28 is the total angular momentum of a system with rotational invariance, and formula_29 the angular momentum measured along any given direction, these quantities can only take on the values\nformula_30", "The Planck constant also occurs in statements of Werner Heisenberg's uncertainty principle.", "Given numerous particles prepared in the same state, the uncertainty in their position, formula_31, and the uncertainty in their momentum, formula_32, obey\nformula_33\nwhere the uncertainty is given as the standard deviation of the measured value from its expected value.", "There are several other such pairs of physically measurable conjugate variables which obey a similar rule.", "One example is time vs. energy.", "The inverse relationship between the uncertainty of the two conjugate variables forces a tradeoff in quantum experiments, as measuring one quantity more precisely results in the other quantity becoming imprecise.", "In addition to some assumptions underlying the interpretation of certain values in the quantum mechanical formulation, one of the fundamental cornerstones to the entire theory lies in the commutator relationship between the position operator formula_34 and the momentum operator formula_35:\nformula_36\nwhere formula_37 is the Kronecker delta.", "The Planck relation connects the particular photon energy with its associated wave frequency :\nformula_38\nThis energy is extremely small in terms of ordinarily perceived everyday objects.", "Since the frequency , wavelength , and speed of light are related by formula_39, the relation can also be expressed as\nformula_40", "In 1923, Louis de Broglie generalized the Planck–Einstein relation by postulating that the Planck constant represents the proportionality between the momentum and the quantum wavelength of not just the photon, but the quantum wavelength of any particle.", "This was confirmed by experiments soon afterward.", "This holds throughout the quantum theory, including electrodynamics.", "The de Broglie wavelength of the particle is given by\nformula_41\nwhere denotes the linear momentum of a particle, such as a photon, or any other elementary particle.", "The energy of a photon with angular frequency is given by\nformula_42\nwhile its linear momentum relates to\nformula_43\nwhere is an angular wavenumber.", "These two relations are the temporal and spatial parts of the special relativistic expression using 4-vectors.", "formula_44", "Classical statistical mechanics requires the existence of (but does not define its value).", "Eventually, following upon Planck's discovery, it was speculated that physical action could not take on an arbitrary value, but instead was restricted to integer multiples of a very small quantity, the \"[elementary] quantum of action\", now called the \"Planck constant\".", "This was a significant conceptual part of the so-called \"old quantum theory\" developed by physicists including Bohr, Sommerfeld, and Ishiwara, in which particle trajectories exist but are hidden, but quantum laws constrain them based on their action.", "This view has been replaced by fully modern quantum theory, in which definite trajectories of motion do not even exist; rather, the particle is represented by a wavefunction spread out in space and in time.", "Thus there is no value of the action as classically defined.", "Related to this is the concept of energy quantization which existed in old quantum theory and also exists in altered form in modern quantum physics.", "Classical physics cannot explain either quantization of energy or the lack of classical particle motion.", "In many cases, such as for monochromatic light or for atoms, quantization of energy also implies that only certain energy levels are allowed, and values in between are forbidden.", "Implicit in the dimensions of the Planck constant is the fact that the SI unit of frequency, the hertz, represents one complete cycle, 360 degrees or radians, per second.", "In applications where it is natural to use the angular frequency (i.e. where the frequency is expressed in terms of radians per second instead of cycles per second or hertz)", "it is often useful to absorb a factor of into the Planck constant.", "The resulting constant is called the reduced Planck constant.", "It is equal to the Planck constant divided by , and is denoted formula_45 (pronounced \"h-bar\"):\nformula_46", "The Planck constant has dimensions of angular momentum.", "In SI units, the Planck constant is expressed in joules per hertz (J⋅Hz or kg⋅m2⋅s−1).", "formula_47\nformula_48\nThe above values have been adopted as fixed in the 2019 redefinition of the SI base units.", "In the system of \"natural units\" used by theoretical physicists, formula_45, the reduced Planck constant, is defined to be exactly one.", "In these units, is then exactly formula_50", "Since 2019, the numerical value of the Planck constant has been fixed, with a finite decimal representation.", "Under the present definition of the kilogram, which states that \"The kilogram [...] is defined by taking the fixed numerical value of to be when expressed in the unit J⋅s, which is equal to kg⋅m2⋅s−1, where the metre and the second are defined in terms of speed of light and duration of hyperfine transition of the ground state of an unperturbed caesium-133 atom .\"", "This implies that mass metrology is now aimed to find the value of one kilogram, and thus it is kilogram which is \"compensating\".", "Every experiment aiming to measure the kilogram (such as the Kibble balance and the X-ray crystal density method), will essentially refine the value of a kilogram.", "As an illustration of this, suppose the decision of making to be exact was taken in 2010, when its measured value was , thus the present definition of kilogram was also enforced.", "In the future, the value of one kilogram must be refined to times the mass of the International Prototype of the Kilogram (IPK).", "The Planck constant is related to the quantization of light and matter.", "It can be seen as a subatomic-scale constant.", "In a unit system adapted to subatomic scales, the electronvolt is the appropriate unit of energy and the petahertz the appropriate unit of frequency.", "Atomic unit systems are based (in part) on the Planck constant.", "The physical meaning of the Planck constant could suggest some basic features of our physical world.", "The Planck constant is one of the smallest constants used in physics.", "This reflects the fact that on a scale adapted to humans, where energies are typical of the order of kilojoules and times are typical of the order of seconds or minutes, the Planck constant is very small.", "One can regard the Planck constant to be only relevant to the microscopic scale instead of the macroscopic scale in our everyday experience.", "Equivalently, the order of the Planck constant reflects the fact that everyday objects and systems are made of a \"large\" number of microscopic particles.", "For example, green light with a wavelength of 555 nanometres (a wavelength that can be perceived by the human eye to be green) has a frequency of ().", "Each photon has an energy .", "That is a very small amount of energy in terms of everyday experience, but everyday experience is not concerned with individual photons any more than with individual atoms or molecules.", "An amount of light more typical in everyday experience (though much larger than the smallest amount perceivable by the human eye) is the energy of one mole of photons; its energy can be computed by multiplying the photon energy by the Avogadro constant, , with the result of , about the food energy in three apples.", "In principle, the Planck constant can be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons, and this is how its value was first calculated in the early twentieth century.", "In practice, these are no longer the most accurate methods.", "Since the value of the Planck constant is fixed now, it is no longer determined or calculated in laboratories.", "Some of the practices given below to determine the Planck constant are now used to determine the mass of the kilogram.", "The below-given methods \"except\" the X-ray crystal density method rely on the theoretical basis of the Josephson effect and the quantum Hall effect.", "The Josephson constant \"K\"J relates the potential difference \"U\" generated by the Josephson effect at a \"Josephson junction\" with the frequency \"ν\" of the microwave radiation.", "The theoretical treatment of Josephson effect suggests very strongly that .", "formula_51\nThe Josephson constant may be measured by comparing the potential difference generated by an array of Josephson junctions with a potential difference which is known in SI volts.", "The measurement of the potential difference in SI units is done by allowing an electrostatic force to cancel out a measurable gravitational force, in a Kibble balance.", "Assuming the validity of the theoretical treatment of the Josephson effect, \"K\"J is related to the Planck constant by\nformula_52", "A Kibble balance (formerly known as a watt balance) is an instrument for comparing two powers, one of which is measured in SI watts and the other of which is measured in conventional electrical units.", "From the definition of the \"conventional\" watt \"W\"90, this gives a measure of the product \"K\"J2\"R\"K in SI units, where \"R\"K is the von Klitzing constant which appears in the quantum Hall effect.", "If the theoretical treatments of the Josephson effect and the quantum Hall effect are valid, and in particular assuming that , the measurement of \"K\"J2\"R\"K is a direct determination of the Planck constant.", "formula_53", "The gyromagnetic ratio \"γ\" is the constant of proportionality between the frequency \"ν\" of nuclear magnetic resonance (or electron paramagnetic resonance for electrons) and the applied magnetic field .", "It is difficult to measure gyromagnetic ratios precisely because of the difficulties in precisely measuring \"B\", but the value for protons in water at is known to better than one part per million.", "The protons are said to be \"shielded\" from the applied magnetic field by the electrons in the water molecule, the same effect that gives rise to chemical shift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, \"γ\"′p.", "The gyromagnetic ratio is related to the shielded proton magnetic moment \"μ\"′p, the spin number \"I\" ( for protons) and the reduced Planck constant.", "formula_54\nThe ratio of the shielded proton magnetic moment \"μ\"′p to the electron magnetic moment \"μ\"e can be measured separately and to high precision, as the imprecisely known value of the applied magnetic field cancels itself out in taking the ratio.", "The value of \"μ\"e in Bohr magnetons is also known: it is half the electron g-factor \"g\"e.", "Hence\nformula_55\nformula_56\nA further complication is that the measurement of \"γ\"′p involves the measurement of an electric current: this is invariably measured in \"conventional\" amperes rather than in SI amperes, so a conversion factor is required.", "The symbol \"Γ\"′p-90 is used for the measured gyromagnetic ratio using conventional electrical units.", "In addition, there are two methods of measuring the value, a \"low-field\" method and a \"high-field\" method, and the conversion factors are different in the two cases.", "Only the high-field value \"Γ\"′p-90(hi) is of interest in determining the Planck constant.", "formula_57\nSubstitution gives the expression for the Planck constant in terms of \"Γ\"′p-90(hi):\nformula_58", "The Faraday constant \"F\" is the charge of one mole of electrons, equal to the Avogadro constant \"N\"A multiplied by the elementary charge \"e\".", "It can be determined by careful electrolysis experiments, measuring the amount of silver dissolved from an electrode in a given time and for a given electric current.", "Substituting the definitions of \"N\"A and \"e\" gives the relation to the Planck constant.", "formula_59", "The X-ray crystal density method is primarily a method for determining the Avogadro constant \"N\"A but as the Avogadro constant is related to the Planck constant it also determines a value for \"h\".", "The principle behind the method is to determine \"N\"A as the ratio between the volume of the unit cell of a crystal, measured by X-ray crystallography, and the molar volume of the substance.", "Crystals of silicon are used, as they are available in high quality and purity by the technology developed for the semiconductor industry.", "The unit cell volume is calculated from the spacing between two crystal planes referred to as \"d\"220.", "The molar volume \"V\"m(Si) requires a knowledge of the density of the crystal and the atomic weight of the silicon used.", "The Planck constant is given by\nformula_60", "The experimental measurement of the Planck constant in the Large Hadron Collider laboratory was carried out in 2011.", "The study called PCC using a giant particle accelerator helped to better understand the relationships between the Planck constant and measuring distances in space." ]

[ 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81 ]

[ "The light quantum behaved in some respects as an electrically neutral particle, and was eventually called a photon." ]

[ "Planck's constant was formulated as part of Max Planck's successful effort to produce a mathematical expression that accurately predicted the observed spectral distribution of thermal radiation from a closed furnace (black-body radiation).", "This mathematical expression is now known as Planck's law.", "In the last years of the 19th century, Max Planck was investigating the problem of black-body radiation first posed by Kirchhoff some 40 years earlier.", "Every physical body spontaneously and continuously emits electromagnetic radiation.", "There was no expression or explanation for the overall shape of the observed emission spectrum.", "At the time, Wien's law fit the data for short wavelengths and high temperatures, but failed for long wavelengths.", "Also around this time, but unknown to Planck, Lord Rayleigh had derived theoretically a formula, now known as the Rayleigh–Jeans law, that could reasonably predict long wavelengths but failed dramatically at short wavelengths.", "Approaching this problem, Planck hypothesized that the equations of motion for light describe a set of harmonic oscillators, one for each possible frequency.", "He examined how the entropy of the oscillators varied with the temperature of the body, trying to match Wien's law, and was able to derive an approximate mathematical function for the black-body spectrum, which gave a simple empirical formula for long wavelengths.", "Planck tried to find a mathematical expression that could reproduce Wien's law (for short wavelengths) and the empirical formula (for long wavelengths).", "This expression included a constant, formula_3, which is thought to be for Hilfsgrösse (auxiliary variable), and subsequently became known as the Planck constant.", "The expression formulated by Planck showed that the spectral radiance of a body for frequency at absolute temperature is given by\nformula_4\nwhere formula_5 is the Boltzmann constant, formula_3 is the Planck constant, and formula_7 is the speed of light in the medium, whether material or vacuum.", "The spectral radiance of a body, formula_8, describes the amount of energy it emits at different radiation frequencies.", "It is the power emitted per unit area of the body, per unit solid angle of emission, per unit frequency.", "The spectral radiance can also be expressed per unit wavelength formula_9 instead of per unit frequency.", "In this case, it is given by\nformula_10\nshowing how radiated energy emitted at shorter wavelengths increases more rapidly with temperature than energy emitted at longer wavelengths.", "Planck's law may also be expressed in other terms, such as the number of photons emitted at a certain wavelength, or the energy density in a volume of radiation.", "The SI units of formula_8 are , while those of formula_12 are .", "Planck soon realized that his solution was not unique.", "There were several different solutions, each of which gave a different value for the entropy of the oscillators.", "To save his theory, Planck resorted to using the then-controversial theory of statistical mechanics, which he described as \"an act of despair …", "I was ready to sacrifice any of my previous convictions about physics.\"", "One of his new boundary conditions was\nWith this new condition, Planck had imposed the quantization of the energy of the oscillators, \"a purely formal assumption …", "actually I did not think much about it ...\" in his own words, but one that would revolutionize physics.", "Applying this new approach to Wien's displacement law showed that the \"energy element\" must be proportional to the frequency of the oscillator, the first version of what is now sometimes termed the \"Planck–Einstein relation\":\nformula_13\nPlanck was able to calculate the value of formula_1 from experimental data on black-body radiation: his result, , is within 1.2% of the currently accepted value.", "He also made the first determination of the Boltzmann constant formula_5 from the same data and theory.", "The black-body problem was revisited in 1905, when Lord Rayleigh and James Jeans (on the one hand) and Albert Einstein (on the other hand) independently proved that classical electromagnetism could \"never\" account for the observed spectrum.", "These proofs are commonly known as the \"ultraviolet catastrophe\", a name coined by Paul Ehrenfest in 1911.", "They contributed greatly (along with Einstein's work on the photoelectric effect) in convincing physicists that Planck's postulate of quantized energy levels was more than a mere mathematical formalism.", "The first Solvay Conference in 1911 was devoted to \"the theory of radiation and quanta\".", "The photoelectric effect is the emission of electrons (called \"photoelectrons\") from a surface when light is shone on it.", "It was first observed by Alexandre Edmond Becquerel in 1839, although credit is usually reserved for Heinrich Hertz, who published the first thorough investigation in 1887.", "Another particularly thorough investigation was published by Philipp Lenard (Lénárd Fülöp) in 1902.", "Einstein's 1905 paper discussing the effect in terms of light quanta would earn him the Nobel Prize in 1921, after his predictions had been confirmed by the experimental work of Robert Andrews Millikan.", "The Nobel committee awarded the prize for his work on the photo-electric effect, rather than relativity, both because of a bias against purely theoretical physics not grounded in discovery or experiment, and dissent amongst its members as to the actual proof that relativity was real.", "Before Einstein's paper, electromagnetic radiation such as visible light was considered to behave as a wave: hence the use of the terms \"frequency\" and \"wavelength\" to characterize different types of radiation.", "The energy transferred by a wave in a given time is called its intensity.", "The light from a theatre spotlight is more \"intense\" than the light from a domestic lightbulb; that is to say that the spotlight gives out more energy per unit time and per unit space (and hence consumes more electricity) than the ordinary bulb, even though the color of the light might be very similar.", "Other waves, such as sound or the waves crashing against a seafront, also have their intensity.", "However, the energy account of the photoelectric effect didn't seem to agree with the wave description of light.", "The \"photoelectrons\" emitted as a result of the photoelectric effect have a certain kinetic energy, which can be measured.", "This kinetic energy (for each photoelectron) is \"independent\" of the intensity of the light, but depends linearly on the frequency; and if the frequency is too low (corresponding to a photon energy that is less than the work function of the material), no photoelectrons are emitted at all, unless a plurality of photons, whose energetic sum is greater than the energy of the photoelectrons, acts virtually simultaneously (multiphoton effect).", "Assuming the frequency is high enough to cause the photoelectric effect, a rise in intensity of the light source causes more photoelectrons to be emitted with the same kinetic energy, rather than the same number of photoelectrons to be emitted with higher kinetic energy.", "Einstein's explanation for these observations was that light itself is quantized; that the energy of light is not transferred continuously as in a classical wave, but only in small \"packets\" or quanta.", "The size of these \"packets\" of energy, which would later be named photons, was to be the same as Planck's \"energy element\", giving the modern version of the Planck–Einstein relation:\nformula_16\nEinstein's postulate was later proven experimentally: the constant of proportionality between the frequency of incident light formula_17 and the kinetic energy of photoelectrons formula_18 was shown to be equal to the Planck constant formula_1.", "It was John William Nicholson in 1912 who introduced h-bar into the theory of the atom which was the first quantum and nuclear atom and the first to quantize angular momentum as \"h\"/2.", "Niels Bohr quoted him in his 1913 paper of the Bohr model of the atom.", "The influence of the work of Nicholson’s nuclear quantum atomic model on Bohr’s model has been written about by many historians.", "Niels Bohr introduced the third quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model.", "The first quantized model of the atom was introduced in 1910 by Arthur Erich Haas and much discussed at the 1911 Solvay conference.", "In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation.", "If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus.", "Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies formula_20\nformula_21\nwhere formula_22 is the speed of light in vacuum, formula_23 is an experimentally determined constant (the Rydberg constant) and formula_24.", "Once the electron reached the lowest energy level (formula_25), it could not get any closer to the nucleus (lower energy).", "This approach also allowed Bohr to account for the Rydberg formula, an empirical description of the atomic spectrum of hydrogen, and to account for the value of the Rydberg constant formula_23 in terms of other fundamental constants.", "Bohr also introduced the quantity formula_27, now known as the reduced Planck constant, as the quantum of angular momentum.", "At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model.", "The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum.", "In modern terms, if formula_28 is the total angular momentum of a system with rotational invariance, and formula_29 the angular momentum measured along any given direction, these quantities can only take on the values\nformula_30", "The Planck constant also occurs in statements of Werner Heisenberg's uncertainty principle.", "Given numerous particles prepared in the same state, the uncertainty in their position, formula_31, and the uncertainty in their momentum, formula_32, obey\nformula_33\nwhere the uncertainty is given as the standard deviation of the measured value from its expected value.", "There are several other such pairs of physically measurable conjugate variables which obey a similar rule.", "One example is time vs. energy.", "The inverse relationship between the uncertainty of the two conjugate variables forces a tradeoff in quantum experiments, as measuring one quantity more precisely results in the other quantity becoming imprecise.", "In addition to some assumptions underlying the interpretation of certain values in the quantum mechanical formulation, one of the fundamental cornerstones to the entire theory lies in the commutator relationship between the position operator formula_34 and the momentum operator formula_35:\nformula_36\nwhere formula_37 is the Kronecker delta.", "The Planck relation connects the particular photon energy with its associated wave frequency :\nformula_38\nThis energy is extremely small in terms of ordinarily perceived everyday objects.", "Since the frequency , wavelength , and speed of light are related by formula_39, the relation can also be expressed as\nformula_40", "In 1923, Louis de Broglie generalized the Planck–Einstein relation by postulating that the Planck constant represents the proportionality between the momentum and the quantum wavelength of not just the photon, but the quantum wavelength of any particle.", "This was confirmed by experiments soon afterward.", "This holds throughout the quantum theory, including electrodynamics.", "The de Broglie wavelength of the particle is given by\nformula_41\nwhere denotes the linear momentum of a particle, such as a photon, or any other elementary particle.", "The energy of a photon with angular frequency is given by\nformula_42\nwhile its linear momentum relates to\nformula_43\nwhere is an angular wavenumber.", "These two relations are the temporal and spatial parts of the special relativistic expression using 4-vectors.", "formula_44", "Classical statistical mechanics requires the existence of (but does not define its value).", "Eventually, following upon Planck's discovery, it was speculated that physical action could not take on an arbitrary value, but instead was restricted to integer multiples of a very small quantity, the \"[elementary] quantum of action\", now called the \"Planck constant\".", "This was a significant conceptual part of the so-called \"old quantum theory\" developed by physicists including Bohr, Sommerfeld, and Ishiwara, in which particle trajectories exist but are hidden, but quantum laws constrain them based on their action.", "This view has been replaced by fully modern quantum theory, in which definite trajectories of motion do not even exist; rather, the particle is represented by a wavefunction spread out in space and in time.", "Thus there is no value of the action as classically defined.", "Related to this is the concept of energy quantization which existed in old quantum theory and also exists in altered form in modern quantum physics.", "Classical physics cannot explain either quantization of energy or the lack of classical particle motion.", "In many cases, such as for monochromatic light or for atoms, quantization of energy also implies that only certain energy levels are allowed, and values in between are forbidden.", "Implicit in the dimensions of the Planck constant is the fact that the SI unit of frequency, the hertz, represents one complete cycle, 360 degrees or radians, per second.", "In applications where it is natural to use the angular frequency (i.e. where the frequency is expressed in terms of radians per second instead of cycles per second or hertz)", "it is often useful to absorb a factor of into the Planck constant.", "The resulting constant is called the reduced Planck constant.", "It is equal to the Planck constant divided by , and is denoted formula_45 (pronounced \"h-bar\"):\nformula_46", "The Planck constant has dimensions of angular momentum.", "In SI units, the Planck constant is expressed in joules per hertz (J⋅Hz or kg⋅m2⋅s−1).", "formula_47\nformula_48\nThe above values have been adopted as fixed in the 2019 redefinition of the SI base units.", "In the system of \"natural units\" used by theoretical physicists, formula_45, the reduced Planck constant, is defined to be exactly one.", "In these units, is then exactly formula_50", "Since 2019, the numerical value of the Planck constant has been fixed, with a finite decimal representation.", "Under the present definition of the kilogram, which states that \"The kilogram [...] is defined by taking the fixed numerical value of to be when expressed in the unit J⋅s, which is equal to kg⋅m2⋅s−1, where the metre and the second are defined in terms of speed of light and duration of hyperfine transition of the ground state of an unperturbed caesium-133 atom .\"", "This implies that mass metrology is now aimed to find the value of one kilogram, and thus it is kilogram which is \"compensating\".", "Every experiment aiming to measure the kilogram (such as the Kibble balance and the X-ray crystal density method), will essentially refine the value of a kilogram.", "As an illustration of this, suppose the decision of making to be exact was taken in 2010, when its measured value was , thus the present definition of kilogram was also enforced.", "In the future, the value of one kilogram must be refined to times the mass of the International Prototype of the Kilogram (IPK).", "The Planck constant is related to the quantization of light and matter.", "It can be seen as a subatomic-scale constant.", "In a unit system adapted to subatomic scales, the electronvolt is the appropriate unit of energy and the petahertz the appropriate unit of frequency.", "Atomic unit systems are based (in part) on the Planck constant.", "The physical meaning of the Planck constant could suggest some basic features of our physical world.", "The Planck constant is one of the smallest constants used in physics.", "This reflects the fact that on a scale adapted to humans, where energies are typical of the order of kilojoules and times are typical of the order of seconds or minutes, the Planck constant is very small.", "One can regard the Planck constant to be only relevant to the microscopic scale instead of the macroscopic scale in our everyday experience.", "Equivalently, the order of the Planck constant reflects the fact that everyday objects and systems are made of a \"large\" number of microscopic particles.", "For example, green light with a wavelength of 555 nanometres (a wavelength that can be perceived by the human eye to be green) has a frequency of ().", "Each photon has an energy .", "That is a very small amount of energy in terms of everyday experience, but everyday experience is not concerned with individual photons any more than with individual atoms or molecules.", "An amount of light more typical in everyday experience (though much larger than the smallest amount perceivable by the human eye) is the energy of one mole of photons; its energy can be computed by multiplying the photon energy by the Avogadro constant, , with the result of , about the food energy in three apples.", "In principle, the Planck constant can be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons, and this is how its value was first calculated in the early twentieth century.", "In practice, these are no longer the most accurate methods.", "Since the value of the Planck constant is fixed now, it is no longer determined or calculated in laboratories.", "Some of the practices given below to determine the Planck constant are now used to determine the mass of the kilogram.", "The below-given methods \"except\" the X-ray crystal density method rely on the theoretical basis of the Josephson effect and the quantum Hall effect.", "The Josephson constant \"K\"J relates the potential difference \"U\" generated by the Josephson effect at a \"Josephson junction\" with the frequency \"ν\" of the microwave radiation.", "The theoretical treatment of Josephson effect suggests very strongly that .", "formula_51\nThe Josephson constant may be measured by comparing the potential difference generated by an array of Josephson junctions with a potential difference which is known in SI volts.", "The measurement of the potential difference in SI units is done by allowing an electrostatic force to cancel out a measurable gravitational force, in a Kibble balance.", "Assuming the validity of the theoretical treatment of the Josephson effect, \"K\"J is related to the Planck constant by\nformula_52", "A Kibble balance (formerly known as a watt balance) is an instrument for comparing two powers, one of which is measured in SI watts and the other of which is measured in conventional electrical units.", "From the definition of the \"conventional\" watt \"W\"90, this gives a measure of the product \"K\"J2\"R\"K in SI units, where \"R\"K is the von Klitzing constant which appears in the quantum Hall effect.", "If the theoretical treatments of the Josephson effect and the quantum Hall effect are valid, and in particular assuming that , the measurement of \"K\"J2\"R\"K is a direct determination of the Planck constant.", "formula_53", "The gyromagnetic ratio \"γ\" is the constant of proportionality between the frequency \"ν\" of nuclear magnetic resonance (or electron paramagnetic resonance for electrons) and the applied magnetic field .", "It is difficult to measure gyromagnetic ratios precisely because of the difficulties in precisely measuring \"B\", but the value for protons in water at is known to better than one part per million.", "The protons are said to be \"shielded\" from the applied magnetic field by the electrons in the water molecule, the same effect that gives rise to chemical shift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, \"γ\"′p.", "The gyromagnetic ratio is related to the shielded proton magnetic moment \"μ\"′p, the spin number \"I\" ( for protons) and the reduced Planck constant.", "formula_54\nThe ratio of the shielded proton magnetic moment \"μ\"′p to the electron magnetic moment \"μ\"e can be measured separately and to high precision, as the imprecisely known value of the applied magnetic field cancels itself out in taking the ratio.", "The value of \"μ\"e in Bohr magnetons is also known: it is half the electron g-factor \"g\"e.", "Hence\nformula_55\nformula_56\nA further complication is that the measurement of \"γ\"′p involves the measurement of an electric current: this is invariably measured in \"conventional\" amperes rather than in SI amperes, so a conversion factor is required.", "The symbol \"Γ\"′p-90 is used for the measured gyromagnetic ratio using conventional electrical units.", "In addition, there are two methods of measuring the value, a \"low-field\" method and a \"high-field\" method, and the conversion factors are different in the two cases.", "Only the high-field value \"Γ\"′p-90(hi) is of interest in determining the Planck constant.", "formula_57\nSubstitution gives the expression for the Planck constant in terms of \"Γ\"′p-90(hi):\nformula_58", "The Faraday constant \"F\" is the charge of one mole of electrons, equal to the Avogadro constant \"N\"A multiplied by the elementary charge \"e\".", "It can be determined by careful electrolysis experiments, measuring the amount of silver dissolved from an electrode in a given time and for a given electric current.", "Substituting the definitions of \"N\"A and \"e\" gives the relation to the Planck constant.", "formula_59", "The X-ray crystal density method is primarily a method for determining the Avogadro constant \"N\"A but as the Avogadro constant is related to the Planck constant it also determines a value for \"h\".", "The principle behind the method is to determine \"N\"A as the ratio between the volume of the unit cell of a crystal, measured by X-ray crystallography, and the molar volume of the substance.", "Crystals of silicon are used, as they are available in high quality and purity by the technology developed for the semiconductor industry.", "The unit cell volume is calculated from the spacing between two crystal planes referred to as \"d\"220.", "The molar volume \"V\"m(Si) requires a knowledge of the density of the crystal and the atomic weight of the silicon used.", "The Planck constant is given by\nformula_60", "The experimental measurement of the Planck constant in the Large Hadron Collider laboratory was carried out in 2011.", "The study called PCC using a giant particle accelerator helped to better understand the relationships between the Planck constant and measuring distances in space." ]

[ 82, 83, 84, 85, 86 ]

[ "In metrology it is used, together with other constants, to define the kilogram, an SI unit." ]

[ "Planck's constant was formulated as part of Max Planck's successful effort to produce a mathematical expression that accurately predicted the observed spectral distribution of thermal radiation from a closed furnace (black-body radiation).", "This mathematical expression is now known as Planck's law.", "In the last years of the 19th century, Max Planck was investigating the problem of black-body radiation first posed by Kirchhoff some 40 years earlier.", "Every physical body spontaneously and continuously emits electromagnetic radiation.", "There was no expression or explanation for the overall shape of the observed emission spectrum.", "At the time, Wien's law fit the data for short wavelengths and high temperatures, but failed for long wavelengths.", "Also around this time, but unknown to Planck, Lord Rayleigh had derived theoretically a formula, now known as the Rayleigh–Jeans law, that could reasonably predict long wavelengths but failed dramatically at short wavelengths.", "Approaching this problem, Planck hypothesized that the equations of motion for light describe a set of harmonic oscillators, one for each possible frequency.", "He examined how the entropy of the oscillators varied with the temperature of the body, trying to match Wien's law, and was able to derive an approximate mathematical function for the black-body spectrum, which gave a simple empirical formula for long wavelengths.", "Planck tried to find a mathematical expression that could reproduce Wien's law (for short wavelengths) and the empirical formula (for long wavelengths).", "This expression included a constant, formula_3, which is thought to be for Hilfsgrösse (auxiliary variable), and subsequently became known as the Planck constant.", "The expression formulated by Planck showed that the spectral radiance of a body for frequency at absolute temperature is given by\nformula_4\nwhere formula_5 is the Boltzmann constant, formula_3 is the Planck constant, and formula_7 is the speed of light in the medium, whether material or vacuum.", "The spectral radiance of a body, formula_8, describes the amount of energy it emits at different radiation frequencies.", "It is the power emitted per unit area of the body, per unit solid angle of emission, per unit frequency.", "The spectral radiance can also be expressed per unit wavelength formula_9 instead of per unit frequency.", "In this case, it is given by\nformula_10\nshowing how radiated energy emitted at shorter wavelengths increases more rapidly with temperature than energy emitted at longer wavelengths.", "Planck's law may also be expressed in other terms, such as the number of photons emitted at a certain wavelength, or the energy density in a volume of radiation.", "The SI units of formula_8 are , while those of formula_12 are .", "Planck soon realized that his solution was not unique.", "There were several different solutions, each of which gave a different value for the entropy of the oscillators.", "To save his theory, Planck resorted to using the then-controversial theory of statistical mechanics, which he described as \"an act of despair …", "I was ready to sacrifice any of my previous convictions about physics.\"", "One of his new boundary conditions was\nWith this new condition, Planck had imposed the quantization of the energy of the oscillators, \"a purely formal assumption …", "actually I did not think much about it ...\" in his own words, but one that would revolutionize physics.", "Applying this new approach to Wien's displacement law showed that the \"energy element\" must be proportional to the frequency of the oscillator, the first version of what is now sometimes termed the \"Planck–Einstein relation\":\nformula_13\nPlanck was able to calculate the value of formula_1 from experimental data on black-body radiation: his result, , is within 1.2% of the currently accepted value.", "He also made the first determination of the Boltzmann constant formula_5 from the same data and theory.", "The black-body problem was revisited in 1905, when Lord Rayleigh and James Jeans (on the one hand) and Albert Einstein (on the other hand) independently proved that classical electromagnetism could \"never\" account for the observed spectrum.", "These proofs are commonly known as the \"ultraviolet catastrophe\", a name coined by Paul Ehrenfest in 1911.", "They contributed greatly (along with Einstein's work on the photoelectric effect) in convincing physicists that Planck's postulate of quantized energy levels was more than a mere mathematical formalism.", "The first Solvay Conference in 1911 was devoted to \"the theory of radiation and quanta\".", "The photoelectric effect is the emission of electrons (called \"photoelectrons\") from a surface when light is shone on it.", "It was first observed by Alexandre Edmond Becquerel in 1839, although credit is usually reserved for Heinrich Hertz, who published the first thorough investigation in 1887.", "Another particularly thorough investigation was published by Philipp Lenard (Lénárd Fülöp) in 1902.", "Einstein's 1905 paper discussing the effect in terms of light quanta would earn him the Nobel Prize in 1921, after his predictions had been confirmed by the experimental work of Robert Andrews Millikan.", "The Nobel committee awarded the prize for his work on the photo-electric effect, rather than relativity, both because of a bias against purely theoretical physics not grounded in discovery or experiment, and dissent amongst its members as to the actual proof that relativity was real.", "Before Einstein's paper, electromagnetic radiation such as visible light was considered to behave as a wave: hence the use of the terms \"frequency\" and \"wavelength\" to characterize different types of radiation.", "The energy transferred by a wave in a given time is called its intensity.", "The light from a theatre spotlight is more \"intense\" than the light from a domestic lightbulb; that is to say that the spotlight gives out more energy per unit time and per unit space (and hence consumes more electricity) than the ordinary bulb, even though the color of the light might be very similar.", "Other waves, such as sound or the waves crashing against a seafront, also have their intensity.", "However, the energy account of the photoelectric effect didn't seem to agree with the wave description of light.", "The \"photoelectrons\" emitted as a result of the photoelectric effect have a certain kinetic energy, which can be measured.", "This kinetic energy (for each photoelectron) is \"independent\" of the intensity of the light, but depends linearly on the frequency; and if the frequency is too low (corresponding to a photon energy that is less than the work function of the material), no photoelectrons are emitted at all, unless a plurality of photons, whose energetic sum is greater than the energy of the photoelectrons, acts virtually simultaneously (multiphoton effect).", "Assuming the frequency is high enough to cause the photoelectric effect, a rise in intensity of the light source causes more photoelectrons to be emitted with the same kinetic energy, rather than the same number of photoelectrons to be emitted with higher kinetic energy.", "Einstein's explanation for these observations was that light itself is quantized; that the energy of light is not transferred continuously as in a classical wave, but only in small \"packets\" or quanta.", "The size of these \"packets\" of energy, which would later be named photons, was to be the same as Planck's \"energy element\", giving the modern version of the Planck–Einstein relation:\nformula_16\nEinstein's postulate was later proven experimentally: the constant of proportionality between the frequency of incident light formula_17 and the kinetic energy of photoelectrons formula_18 was shown to be equal to the Planck constant formula_1.", "It was John William Nicholson in 1912 who introduced h-bar into the theory of the atom which was the first quantum and nuclear atom and the first to quantize angular momentum as \"h\"/2.", "Niels Bohr quoted him in his 1913 paper of the Bohr model of the atom.", "The influence of the work of Nicholson’s nuclear quantum atomic model on Bohr’s model has been written about by many historians.", "Niels Bohr introduced the third quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model.", "The first quantized model of the atom was introduced in 1910 by Arthur Erich Haas and much discussed at the 1911 Solvay conference.", "In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation.", "If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus.", "Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies formula_20\nformula_21\nwhere formula_22 is the speed of light in vacuum, formula_23 is an experimentally determined constant (the Rydberg constant) and formula_24.", "Once the electron reached the lowest energy level (formula_25), it could not get any closer to the nucleus (lower energy).", "This approach also allowed Bohr to account for the Rydberg formula, an empirical description of the atomic spectrum of hydrogen, and to account for the value of the Rydberg constant formula_23 in terms of other fundamental constants.", "Bohr also introduced the quantity formula_27, now known as the reduced Planck constant, as the quantum of angular momentum.", "At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model.", "The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum.", "In modern terms, if formula_28 is the total angular momentum of a system with rotational invariance, and formula_29 the angular momentum measured along any given direction, these quantities can only take on the values\nformula_30", "The Planck constant also occurs in statements of Werner Heisenberg's uncertainty principle.", "Given numerous particles prepared in the same state, the uncertainty in their position, formula_31, and the uncertainty in their momentum, formula_32, obey\nformula_33\nwhere the uncertainty is given as the standard deviation of the measured value from its expected value.", "There are several other such pairs of physically measurable conjugate variables which obey a similar rule.", "One example is time vs. energy.", "The inverse relationship between the uncertainty of the two conjugate variables forces a tradeoff in quantum experiments, as measuring one quantity more precisely results in the other quantity becoming imprecise.", "In addition to some assumptions underlying the interpretation of certain values in the quantum mechanical formulation, one of the fundamental cornerstones to the entire theory lies in the commutator relationship between the position operator formula_34 and the momentum operator formula_35:\nformula_36\nwhere formula_37 is the Kronecker delta.", "The Planck relation connects the particular photon energy with its associated wave frequency :\nformula_38\nThis energy is extremely small in terms of ordinarily perceived everyday objects.", "Since the frequency , wavelength , and speed of light are related by formula_39, the relation can also be expressed as\nformula_40", "In 1923, Louis de Broglie generalized the Planck–Einstein relation by postulating that the Planck constant represents the proportionality between the momentum and the quantum wavelength of not just the photon, but the quantum wavelength of any particle.", "This was confirmed by experiments soon afterward.", "This holds throughout the quantum theory, including electrodynamics.", "The de Broglie wavelength of the particle is given by\nformula_41\nwhere denotes the linear momentum of a particle, such as a photon, or any other elementary particle.", "The energy of a photon with angular frequency is given by\nformula_42\nwhile its linear momentum relates to\nformula_43\nwhere is an angular wavenumber.", "These two relations are the temporal and spatial parts of the special relativistic expression using 4-vectors.", "formula_44", "Classical statistical mechanics requires the existence of (but does not define its value).", "Eventually, following upon Planck's discovery, it was speculated that physical action could not take on an arbitrary value, but instead was restricted to integer multiples of a very small quantity, the \"[elementary] quantum of action\", now called the \"Planck constant\".", "This was a significant conceptual part of the so-called \"old quantum theory\" developed by physicists including Bohr, Sommerfeld, and Ishiwara, in which particle trajectories exist but are hidden, but quantum laws constrain them based on their action.", "This view has been replaced by fully modern quantum theory, in which definite trajectories of motion do not even exist; rather, the particle is represented by a wavefunction spread out in space and in time.", "Thus there is no value of the action as classically defined.", "Related to this is the concept of energy quantization which existed in old quantum theory and also exists in altered form in modern quantum physics.", "Classical physics cannot explain either quantization of energy or the lack of classical particle motion.", "In many cases, such as for monochromatic light or for atoms, quantization of energy also implies that only certain energy levels are allowed, and values in between are forbidden.", "Implicit in the dimensions of the Planck constant is the fact that the SI unit of frequency, the hertz, represents one complete cycle, 360 degrees or radians, per second.", "In applications where it is natural to use the angular frequency (i.e. where the frequency is expressed in terms of radians per second instead of cycles per second or hertz)", "it is often useful to absorb a factor of into the Planck constant.", "The resulting constant is called the reduced Planck constant.", "It is equal to the Planck constant divided by , and is denoted formula_45 (pronounced \"h-bar\"):\nformula_46", "The Planck constant has dimensions of angular momentum.", "In SI units, the Planck constant is expressed in joules per hertz (J⋅Hz or kg⋅m2⋅s−1).", "formula_47\nformula_48\nThe above values have been adopted as fixed in the 2019 redefinition of the SI base units.", "In the system of \"natural units\" used by theoretical physicists, formula_45, the reduced Planck constant, is defined to be exactly one.", "In these units, is then exactly formula_50", "Since 2019, the numerical value of the Planck constant has been fixed, with a finite decimal representation.", "Under the present definition of the kilogram, which states that \"The kilogram [...] is defined by taking the fixed numerical value of to be when expressed in the unit J⋅s, which is equal to kg⋅m2⋅s−1, where the metre and the second are defined in terms of speed of light and duration of hyperfine transition of the ground state of an unperturbed caesium-133 atom .\"", "This implies that mass metrology is now aimed to find the value of one kilogram, and thus it is kilogram which is \"compensating\".", "Every experiment aiming to measure the kilogram (such as the Kibble balance and the X-ray crystal density method), will essentially refine the value of a kilogram.", "As an illustration of this, suppose the decision of making to be exact was taken in 2010, when its measured value was , thus the present definition of kilogram was also enforced.", "In the future, the value of one kilogram must be refined to times the mass of the International Prototype of the Kilogram (IPK).", "The Planck constant is related to the quantization of light and matter.", "It can be seen as a subatomic-scale constant.", "In a unit system adapted to subatomic scales, the electronvolt is the appropriate unit of energy and the petahertz the appropriate unit of frequency.", "Atomic unit systems are based (in part) on the Planck constant.", "The physical meaning of the Planck constant could suggest some basic features of our physical world.", "The Planck constant is one of the smallest constants used in physics.", "This reflects the fact that on a scale adapted to humans, where energies are typical of the order of kilojoules and times are typical of the order of seconds or minutes, the Planck constant is very small.", "One can regard the Planck constant to be only relevant to the microscopic scale instead of the macroscopic scale in our everyday experience.", "Equivalently, the order of the Planck constant reflects the fact that everyday objects and systems are made of a \"large\" number of microscopic particles.", "For example, green light with a wavelength of 555 nanometres (a wavelength that can be perceived by the human eye to be green) has a frequency of ().", "Each photon has an energy .", "That is a very small amount of energy in terms of everyday experience, but everyday experience is not concerned with individual photons any more than with individual atoms or molecules.", "An amount of light more typical in everyday experience (though much larger than the smallest amount perceivable by the human eye) is the energy of one mole of photons; its energy can be computed by multiplying the photon energy by the Avogadro constant, , with the result of , about the food energy in three apples.", "In principle, the Planck constant can be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons, and this is how its value was first calculated in the early twentieth century.", "In practice, these are no longer the most accurate methods.", "Since the value of the Planck constant is fixed now, it is no longer determined or calculated in laboratories.", "Some of the practices given below to determine the Planck constant are now used to determine the mass of the kilogram.", "The below-given methods \"except\" the X-ray crystal density method rely on the theoretical basis of the Josephson effect and the quantum Hall effect.", "The Josephson constant \"K\"J relates the potential difference \"U\" generated by the Josephson effect at a \"Josephson junction\" with the frequency \"ν\" of the microwave radiation.", "The theoretical treatment of Josephson effect suggests very strongly that .", "formula_51\nThe Josephson constant may be measured by comparing the potential difference generated by an array of Josephson junctions with a potential difference which is known in SI volts.", "The measurement of the potential difference in SI units is done by allowing an electrostatic force to cancel out a measurable gravitational force, in a Kibble balance.", "Assuming the validity of the theoretical treatment of the Josephson effect, \"K\"J is related to the Planck constant by\nformula_52", "A Kibble balance (formerly known as a watt balance) is an instrument for comparing two powers, one of which is measured in SI watts and the other of which is measured in conventional electrical units.", "From the definition of the \"conventional\" watt \"W\"90, this gives a measure of the product \"K\"J2\"R\"K in SI units, where \"R\"K is the von Klitzing constant which appears in the quantum Hall effect.", "If the theoretical treatments of the Josephson effect and the quantum Hall effect are valid, and in particular assuming that , the measurement of \"K\"J2\"R\"K is a direct determination of the Planck constant.", "formula_53", "The gyromagnetic ratio \"γ\" is the constant of proportionality between the frequency \"ν\" of nuclear magnetic resonance (or electron paramagnetic resonance for electrons) and the applied magnetic field .", "It is difficult to measure gyromagnetic ratios precisely because of the difficulties in precisely measuring \"B\", but the value for protons in water at is known to better than one part per million.", "The protons are said to be \"shielded\" from the applied magnetic field by the electrons in the water molecule, the same effect that gives rise to chemical shift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, \"γ\"′p.", "The gyromagnetic ratio is related to the shielded proton magnetic moment \"μ\"′p, the spin number \"I\" ( for protons) and the reduced Planck constant.", "formula_54\nThe ratio of the shielded proton magnetic moment \"μ\"′p to the electron magnetic moment \"μ\"e can be measured separately and to high precision, as the imprecisely known value of the applied magnetic field cancels itself out in taking the ratio.", "The value of \"μ\"e in Bohr magnetons is also known: it is half the electron g-factor \"g\"e.", "Hence\nformula_55\nformula_56\nA further complication is that the measurement of \"γ\"′p involves the measurement of an electric current: this is invariably measured in \"conventional\" amperes rather than in SI amperes, so a conversion factor is required.", "The symbol \"Γ\"′p-90 is used for the measured gyromagnetic ratio using conventional electrical units.", "In addition, there are two methods of measuring the value, a \"low-field\" method and a \"high-field\" method, and the conversion factors are different in the two cases.", "Only the high-field value \"Γ\"′p-90(hi) is of interest in determining the Planck constant.", "formula_57\nSubstitution gives the expression for the Planck constant in terms of \"Γ\"′p-90(hi):\nformula_58", "The Faraday constant \"F\" is the charge of one mole of electrons, equal to the Avogadro constant \"N\"A multiplied by the elementary charge \"e\".", "It can be determined by careful electrolysis experiments, measuring the amount of silver dissolved from an electrode in a given time and for a given electric current.", "Substituting the definitions of \"N\"A and \"e\" gives the relation to the Planck constant.", "formula_59", "The X-ray crystal density method is primarily a method for determining the Avogadro constant \"N\"A but as the Avogadro constant is related to the Planck constant it also determines a value for \"h\".", "The principle behind the method is to determine \"N\"A as the ratio between the volume of the unit cell of a crystal, measured by X-ray crystallography, and the molar volume of the substance.", "Crystals of silicon are used, as they are available in high quality and purity by the technology developed for the semiconductor industry.", "The unit cell volume is calculated from the spacing between two crystal planes referred to as \"d\"220.", "The molar volume \"V\"m(Si) requires a knowledge of the density of the crystal and the atomic weight of the silicon used.", "The Planck constant is given by\nformula_60", "The experimental measurement of the Planck constant in the Large Hadron Collider laboratory was carried out in 2011.", "The study called PCC using a giant particle accelerator helped to better understand the relationships between the Planck constant and measuring distances in space." ]

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[ "A photon's energy is equal to its frequency multiplied by the Planck constant.", "Due to mass–energy equivalence, the Planck constant also relates mass to frequency.", "In metrology it is used, together with other constants, to define the kilogram, an SI unit.", "The SI units are defined in such a way that, when the Planck constant is expressed in SI units, it has the exact value" ]

[ "Planck's constant was formulated as part of Max Planck's successful effort to produce a mathematical expression that accurately predicted the observed spectral distribution of thermal radiation from a closed furnace (black-body radiation).", "This mathematical expression is now known as Planck's law.", "In the last years of the 19th century, Max Planck was investigating the problem of black-body radiation first posed by Kirchhoff some 40 years earlier.", "Every physical body spontaneously and continuously emits electromagnetic radiation.", "There was no expression or explanation for the overall shape of the observed emission spectrum.", "At the time, Wien's law fit the data for short wavelengths and high temperatures, but failed for long wavelengths.", "Also around this time, but unknown to Planck, Lord Rayleigh had derived theoretically a formula, now known as the Rayleigh–Jeans law, that could reasonably predict long wavelengths but failed dramatically at short wavelengths.", "Approaching this problem, Planck hypothesized that the equations of motion for light describe a set of harmonic oscillators, one for each possible frequency.", "He examined how the entropy of the oscillators varied with the temperature of the body, trying to match Wien's law, and was able to derive an approximate mathematical function for the black-body spectrum, which gave a simple empirical formula for long wavelengths.", "Planck tried to find a mathematical expression that could reproduce Wien's law (for short wavelengths) and the empirical formula (for long wavelengths).", "This expression included a constant, formula_3, which is thought to be for Hilfsgrösse (auxiliary variable), and subsequently became known as the Planck constant.", "The expression formulated by Planck showed that the spectral radiance of a body for frequency at absolute temperature is given by\nformula_4\nwhere formula_5 is the Boltzmann constant, formula_3 is the Planck constant, and formula_7 is the speed of light in the medium, whether material or vacuum.", "The spectral radiance of a body, formula_8, describes the amount of energy it emits at different radiation frequencies.", "It is the power emitted per unit area of the body, per unit solid angle of emission, per unit frequency.", "The spectral radiance can also be expressed per unit wavelength formula_9 instead of per unit frequency.", "In this case, it is given by\nformula_10\nshowing how radiated energy emitted at shorter wavelengths increases more rapidly with temperature than energy emitted at longer wavelengths.", "Planck's law may also be expressed in other terms, such as the number of photons emitted at a certain wavelength, or the energy density in a volume of radiation.", "The SI units of formula_8 are , while those of formula_12 are .", "Planck soon realized that his solution was not unique.", "There were several different solutions, each of which gave a different value for the entropy of the oscillators.", "To save his theory, Planck resorted to using the then-controversial theory of statistical mechanics, which he described as \"an act of despair …", "I was ready to sacrifice any of my previous convictions about physics.\"", "One of his new boundary conditions was\nWith this new condition, Planck had imposed the quantization of the energy of the oscillators, \"a purely formal assumption …", "actually I did not think much about it ...\" in his own words, but one that would revolutionize physics.", "Applying this new approach to Wien's displacement law showed that the \"energy element\" must be proportional to the frequency of the oscillator, the first version of what is now sometimes termed the \"Planck–Einstein relation\":\nformula_13\nPlanck was able to calculate the value of formula_1 from experimental data on black-body radiation: his result, , is within 1.2% of the currently accepted value.", "He also made the first determination of the Boltzmann constant formula_5 from the same data and theory.", "The black-body problem was revisited in 1905, when Lord Rayleigh and James Jeans (on the one hand) and Albert Einstein (on the other hand) independently proved that classical electromagnetism could \"never\" account for the observed spectrum.", "These proofs are commonly known as the \"ultraviolet catastrophe\", a name coined by Paul Ehrenfest in 1911.", "They contributed greatly (along with Einstein's work on the photoelectric effect) in convincing physicists that Planck's postulate of quantized energy levels was more than a mere mathematical formalism.", "The first Solvay Conference in 1911 was devoted to \"the theory of radiation and quanta\".", "The photoelectric effect is the emission of electrons (called \"photoelectrons\") from a surface when light is shone on it.", "It was first observed by Alexandre Edmond Becquerel in 1839, although credit is usually reserved for Heinrich Hertz, who published the first thorough investigation in 1887.", "Another particularly thorough investigation was published by Philipp Lenard (Lénárd Fülöp) in 1902.", "Einstein's 1905 paper discussing the effect in terms of light quanta would earn him the Nobel Prize in 1921, after his predictions had been confirmed by the experimental work of Robert Andrews Millikan.", "The Nobel committee awarded the prize for his work on the photo-electric effect, rather than relativity, both because of a bias against purely theoretical physics not grounded in discovery or experiment, and dissent amongst its members as to the actual proof that relativity was real.", "Before Einstein's paper, electromagnetic radiation such as visible light was considered to behave as a wave: hence the use of the terms \"frequency\" and \"wavelength\" to characterize different types of radiation.", "The energy transferred by a wave in a given time is called its intensity.", "The light from a theatre spotlight is more \"intense\" than the light from a domestic lightbulb; that is to say that the spotlight gives out more energy per unit time and per unit space (and hence consumes more electricity) than the ordinary bulb, even though the color of the light might be very similar.", "Other waves, such as sound or the waves crashing against a seafront, also have their intensity.", "However, the energy account of the photoelectric effect didn't seem to agree with the wave description of light.", "The \"photoelectrons\" emitted as a result of the photoelectric effect have a certain kinetic energy, which can be measured.", "This kinetic energy (for each photoelectron) is \"independent\" of the intensity of the light, but depends linearly on the frequency; and if the frequency is too low (corresponding to a photon energy that is less than the work function of the material), no photoelectrons are emitted at all, unless a plurality of photons, whose energetic sum is greater than the energy of the photoelectrons, acts virtually simultaneously (multiphoton effect).", "Assuming the frequency is high enough to cause the photoelectric effect, a rise in intensity of the light source causes more photoelectrons to be emitted with the same kinetic energy, rather than the same number of photoelectrons to be emitted with higher kinetic energy.", "Einstein's explanation for these observations was that light itself is quantized; that the energy of light is not transferred continuously as in a classical wave, but only in small \"packets\" or quanta.", "The size of these \"packets\" of energy, which would later be named photons, was to be the same as Planck's \"energy element\", giving the modern version of the Planck–Einstein relation:\nformula_16\nEinstein's postulate was later proven experimentally: the constant of proportionality between the frequency of incident light formula_17 and the kinetic energy of photoelectrons formula_18 was shown to be equal to the Planck constant formula_1.", "It was John William Nicholson in 1912 who introduced h-bar into the theory of the atom which was the first quantum and nuclear atom and the first to quantize angular momentum as \"h\"/2.", "Niels Bohr quoted him in his 1913 paper of the Bohr model of the atom.", "The influence of the work of Nicholson’s nuclear quantum atomic model on Bohr’s model has been written about by many historians.", "Niels Bohr introduced the third quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model.", "The first quantized model of the atom was introduced in 1910 by Arthur Erich Haas and much discussed at the 1911 Solvay conference.", "In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation.", "If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus.", "Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies formula_20\nformula_21\nwhere formula_22 is the speed of light in vacuum, formula_23 is an experimentally determined constant (the Rydberg constant) and formula_24.", "Once the electron reached the lowest energy level (formula_25), it could not get any closer to the nucleus (lower energy).", "This approach also allowed Bohr to account for the Rydberg formula, an empirical description of the atomic spectrum of hydrogen, and to account for the value of the Rydberg constant formula_23 in terms of other fundamental constants.", "Bohr also introduced the quantity formula_27, now known as the reduced Planck constant, as the quantum of angular momentum.", "At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model.", "The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum.", "In modern terms, if formula_28 is the total angular momentum of a system with rotational invariance, and formula_29 the angular momentum measured along any given direction, these quantities can only take on the values\nformula_30", "The Planck constant also occurs in statements of Werner Heisenberg's uncertainty principle.", "Given numerous particles prepared in the same state, the uncertainty in their position, formula_31, and the uncertainty in their momentum, formula_32, obey\nformula_33\nwhere the uncertainty is given as the standard deviation of the measured value from its expected value.", "There are several other such pairs of physically measurable conjugate variables which obey a similar rule.", "One example is time vs. energy.", "The inverse relationship between the uncertainty of the two conjugate variables forces a tradeoff in quantum experiments, as measuring one quantity more precisely results in the other quantity becoming imprecise.", "In addition to some assumptions underlying the interpretation of certain values in the quantum mechanical formulation, one of the fundamental cornerstones to the entire theory lies in the commutator relationship between the position operator formula_34 and the momentum operator formula_35:\nformula_36\nwhere formula_37 is the Kronecker delta.", "The Planck relation connects the particular photon energy with its associated wave frequency :\nformula_38\nThis energy is extremely small in terms of ordinarily perceived everyday objects.", "Since the frequency , wavelength , and speed of light are related by formula_39, the relation can also be expressed as\nformula_40", "In 1923, Louis de Broglie generalized the Planck–Einstein relation by postulating that the Planck constant represents the proportionality between the momentum and the quantum wavelength of not just the photon, but the quantum wavelength of any particle.", "This was confirmed by experiments soon afterward.", "This holds throughout the quantum theory, including electrodynamics.", "The de Broglie wavelength of the particle is given by\nformula_41\nwhere denotes the linear momentum of a particle, such as a photon, or any other elementary particle.", "The energy of a photon with angular frequency is given by\nformula_42\nwhile its linear momentum relates to\nformula_43\nwhere is an angular wavenumber.", "These two relations are the temporal and spatial parts of the special relativistic expression using 4-vectors.", "formula_44", "Classical statistical mechanics requires the existence of (but does not define its value).", "Eventually, following upon Planck's discovery, it was speculated that physical action could not take on an arbitrary value, but instead was restricted to integer multiples of a very small quantity, the \"[elementary] quantum of action\", now called the \"Planck constant\".", "This was a significant conceptual part of the so-called \"old quantum theory\" developed by physicists including Bohr, Sommerfeld, and Ishiwara, in which particle trajectories exist but are hidden, but quantum laws constrain them based on their action.", "This view has been replaced by fully modern quantum theory, in which definite trajectories of motion do not even exist; rather, the particle is represented by a wavefunction spread out in space and in time.", "Thus there is no value of the action as classically defined.", "Related to this is the concept of energy quantization which existed in old quantum theory and also exists in altered form in modern quantum physics.", "Classical physics cannot explain either quantization of energy or the lack of classical particle motion.", "In many cases, such as for monochromatic light or for atoms, quantization of energy also implies that only certain energy levels are allowed, and values in between are forbidden.", "Implicit in the dimensions of the Planck constant is the fact that the SI unit of frequency, the hertz, represents one complete cycle, 360 degrees or radians, per second.", "In applications where it is natural to use the angular frequency (i.e. where the frequency is expressed in terms of radians per second instead of cycles per second or hertz)", "it is often useful to absorb a factor of into the Planck constant.", "The resulting constant is called the reduced Planck constant.", "It is equal to the Planck constant divided by , and is denoted formula_45 (pronounced \"h-bar\"):\nformula_46", "The Planck constant has dimensions of angular momentum.", "In SI units, the Planck constant is expressed in joules per hertz (J⋅Hz or kg⋅m2⋅s−1).", "formula_47\nformula_48\nThe above values have been adopted as fixed in the 2019 redefinition of the SI base units.", "In the system of \"natural units\" used by theoretical physicists, formula_45, the reduced Planck constant, is defined to be exactly one.", "In these units, is then exactly formula_50", "Since 2019, the numerical value of the Planck constant has been fixed, with a finite decimal representation.", "Under the present definition of the kilogram, which states that \"The kilogram [...] is defined by taking the fixed numerical value of to be when expressed in the unit J⋅s, which is equal to kg⋅m2⋅s−1, where the metre and the second are defined in terms of speed of light and duration of hyperfine transition of the ground state of an unperturbed caesium-133 atom .\"", "This implies that mass metrology is now aimed to find the value of one kilogram, and thus it is kilogram which is \"compensating\".", "Every experiment aiming to measure the kilogram (such as the Kibble balance and the X-ray crystal density method), will essentially refine the value of a kilogram.", "As an illustration of this, suppose the decision of making to be exact was taken in 2010, when its measured value was , thus the present definition of kilogram was also enforced.", "In the future, the value of one kilogram must be refined to times the mass of the International Prototype of the Kilogram (IPK).", "The Planck constant is related to the quantization of light and matter.", "It can be seen as a subatomic-scale constant.", "In a unit system adapted to subatomic scales, the electronvolt is the appropriate unit of energy and the petahertz the appropriate unit of frequency.", "Atomic unit systems are based (in part) on the Planck constant.", "The physical meaning of the Planck constant could suggest some basic features of our physical world.", "The Planck constant is one of the smallest constants used in physics.", "This reflects the fact that on a scale adapted to humans, where energies are typical of the order of kilojoules and times are typical of the order of seconds or minutes, the Planck constant is very small.", "One can regard the Planck constant to be only relevant to the microscopic scale instead of the macroscopic scale in our everyday experience.", "Equivalently, the order of the Planck constant reflects the fact that everyday objects and systems are made of a \"large\" number of microscopic particles.", "For example, green light with a wavelength of 555 nanometres (a wavelength that can be perceived by the human eye to be green) has a frequency of ().", "Each photon has an energy .", "That is a very small amount of energy in terms of everyday experience, but everyday experience is not concerned with individual photons any more than with individual atoms or molecules.", "An amount of light more typical in everyday experience (though much larger than the smallest amount perceivable by the human eye) is the energy of one mole of photons; its energy can be computed by multiplying the photon energy by the Avogadro constant, , with the result of , about the food energy in three apples.", "In principle, the Planck constant can be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons, and this is how its value was first calculated in the early twentieth century.", "In practice, these are no longer the most accurate methods.", "Since the value of the Planck constant is fixed now, it is no longer determined or calculated in laboratories.", "Some of the practices given below to determine the Planck constant are now used to determine the mass of the kilogram.", "The below-given methods \"except\" the X-ray crystal density method rely on the theoretical basis of the Josephson effect and the quantum Hall effect.", "The Josephson constant \"K\"J relates the potential difference \"U\" generated by the Josephson effect at a \"Josephson junction\" with the frequency \"ν\" of the microwave radiation.", "The theoretical treatment of Josephson effect suggests very strongly that .", "formula_51\nThe Josephson constant may be measured by comparing the potential difference generated by an array of Josephson junctions with a potential difference which is known in SI volts.", "The measurement of the potential difference in SI units is done by allowing an electrostatic force to cancel out a measurable gravitational force, in a Kibble balance.", "Assuming the validity of the theoretical treatment of the Josephson effect, \"K\"J is related to the Planck constant by\nformula_52", "A Kibble balance (formerly known as a watt balance) is an instrument for comparing two powers, one of which is measured in SI watts and the other of which is measured in conventional electrical units.", "From the definition of the \"conventional\" watt \"W\"90, this gives a measure of the product \"K\"J2\"R\"K in SI units, where \"R\"K is the von Klitzing constant which appears in the quantum Hall effect.", "If the theoretical treatments of the Josephson effect and the quantum Hall effect are valid, and in particular assuming that , the measurement of \"K\"J2\"R\"K is a direct determination of the Planck constant.", "formula_53", "The gyromagnetic ratio \"γ\" is the constant of proportionality between the frequency \"ν\" of nuclear magnetic resonance (or electron paramagnetic resonance for electrons) and the applied magnetic field .", "It is difficult to measure gyromagnetic ratios precisely because of the difficulties in precisely measuring \"B\", but the value for protons in water at is known to better than one part per million.", "The protons are said to be \"shielded\" from the applied magnetic field by the electrons in the water molecule, the same effect that gives rise to chemical shift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, \"γ\"′p.", "The gyromagnetic ratio is related to the shielded proton magnetic moment \"μ\"′p, the spin number \"I\" ( for protons) and the reduced Planck constant.", "formula_54\nThe ratio of the shielded proton magnetic moment \"μ\"′p to the electron magnetic moment \"μ\"e can be measured separately and to high precision, as the imprecisely known value of the applied magnetic field cancels itself out in taking the ratio.", "The value of \"μ\"e in Bohr magnetons is also known: it is half the electron g-factor \"g\"e.", "Hence\nformula_55\nformula_56\nA further complication is that the measurement of \"γ\"′p involves the measurement of an electric current: this is invariably measured in \"conventional\" amperes rather than in SI amperes, so a conversion factor is required.", "The symbol \"Γ\"′p-90 is used for the measured gyromagnetic ratio using conventional electrical units.", "In addition, there are two methods of measuring the value, a \"low-field\" method and a \"high-field\" method, and the conversion factors are different in the two cases.", "Only the high-field value \"Γ\"′p-90(hi) is of interest in determining the Planck constant.", "formula_57\nSubstitution gives the expression for the Planck constant in terms of \"Γ\"′p-90(hi):\nformula_58", "The Faraday constant \"F\" is the charge of one mole of electrons, equal to the Avogadro constant \"N\"A multiplied by the elementary charge \"e\".", "It can be determined by careful electrolysis experiments, measuring the amount of silver dissolved from an electrode in a given time and for a given electric current.", "Substituting the definitions of \"N\"A and \"e\" gives the relation to the Planck constant.", "formula_59", "The X-ray crystal density method is primarily a method for determining the Avogadro constant \"N\"A but as the Avogadro constant is related to the Planck constant it also determines a value for \"h\".", "The principle behind the method is to determine \"N\"A as the ratio between the volume of the unit cell of a crystal, measured by X-ray crystallography, and the molar volume of the substance.", "Crystals of silicon are used, as they are available in high quality and purity by the technology developed for the semiconductor industry.", "The unit cell volume is calculated from the spacing between two crystal planes referred to as \"d\"220.", "The molar volume \"V\"m(Si) requires a knowledge of the density of the crystal and the atomic weight of the silicon used.", "The Planck constant is given by\nformula_60", "The experimental measurement of the Planck constant in the Large Hadron Collider laboratory was carried out in 2011.", "The study called PCC using a giant particle accelerator helped to better understand the relationships between the Planck constant and measuring distances in space." ]

[ 92, 93, 94, 95, 96, 97 ]

[ "In metrology it is used, together with other constants, to define the kilogram, an SI unit." ]

[ "Planck's constant was formulated as part of Max Planck's successful effort to produce a mathematical expression that accurately predicted the observed spectral distribution of thermal radiation from a closed furnace (black-body radiation).", "This mathematical expression is now known as Planck's law.", "In the last years of the 19th century, Max Planck was investigating the problem of black-body radiation first posed by Kirchhoff some 40 years earlier.", "Every physical body spontaneously and continuously emits electromagnetic radiation.", "There was no expression or explanation for the overall shape of the observed emission spectrum.", "At the time, Wien's law fit the data for short wavelengths and high temperatures, but failed for long wavelengths.", "Also around this time, but unknown to Planck, Lord Rayleigh had derived theoretically a formula, now known as the Rayleigh–Jeans law, that could reasonably predict long wavelengths but failed dramatically at short wavelengths.", "Approaching this problem, Planck hypothesized that the equations of motion for light describe a set of harmonic oscillators, one for each possible frequency.", "He examined how the entropy of the oscillators varied with the temperature of the body, trying to match Wien's law, and was able to derive an approximate mathematical function for the black-body spectrum, which gave a simple empirical formula for long wavelengths.", "Planck tried to find a mathematical expression that could reproduce Wien's law (for short wavelengths) and the empirical formula (for long wavelengths).", "This expression included a constant, formula_3, which is thought to be for Hilfsgrösse (auxiliary variable), and subsequently became known as the Planck constant.", "The expression formulated by Planck showed that the spectral radiance of a body for frequency at absolute temperature is given by\nformula_4\nwhere formula_5 is the Boltzmann constant, formula_3 is the Planck constant, and formula_7 is the speed of light in the medium, whether material or vacuum.", "The spectral radiance of a body, formula_8, describes the amount of energy it emits at different radiation frequencies.", "It is the power emitted per unit area of the body, per unit solid angle of emission, per unit frequency.", "The spectral radiance can also be expressed per unit wavelength formula_9 instead of per unit frequency.", "In this case, it is given by\nformula_10\nshowing how radiated energy emitted at shorter wavelengths increases more rapidly with temperature than energy emitted at longer wavelengths.", "Planck's law may also be expressed in other terms, such as the number of photons emitted at a certain wavelength, or the energy density in a volume of radiation.", "The SI units of formula_8 are , while those of formula_12 are .", "Planck soon realized that his solution was not unique.", "There were several different solutions, each of which gave a different value for the entropy of the oscillators.", "To save his theory, Planck resorted to using the then-controversial theory of statistical mechanics, which he described as \"an act of despair …", "I was ready to sacrifice any of my previous convictions about physics.\"", "One of his new boundary conditions was\nWith this new condition, Planck had imposed the quantization of the energy of the oscillators, \"a purely formal assumption …", "actually I did not think much about it ...\" in his own words, but one that would revolutionize physics.", "Applying this new approach to Wien's displacement law showed that the \"energy element\" must be proportional to the frequency of the oscillator, the first version of what is now sometimes termed the \"Planck–Einstein relation\":\nformula_13\nPlanck was able to calculate the value of formula_1 from experimental data on black-body radiation: his result, , is within 1.2% of the currently accepted value.", "He also made the first determination of the Boltzmann constant formula_5 from the same data and theory.", "The black-body problem was revisited in 1905, when Lord Rayleigh and James Jeans (on the one hand) and Albert Einstein (on the other hand) independently proved that classical electromagnetism could \"never\" account for the observed spectrum.", "These proofs are commonly known as the \"ultraviolet catastrophe\", a name coined by Paul Ehrenfest in 1911.", "They contributed greatly (along with Einstein's work on the photoelectric effect) in convincing physicists that Planck's postulate of quantized energy levels was more than a mere mathematical formalism.", "The first Solvay Conference in 1911 was devoted to \"the theory of radiation and quanta\".", "The photoelectric effect is the emission of electrons (called \"photoelectrons\") from a surface when light is shone on it.", "It was first observed by Alexandre Edmond Becquerel in 1839, although credit is usually reserved for Heinrich Hertz, who published the first thorough investigation in 1887.", "Another particularly thorough investigation was published by Philipp Lenard (Lénárd Fülöp) in 1902.", "Einstein's 1905 paper discussing the effect in terms of light quanta would earn him the Nobel Prize in 1921, after his predictions had been confirmed by the experimental work of Robert Andrews Millikan.", "The Nobel committee awarded the prize for his work on the photo-electric effect, rather than relativity, both because of a bias against purely theoretical physics not grounded in discovery or experiment, and dissent amongst its members as to the actual proof that relativity was real.", "Before Einstein's paper, electromagnetic radiation such as visible light was considered to behave as a wave: hence the use of the terms \"frequency\" and \"wavelength\" to characterize different types of radiation.", "The energy transferred by a wave in a given time is called its intensity.", "The light from a theatre spotlight is more \"intense\" than the light from a domestic lightbulb; that is to say that the spotlight gives out more energy per unit time and per unit space (and hence consumes more electricity) than the ordinary bulb, even though the color of the light might be very similar.", "Other waves, such as sound or the waves crashing against a seafront, also have their intensity.", "However, the energy account of the photoelectric effect didn't seem to agree with the wave description of light.", "The \"photoelectrons\" emitted as a result of the photoelectric effect have a certain kinetic energy, which can be measured.", "This kinetic energy (for each photoelectron) is \"independent\" of the intensity of the light, but depends linearly on the frequency; and if the frequency is too low (corresponding to a photon energy that is less than the work function of the material), no photoelectrons are emitted at all, unless a plurality of photons, whose energetic sum is greater than the energy of the photoelectrons, acts virtually simultaneously (multiphoton effect).", "Assuming the frequency is high enough to cause the photoelectric effect, a rise in intensity of the light source causes more photoelectrons to be emitted with the same kinetic energy, rather than the same number of photoelectrons to be emitted with higher kinetic energy.", "Einstein's explanation for these observations was that light itself is quantized; that the energy of light is not transferred continuously as in a classical wave, but only in small \"packets\" or quanta.", "The size of these \"packets\" of energy, which would later be named photons, was to be the same as Planck's \"energy element\", giving the modern version of the Planck–Einstein relation:\nformula_16\nEinstein's postulate was later proven experimentally: the constant of proportionality between the frequency of incident light formula_17 and the kinetic energy of photoelectrons formula_18 was shown to be equal to the Planck constant formula_1.", "It was John William Nicholson in 1912 who introduced h-bar into the theory of the atom which was the first quantum and nuclear atom and the first to quantize angular momentum as \"h\"/2.", "Niels Bohr quoted him in his 1913 paper of the Bohr model of the atom.", "The influence of the work of Nicholson’s nuclear quantum atomic model on Bohr’s model has been written about by many historians.", "Niels Bohr introduced the third quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model.", "The first quantized model of the atom was introduced in 1910 by Arthur Erich Haas and much discussed at the 1911 Solvay conference.", "In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation.", "If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus.", "Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies formula_20\nformula_21\nwhere formula_22 is the speed of light in vacuum, formula_23 is an experimentally determined constant (the Rydberg constant) and formula_24.", "Once the electron reached the lowest energy level (formula_25), it could not get any closer to the nucleus (lower energy).", "This approach also allowed Bohr to account for the Rydberg formula, an empirical description of the atomic spectrum of hydrogen, and to account for the value of the Rydberg constant formula_23 in terms of other fundamental constants.", "Bohr also introduced the quantity formula_27, now known as the reduced Planck constant, as the quantum of angular momentum.", "At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model.", "The correct quantization rules for electrons – in which the energy reduces to the Bohr model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum.", "In modern terms, if formula_28 is the total angular momentum of a system with rotational invariance, and formula_29 the angular momentum measured along any given direction, these quantities can only take on the values\nformula_30", "The Planck constant also occurs in statements of Werner Heisenberg's uncertainty principle.", "Given numerous particles prepared in the same state, the uncertainty in their position, formula_31, and the uncertainty in their momentum, formula_32, obey\nformula_33\nwhere the uncertainty is given as the standard deviation of the measured value from its expected value.", "There are several other such pairs of physically measurable conjugate variables which obey a similar rule.", "One example is time vs. energy.", "The inverse relationship between the uncertainty of the two conjugate variables forces a tradeoff in quantum experiments, as measuring one quantity more precisely results in the other quantity becoming imprecise.", "In addition to some assumptions underlying the interpretation of certain values in the quantum mechanical formulation, one of the fundamental cornerstones to the entire theory lies in the commutator relationship between the position operator formula_34 and the momentum operator formula_35:\nformula_36\nwhere formula_37 is the Kronecker delta.", "The Planck relation connects the particular photon energy with its associated wave frequency :\nformula_38\nThis energy is extremely small in terms of ordinarily perceived everyday objects.", "Since the frequency , wavelength , and speed of light are related by formula_39, the relation can also be expressed as\nformula_40", "In 1923, Louis de Broglie generalized the Planck–Einstein relation by postulating that the Planck constant represents the proportionality between the momentum and the quantum wavelength of not just the photon, but the quantum wavelength of any particle.", "This was confirmed by experiments soon afterward.", "This holds throughout the quantum theory, including electrodynamics.", "The de Broglie wavelength of the particle is given by\nformula_41\nwhere denotes the linear momentum of a particle, such as a photon, or any other elementary particle.", "The energy of a photon with angular frequency is given by\nformula_42\nwhile its linear momentum relates to\nformula_43\nwhere is an angular wavenumber.", "These two relations are the temporal and spatial parts of the special relativistic expression using 4-vectors.", "formula_44", "Classical statistical mechanics requires the existence of (but does not define its value).", "Eventually, following upon Planck's discovery, it was speculated that physical action could not take on an arbitrary value, but instead was restricted to integer multiples of a very small quantity, the \"[elementary] quantum of action\", now called the \"Planck constant\".", "This was a significant conceptual part of the so-called \"old quantum theory\" developed by physicists including Bohr, Sommerfeld, and Ishiwara, in which particle trajectories exist but are hidden, but quantum laws constrain them based on their action.", "This view has been replaced by fully modern quantum theory, in which definite trajectories of motion do not even exist; rather, the particle is represented by a wavefunction spread out in space and in time.", "Thus there is no value of the action as classically defined.", "Related to this is the concept of energy quantization which existed in old quantum theory and also exists in altered form in modern quantum physics.", "Classical physics cannot explain either quantization of energy or the lack of classical particle motion.", "In many cases, such as for monochromatic light or for atoms, quantization of energy also implies that only certain energy levels are allowed, and values in between are forbidden.", "Implicit in the dimensions of the Planck constant is the fact that the SI unit of frequency, the hertz, represents one complete cycle, 360 degrees or radians, per second.", "In applications where it is natural to use the angular frequency (i.e. where the frequency is expressed in terms of radians per second instead of cycles per second or hertz)", "it is often useful to absorb a factor of into the Planck constant.", "The resulting constant is called the reduced Planck constant.", "It is equal to the Planck constant divided by , and is denoted formula_45 (pronounced \"h-bar\"):\nformula_46", "The Planck constant has dimensions of angular momentum.", "In SI units, the Planck constant is expressed in joules per hertz (J⋅Hz or kg⋅m2⋅s−1).", "formula_47\nformula_48\nThe above values have been adopted as fixed in the 2019 redefinition of the SI base units.", "In the system of \"natural units\" used by theoretical physicists, formula_45, the reduced Planck constant, is defined to be exactly one.", "In these units, is then exactly formula_50", "Since 2019, the numerical value of the Planck constant has been fixed, with a finite decimal representation.", "Under the present definition of the kilogram, which states that \"The kilogram [...] is defined by taking the fixed numerical value of to be when expressed in the unit J⋅s, which is equal to kg⋅m2⋅s−1, where the metre and the second are defined in terms of speed of light and duration of hyperfine transition of the ground state of an unperturbed caesium-133 atom .\"", "This implies that mass metrology is now aimed to find the value of one kilogram, and thus it is kilogram which is \"compensating\".", "Every experiment aiming to measure the kilogram (such as the Kibble balance and the X-ray crystal density method), will essentially refine the value of a kilogram.", "As an illustration of this, suppose the decision of making to be exact was taken in 2010, when its measured value was , thus the present definition of kilogram was also enforced.", "In the future, the value of one kilogram must be refined to times the mass of the International Prototype of the Kilogram (IPK).", "The Planck constant is related to the quantization of light and matter.", "It can be seen as a subatomic-scale constant.", "In a unit system adapted to subatomic scales, the electronvolt is the appropriate unit of energy and the petahertz the appropriate unit of frequency.", "Atomic unit systems are based (in part) on the Planck constant.", "The physical meaning of the Planck constant could suggest some basic features of our physical world.", "The Planck constant is one of the smallest constants used in physics.", "This reflects the fact that on a scale adapted to humans, where energies are typical of the order of kilojoules and times are typical of the order of seconds or minutes, the Planck constant is very small.", "One can regard the Planck constant to be only relevant to the microscopic scale instead of the macroscopic scale in our everyday experience.", "Equivalently, the order of the Planck constant reflects the fact that everyday objects and systems are made of a \"large\" number of microscopic particles.", "For example, green light with a wavelength of 555 nanometres (a wavelength that can be perceived by the human eye to be green) has a frequency of ().", "Each photon has an energy .", "That is a very small amount of energy in terms of everyday experience, but everyday experience is not concerned with individual photons any more than with individual atoms or molecules.", "An amount of light more typical in everyday experience (though much larger than the smallest amount perceivable by the human eye) is the energy of one mole of photons; its energy can be computed by multiplying the photon energy by the Avogadro constant, , with the result of , about the food energy in three apples.", "In principle, the Planck constant can be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons, and this is how its value was first calculated in the early twentieth century.", "In practice, these are no longer the most accurate methods.", "Since the value of the Planck constant is fixed now, it is no longer determined or calculated in laboratories.", "Some of the practices given below to determine the Planck constant are now used to determine the mass of the kilogram.", "The below-given methods \"except\" the X-ray crystal density method rely on the theoretical basis of the Josephson effect and the quantum Hall effect.", "The Josephson constant \"K\"J relates the potential difference \"U\" generated by the Josephson effect at a \"Josephson junction\" with the frequency \"ν\" of the microwave radiation.", "The theoretical treatment of Josephson effect suggests very strongly that .", "formula_51\nThe Josephson constant may be measured by comparing the potential difference generated by an array of Josephson junctions with a potential difference which is known in SI volts.", "The measurement of the potential difference in SI units is done by allowing an electrostatic force to cancel out a measurable gravitational force, in a Kibble balance.", "Assuming the validity of the theoretical treatment of the Josephson effect, \"K\"J is related to the Planck constant by\nformula_52", "A Kibble balance (formerly known as a watt balance) is an instrument for comparing two powers, one of which is measured in SI watts and the other of which is measured in conventional electrical units.", "From the definition of the \"conventional\" watt \"W\"90, this gives a measure of the product \"K\"J2\"R\"K in SI units, where \"R\"K is the von Klitzing constant which appears in the quantum Hall effect.", "If the theoretical treatments of the Josephson effect and the quantum Hall effect are valid, and in particular assuming that , the measurement of \"K\"J2\"R\"K is a direct determination of the Planck constant.", "formula_53", "The gyromagnetic ratio \"γ\" is the constant of proportionality between the frequency \"ν\" of nuclear magnetic resonance (or electron paramagnetic resonance for electrons) and the applied magnetic field .", "It is difficult to measure gyromagnetic ratios precisely because of the difficulties in precisely measuring \"B\", but the value for protons in water at is known to better than one part per million.", "The protons are said to be \"shielded\" from the applied magnetic field by the electrons in the water molecule, the same effect that gives rise to chemical shift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, \"γ\"′p.", "The gyromagnetic ratio is related to the shielded proton magnetic moment \"μ\"′p, the spin number \"I\" ( for protons) and the reduced Planck constant.", "formula_54\nThe ratio of the shielded proton magnetic moment \"μ\"′p to the electron magnetic moment \"μ\"e can be measured separately and to high precision, as the imprecisely known value of the applied magnetic field cancels itself out in taking the ratio.", "The value of \"μ\"e in Bohr magnetons is also known: it is half the electron g-factor \"g\"e.", "Hence\nformula_55\nformula_56\nA further complication is that the measurement of \"γ\"′p involves the measurement of an electric current: this is invariably measured in \"conventional\" amperes rather than in SI amperes, so a conversion factor is required.", "The symbol \"Γ\"′p-90 is used for the measured gyromagnetic ratio using conventional electrical units.", "In addition, there are two methods of measuring the value, a \"low-field\" method and a \"high-field\" method, and the conversion factors are different in the two cases.", "Only the high-field value \"Γ\"′p-90(hi) is of interest in determining the Planck constant.", "formula_57\nSubstitution gives the expression for the Planck constant in terms of \"Γ\"′p-90(hi):\nformula_58", "The Faraday constant \"F\" is the charge of one mole of electrons, equal to the Avogadro constant \"N\"A multiplied by the elementary charge \"e\".", "It can be determined by careful electrolysis experiments, measuring the amount of silver dissolved from an electrode in a given time and for a given electric current.", "Substituting the definitions of \"N\"A and \"e\" gives the relation to the Planck constant.", "formula_59", "The X-ray crystal density method is primarily a method for determining the Avogadro constant \"N\"A but as the Avogadro constant is related to the Planck constant it also determines a value for \"h\".", "The principle behind the method is to determine \"N\"A as the ratio between the volume of the unit cell of a crystal, measured by X-ray crystallography, and the molar volume of the substance.", "Crystals of silicon are used, as they are available in high quality and purity by the technology developed for the semiconductor industry.", "The unit cell volume is calculated from the spacing between two crystal planes referred to as \"d\"220.", "The molar volume \"V\"m(Si) requires a knowledge of the density of the crystal and the atomic weight of the silicon used.", "The Planck constant is given by\nformula_60", "The experimental measurement of the Planck constant in the Large Hadron Collider laboratory was carried out in 2011.", "The study called PCC using a giant particle accelerator helped to better understand the relationships between the Planck constant and measuring distances in space." ]

[ 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110 ]

[ "A photon's energy is equal to its frequency multiplied by the Planck constant." ]

[ "Maria do Couto Maia-Lopes (24 October 1890 – 25 July 2005) is the 2nd longest-lived person to be documented in Portugal.", "She was born and lived in Grijó, in Vila Nova de Gaia, which is near the city of Porto.", "She remembered the day when the last king of Portugal, D. Manuel II, visited the nearby town of Espinho, on 23 November 1908.", "She had a total of eight daughters, seven grandchildren, ten great-grandchildren and five great-great-grandchildren.", "Her husband died in 1942.", "One of her great-granddaughters married a grandson of Portugal's oldest ever man, Augusto Moreira de Oliveira (1896 – 2009).", "Maia-Lopes died on 25 July 2005, aged 114 years 274 days.", "Alice Sanders (São Jorge Island, 12 May 1897 – Merced, California, 7 November 2007) was one of the last survivors of the 1906 San Francisco earthquake.", "Alice Catarina Matos was born in the Azores archipelago.", "Her family emigrated to Half Moon Bay (California) in 1903, when Alice was 6 years old.", "The April 18, 1906 San Francisco earthquake, a few weeks prior to Alice's ninth birthday, was a traumatic experience to her family, since they believed the end of the world had come.", "In 1912, the Matos family moved to Gustine, where Alice met Clarence Leonard Sanders, who became her husband on Christmas Day in 1913." ]

[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ]

[ "Maria de Jesus was the oldest Portuguese citizen whose age was validated; she lived 115 years and 114 days, from 1893 to 2009." ]

[ "Maria do Couto Maia-Lopes (24 October 1890 – 25 July 2005) is the 2nd longest-lived person to be documented in Portugal.", "She was born and lived in Grijó, in Vila Nova de Gaia, which is near the city of Porto.", "She remembered the day when the last king of Portugal, D. Manuel II, visited the nearby town of Espinho, on 23 November 1908.", "She had a total of eight daughters, seven grandchildren, ten great-grandchildren and five great-great-grandchildren.", "Her husband died in 1942.", "One of her great-granddaughters married a grandson of Portugal's oldest ever man, Augusto Moreira de Oliveira (1896 – 2009).", "Maia-Lopes died on 25 July 2005, aged 114 years 274 days.", "Alice Sanders (São Jorge Island, 12 May 1897 – Merced, California, 7 November 2007) was one of the last survivors of the 1906 San Francisco earthquake.", "Alice Catarina Matos was born in the Azores archipelago.", "Her family emigrated to Half Moon Bay (California) in 1903, when Alice was 6 years old.", "The April 18, 1906 San Francisco earthquake, a few weeks prior to Alice's ninth birthday, was a traumatic experience to her family, since they believed the end of the world had come.", "In 1912, the Matos family moved to Gustine, where Alice met Clarence Leonard Sanders, who became her husband on Christmas Day in 1913." ]

[ 0, 1, 2, 3, 4, 5, 6 ]

[ "Maria de Jesus was the oldest Portuguese citizen whose age was validated; she lived 115 years and 114 days, from 1893 to 2009." ]

[ "The Vincent Award was established in 2000 by the Broere Charitable Foundation in memory of Monique Zajfen, a beloved friend of the Broere family and holder of the Gallery 121 in Antwerp.", "The art collection of Monique Zajfen constituted of the works by The Vincent Award winners and other contemporary artists.", "Zaifen's collection was given to the Stedelijk Museum of Amsterdam on long-term loan.", "The award first took place at the Bonnefanten Museum in Maastricht.", "From 2006, The Vincent Award was hosted by the Stedelijk Museum in Amsterdam.", "The winner is decided by six jury members headed by the director of the Stedelijk Museum.", "The jury consists of professionals in the sphere of the European Arts.", "#Manuel Borja-Villel (director of MACBA, Barcelona)\n#Ian Dunlop (art historian, London)\n#Ingvild Goetz (Sammlung Goetz, Munich)\n#Viktor Misiano (critic and curator, Moscow)\n#Beatrix Ruf (director of Kunsthalle, Zurich)\n#Gijs van Tuyl (director of Stedelijk Museum, Amsterdam)", "#2014 - Anri Sala\n# 2008 - Deimantas Narkevicius, Francis Alÿs\n#2006 - Wilhelm Sasnal\n#2004 - Paweł Althamer\n#2002 - Neo Rauch\n#2000 - Eija-Liisa Ahtila" ]

[ 0, 1, 2, 3, 4, 5, 6, 7 ]

[ "The Vincent Award is a Dutch prize awarded to a European artist whose works are deemed highly relevant in contemporary art.", "Five artists are nominated for the award, and are exhibited at the Stedelijk Museum in Amsterdam." ]

[ "Located on the South Rim of the Grand Canyon, the Albright Training Center provides resources, context, and stimulus for personal and professional growth in support of the National Park Service mission.", "The Capital Training Center is located in Washington, D.C.", "It serves as the headquarters for the National Park Service's Employee Development program and provides training to the park employees in the Washington area.", "Their programs emphasize Planning, Design, and Construction; Recreation and Conservation Program; Information Management; Specialty Field; and Organizational Development.", "The Capital Training Center also coordinates special training programs, including USDA's Graduate School, the Albright-Wirth Grant Program Team, Team Leadership Program, Executive Potential Program, Executive Leadership for Middle Level Employees, New Leader Program, and the Aspiring Leader Program.", "The Federal Law Enforcement Training Center (FLETC) is an interagency federal police training academy run by the U.S. Department of Homeland Security in Glynco, Georgia.", "All federal agencies with police powers train at FLETC.", "The National Park Service has a full-time staff on duty to manage the Park Ranger trainees at the site.", "State and local law enforcement agencies can make use of the facility.", "The Center teaches the full range of law enforcement skills, from taking fingerprints to tracking financial transactions, riding patrol protecting VIPs, searching a crime scene, and securing a building.", "The Historic Preservation Training Center (HPTC) teaches the craft skills that created the fabric of America.", "Trainees come to Frederick, Maryland to learn historic carpentry, masonry and a myriad of other skills needed to maintain the structures of America's heritage.", "The National Park Service established Stephen T. Mather Training Center in 1964 to teach interpretive skills, administrative skills and a variety of skills not being taught at the Albright center.", "Located in Storer College in Harpers Ferry, West Virginia, the facility makes use of the opportunities presented by having the Harpers Ferry National Historical Park surrounding the facility.", "The National Conservation Training Center, located in Shepherdstown, West Virginia, is the primary training center and Home of the U. S. Fish and Wildlife Service.", "Established in 1997 by the U.S. Fish and Wildlife Service, the center was created to train conservation professionals from all sectors in a wide range of technical and non technical conservation topics.", "The National Center for Preservation Technology and Training (NCPTT) was established by the United States Congress in 1994 to advance the application of science and technology to historic preservation.", "Working in the fields of archeology, architecture, landscape architecture and materials conservation, NCPTT accomplishes its mission through training, education, research, technology transfer and partnerships.", "The offices and laboratory facilities of NCPTT are located in Lee H. Nelson Hall on the campus of Northwestern State University in Natchitoches, Louisiana." ]

[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 ]

[ "The U.S. National Park Service has a long history of specialized training needs.", "One of the service's earliest training programs was Ranger Skills, a nine-week course held at the Grand Canyon.", "Over the years, the variety of skills has increased and the bureau has created training centers to meet those needs." ]

[ "Located on the South Rim of the Grand Canyon, the Albright Training Center provides resources, context, and stimulus for personal and professional growth in support of the National Park Service mission.", "The Capital Training Center is located in Washington, D.C.", "It serves as the headquarters for the National Park Service's Employee Development program and provides training to the park employees in the Washington area.", "Their programs emphasize Planning, Design, and Construction; Recreation and Conservation Program; Information Management; Specialty Field; and Organizational Development.", "The Capital Training Center also coordinates special training programs, including USDA's Graduate School, the Albright-Wirth Grant Program Team, Team Leadership Program, Executive Potential Program, Executive Leadership for Middle Level Employees, New Leader Program, and the Aspiring Leader Program.", "The Federal Law Enforcement Training Center (FLETC) is an interagency federal police training academy run by the U.S. Department of Homeland Security in Glynco, Georgia.", "All federal agencies with police powers train at FLETC.", "The National Park Service has a full-time staff on duty to manage the Park Ranger trainees at the site.", "State and local law enforcement agencies can make use of the facility.", "The Center teaches the full range of law enforcement skills, from taking fingerprints to tracking financial transactions, riding patrol protecting VIPs, searching a crime scene, and securing a building.", "The Historic Preservation Training Center (HPTC) teaches the craft skills that created the fabric of America.", "Trainees come to Frederick, Maryland to learn historic carpentry, masonry and a myriad of other skills needed to maintain the structures of America's heritage.", "The National Park Service established Stephen T. Mather Training Center in 1964 to teach interpretive skills, administrative skills and a variety of skills not being taught at the Albright center.", "Located in Storer College in Harpers Ferry, West Virginia, the facility makes use of the opportunities presented by having the Harpers Ferry National Historical Park surrounding the facility.", "The National Conservation Training Center, located in Shepherdstown, West Virginia, is the primary training center and Home of the U. S. Fish and Wildlife Service.", "Established in 1997 by the U.S. Fish and Wildlife Service, the center was created to train conservation professionals from all sectors in a wide range of technical and non technical conservation topics.", "The National Center for Preservation Technology and Training (NCPTT) was established by the United States Congress in 1994 to advance the application of science and technology to historic preservation.", "Working in the fields of archeology, architecture, landscape architecture and materials conservation, NCPTT accomplishes its mission through training, education, research, technology transfer and partnerships.", "The offices and laboratory facilities of NCPTT are located in Lee H. Nelson Hall on the campus of Northwestern State University in Natchitoches, Louisiana." ]

[ 1, 2, 3, 4 ]

[ "The U.S. National Park Service has a long history of specialized training needs." ]

[ "Located on the South Rim of the Grand Canyon, the Albright Training Center provides resources, context, and stimulus for personal and professional growth in support of the National Park Service mission.", "The Capital Training Center is located in Washington, D.C.", "It serves as the headquarters for the National Park Service's Employee Development program and provides training to the park employees in the Washington area.", "Their programs emphasize Planning, Design, and Construction; Recreation and Conservation Program; Information Management; Specialty Field; and Organizational Development.", "The Capital Training Center also coordinates special training programs, including USDA's Graduate School, the Albright-Wirth Grant Program Team, Team Leadership Program, Executive Potential Program, Executive Leadership for Middle Level Employees, New Leader Program, and the Aspiring Leader Program.", "The Federal Law Enforcement Training Center (FLETC) is an interagency federal police training academy run by the U.S. Department of Homeland Security in Glynco, Georgia.", "All federal agencies with police powers train at FLETC.", "The National Park Service has a full-time staff on duty to manage the Park Ranger trainees at the site.", "State and local law enforcement agencies can make use of the facility.", "The Center teaches the full range of law enforcement skills, from taking fingerprints to tracking financial transactions, riding patrol protecting VIPs, searching a crime scene, and securing a building.", "The Historic Preservation Training Center (HPTC) teaches the craft skills that created the fabric of America.", "Trainees come to Frederick, Maryland to learn historic carpentry, masonry and a myriad of other skills needed to maintain the structures of America's heritage.", "The National Park Service established Stephen T. Mather Training Center in 1964 to teach interpretive skills, administrative skills and a variety of skills not being taught at the Albright center.", "Located in Storer College in Harpers Ferry, West Virginia, the facility makes use of the opportunities presented by having the Harpers Ferry National Historical Park surrounding the facility.", "The National Conservation Training Center, located in Shepherdstown, West Virginia, is the primary training center and Home of the U. S. Fish and Wildlife Service.", "Established in 1997 by the U.S. Fish and Wildlife Service, the center was created to train conservation professionals from all sectors in a wide range of technical and non technical conservation topics.", "The National Center for Preservation Technology and Training (NCPTT) was established by the United States Congress in 1994 to advance the application of science and technology to historic preservation.", "Working in the fields of archeology, architecture, landscape architecture and materials conservation, NCPTT accomplishes its mission through training, education, research, technology transfer and partnerships.", "The offices and laboratory facilities of NCPTT are located in Lee H. Nelson Hall on the campus of Northwestern State University in Natchitoches, Louisiana." ]

[ 10, 11 ]

[ "Over the years, the variety of skills has increased and the bureau has created training centers to meet those needs." ]

[ "Crazy Horse was a Native American war leader of the Oglala Lakota.", "He took up arms against the U.S. Federal government to fight against encroachments on the territories and way of life of the Lakota people.", "His most famous actions against the U.S. military included the Fetterman Fight (21 December 1866) and the Battle of the Little Bighorn (25–26 June 1876).", "He surrendered to U.S. troops under General Crook in May 1877 and was fatally wounded by a military guard, allegedly while resisting imprisonment at Camp Robinson in present-day Nebraska.", "He ranks among the most notable and iconic of Native American tribal members and was honored by the U.S. Postal Service in 1982 with a 13¢ postage stamp that is part of its Great Americans series.", "Henry Standing Bear (\"Mato Naji\"), an Oglala Lakota chief, and well-known statesman and elder in the Native American community, recruited and commissioned Polish-American sculptor Korczak Ziolkowski to build the Crazy Horse Memorial in the Black Hills of South Dakota.", "In October 1931, Luther Standing Bear, Henry's older brother, wrote to sculptor Gutzon Borglum, who was carving the heads of four American presidents at Mount Rushmore.", "Luther suggested that it would be \"most fitting to have the face of Crazy Horse sculpted there.", "Crazy Horse is the real patriot of the Sioux tribe and the only one worthy to place by the side of Washington and Lincoln.\"", "Borglum never replied.", "Thereafter, Henry Standing Bear began a campaign to have Borglum carve an image of Crazy Horse on Mount Rushmore.", "In summer of 1935, Standing Bear, frustrated over the stalled Crazy Horse project, wrote to James H. Cook, a long time friend of Chief Red Cloud's, \"I am struggling hopelessly with this because I am without funds, no employment and no assistance from any Indian or White.\"", "On November 7, 1939, Henry Standing Bear wrote to the Polish-American sculptor Korczak Ziolkowski, who worked on Mount Rushmore under Gutzon Borglum.", "He informed the sculptor, \"My fellow chiefs and I would like the white man to know that the red man has great heroes, too.\"", "Standing Bear also wrote a letter to Undersecretary Oscar Chapman of the Department of the Interior, offering all his own fertile 900 acres (365 ha) in exchange for the barren mountain for the purpose of paying honor to Crazy Horse.", "The government responded positively, and the U.S. Forest Service, responsible for the land, agreed to grant a permit for the use of the land, with a commission to oversee the project.", "Standing Bear chose not to seek government funds and relied instead upon influential Americans interested in the welfare of the American Indian to privately fund the project.", "In the spring of 1940, Ziolkowski spent three weeks with Standing Bear at Pine Ridge, South Dakota, discussing land ownership issues and learning about Crazy Horse and the Lakota way of life.", "According to Ziolkowski, \"Standing Bear grew very angry when he spoke of the broken Treaty of Fort Laramie (1868).", "That was the one I'd read about in which the President promised the Black Hills would belong to the Indians forever.", "I remember how his old eyes flashed out of that dark mahogany face, then he would shake his head and fall silent for a long while.", "\"", "The memorial is a non-profit undertaking, and does not accept federal or state funding.", "The Memorial Foundation finances the project by charging fees for its visitor centers, earning revenue from its gift shops and receiving private contributions.", "Ziolkowski reportedly was offered 10 million for the project from the federal government on two occasions, but he turned the offers down.", "He felt the project was more than just a mountain carving, and he feared that his plans for the broader educational and cultural goals of the memorial would be overturned by federal involvement.", "After Ziolkowski died in 1982 at age 74, his widow Ruth Ziolkowski, took charge of the sculpture, overseeing work on the project as CEO from the 1980s to the 2010s.", "Ruth Ziolkowski decided to focus on the completion of Crazy Horse's face first, instead of the horse as her husband had originally planned.", "She believed that Crazy Horse's face, once completed, would increase the sculpture's draw as a tourist attraction, which would provide additional funding.", "She also oversaw the staff, which included seven of her children.", "Sixteen years later, in 1998, both the head and face of Crazy Horse were completed and dedicated; Crazy Horse's eyes are wide, while his head is high.", "Ruth Ziolkowski and seven of the Ziolkowskis' 10 children carried on work at the memorial.", "Daughter Monique Ziolkowski, herself a sculptor, modified some of her father's plans to ensure that the weight of the outstretched arm was supported sufficiently.", "The foundation commissioned reports from two engineering firms in 2009 to help guide completion of the project.", "Work commenced on the horse after two years of careful planning and measurements.", "Since the completion of the head and face, much of the monument's sculpting work has been dedicated to the much larger horse portion.", "Ruth Ziolkowski died on May 21, 2014, at the age of 87.", "Monique Ziolkowski became CEO and three of her siblings continue to work on the project, as well as three of the Ziolkowskis' grandsons.", "The memorial is to be the centerpiece of an educational/cultural center, to include a satellite campus of the University of South Dakota, with a classroom building and residence hall, made possible by a 2.5 million donation in 2007 from T. Denny Sanford, a philanthropist from Sioux Falls, South Dakota.", "It is called the Indian University of North America and the Indian Museum of North America.", "The current visitor complex will anchor the center.", "Sanford also donated 5 million to the memorial, to be paid 1 million a year for five years as matching donations were raised, specifically to further work on the horse's head.", "Paul and Donna \"Muffy\" Christen of Huron, South Dakota, in July 2010, announced they were donating 5 million in two installments to an endowment to support the operation of the satellite campus.", "It holds classes in math, English, and American Indian studies courses for college credit, as well as outreach classes.", "The memorial foundation has awarded more than 1.2 million in scholarships, with the majority going to Native students within South Dakota.", "The Memorial foundation began its first national fund drive in October 2006.", "The goal was to raise 16.5 million by 2011.", "The first planned project was a 1.4 million dormitory to house 40 American Indian students who would work as interns at the memorial.", "Crazy Horse resisted being photographed and was deliberately buried where his grave would not be found.", "Ziolkowski envisioned the monument as a metaphoric tribute to the spirit of Crazy Horse and Native Americans.", "He reportedly said, \"My lands are where my dead lie buried.\"", "His extended hand on the monument is to symbolize that statement.", "Elaine Quiver, a descendant of one of Crazy Horse's aunts, said in 2003 that the elder Standing Bear should not have independently petitioned Ziolkowski to create the memorial, because Lakota culture dictates consensus from family members for such a decision, which was not obtained before the first rock was dynamited in 1948.", "She said:\nThey don't respect our culture because we didn't give permission for someone to carve the sacred Black Hills where our burial grounds are.", "They were there for us to enjoy and they were there for us to pray.", "But it wasn't meant to be carved into images, which is very wrong for all of us.", "The more I think about it, the more it's a desecration of our Indian culture.", "Not just Crazy Horse, but all of us.", "Seth Big Crow, whose great-grandmother was an aunt of Crazy Horse's, said he wondered about the millions of dollars which the Ziolkowski family had collected from the visitor center and shops associated with the memorial, and \"the amount of money being generated by his ancestor's name\".", "He said:\nOr did it give them free hand to try to take over the name and make money off it as long as they're alive and we're alive?", "When you start making money rather than to try to complete the project, that's when, to me, it's going off in the wrong direction.", "Other traditional Lakota oppose the memorial.", "In his 1972 autobiography, John Fire Lame Deer, a Lakota medicine man, said: \"The whole idea of making a beautiful wild mountain into a statue of him is a pollution of the landscape.", "It is against the spirit of Crazy Horse.\"", "In a 2001 interview, Lakota activist Russell Means said: \"Imagine going to the holy land in Israel, whether you're a Christian or a Jew or a Muslim, and start carving up the mountain of Zion.", "It's an insult to our entire being.", "It's bad enough getting four white faces carved in up there, the shrine of hypocrisy.", "\"\nIn his 2019 \"New Yorker\" article, ‘Who Speaks for Crazy Horse?’, author Brooke Jarvis states: “On Pine Ridge and in Rapid City, I heard a number of Lakota say that the memorial has become a tribute not to Crazy Horse but to Ziolkowski and his family”." ]

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[ "The memorial was commissioned by Henry Standing Bear, a Lakota elder, to be sculpted by Korczak Ziolkowski." ]