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<!--  Do not use: {{lowercase}} - kelvin (temperature) is treated as a common noun, capitalized in TITLES and start of a sentence -->
{{Short description|SI unit of temperature}}
{{About|the unit of temperature|the person|Lord Kelvin|other uses}}
{{Use dmy dates|date=December 2020|cs1-dates=y}}
{{Use British English|date=November 2018}}
{{Infobox Unit
| name          = kelvin <!--not capitalized-->
| image         = Temperature-scales-comparison.svg
| caption       = Equivalent temperatures in kelvin&nbsp;(K), Celsius&nbsp;(°C), and [[Fahrenheit]]&nbsp;(°F)
| standard      = [[SI]]
| quantity      = temperature
| symbol        = K
| namedafter    = [[William Thomson, 1st Baron Kelvin]]
| conversionslink = [[Conversion of scales of temperature#Kelvin scale|Conversions]]
| calcinput = {{calculator|id=k|type=number|min=0|size=6|default=273.15}}
| units1        = [[SI derived units]]
| inunits1      = {{calculator|id=c|type=plain|size=9|NaN-text=?|formula=round(k-273.15,5)|default=0}}&nbsp;°C
| units2        = [[Imperial units|Imperial]]/[[US customary units|US]] units
| inunits2      = {{calculator|id=f|type=plain|size=9|NaN-text=?|formula=round((k-273.15)*9/5+32,5)|default=32}}&nbsp;[[Fahrenheit|°F]]
| units3        = Imperial/US absolute scale
| inunits3      = {{calculator|id=ra|type=plain|size=9|NaN-text=?|formula=round(k*1.8,5)|default=491.67}}&nbsp;[[Rankine scale|°Ra]]
| extraheader   = 
| extralabel    = 2019 definition
| extradata     = [[Boltzmann constant|{{math|''k''<sub>B</sub>}}]] ≝ {{val|1.380649|e=-23}}&nbsp;{{sfrac|[[Joules|J]]|K}}
}}

The '''kelvin''' (symbol: '''K''') is the [[SI base unit|base unit]] for [[temperature]] in the [[International System of Units]] (SI). The '''Kelvin scale''' is an [[absolute scale|absolute]] [[temperature scale]] that starts at the lowest possible temperature ([[absolute zero]]), taken to be 0&nbsp;K.<ref name="MEP for kelvin 2019"/><ref name="SI Brochure 9"/><ref name="BIPM web page for kelvin"/><ref name="NIST SI redefinition"/> By definition, the [[Celsius]] scale (symbol °C) and the Kelvin scale have the exact same magnitude; that is, a rise of 1&nbsp;K is equal to a rise of 1&nbsp;°C and vice versa, and any temperature in degrees Celsius can be converted to kelvin by adding 273.15.<ref name="MEP for kelvin 2019" /><ref name="nist intro" />

The 19th century British scientist [[Lord Kelvin]] first developed and proposed the scale.<ref name="nist intro"/> It was often called the "absolute Celsius" scale in the early 20th century.<ref name="absoluteC"/> The kelvin was formally added to the International System of Units in 1954, defining 273.16&nbsp;K to be the [[triple point of water]]. The Celsius, [[Fahrenheit]], and [[Rankine scale|Rankine]] scales were redefined in terms of the Kelvin scale using this definition.<ref name="SI Brochure 9" /><ref name="Busting Myths about the Metric System" /><ref name="NIST HB44 Appendix C" /> The [[2019 revision of the SI]] now defines the kelvin in terms of energy by setting the [[Boltzmann constant]] to ''exactly'' {{physconst|k|ref=no|symbol=no|unit=[[joules]] per kelvin}};<ref name="SI Brochure 9" /> every 1&nbsp;K change of [[thermodynamic temperature]] corresponds to a [[thermal energy]] change of exactly {{val|1.380649|e=−23|u=J}}.

== History ==
{{see also|Thermodynamic temperature#History}}

=== Precursors ===
[[File:Melting ice thermometer.jpg|thumb|An ice water bath offered a practical [[calibration]] point for [[thermometers]] (shown here in Celsius) before the physical nature of heat was well understood.]]

During the 18th century, [[Conversion of scales of temperature|multiple temperature scales]] were developed,<ref name="NIST kelvin history">{{cite journal |title=Kelvin: History |url=https://www.nist.gov/si-redefinition/kelvin-history |journal=NIST |date=14 May 2018 |access-date=21 February 2022}}</ref> notably [[Fahrenheit]] and centigrade (later Celsius). These scales predated much of the modern science of [[thermodynamics]], including [[atomic theory]] and the [[kinetic theory of gases]] which underpin the concept of absolute zero. Instead, they chose defining points within the range of human experience that could be reproduced easily and with reasonable accuracy, but lacked 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 ice served as such a starting point, with Celsius being defined (from the [[1740s]] to the [[1940s]]) by calibrating a thermometer such that:
* Water's [[freezing point]] is 0&nbsp;°C.
* Water's [[boiling point]] is 100&nbsp;°C.

This definition assumes pure water at a specific [[pressure]] chosen to approximate the natural air pressure at sea level. Thus, an increment of 1&nbsp;°C equals {{sfrac|1|100}} of the temperature difference between the melting and boiling points. The same temperature interval was later used for the Kelvin scale.

=== Charles's law ===
From 1787 to 1802, it was determined by [[Jacques Charles]] (unpublished), [[John Dalton]],<ref name="Dalton_1801_1"/><ref name="Dalton_1801_2"/> and [[Joseph Louis Gay-Lussac]]<ref name="Gay-Lussac_1802"/> that, at constant pressure, ideal gases expanded or contracted their volume linearly ([[Charles's law]]) by about 1/273 parts per degree Celsius of temperature's change up or down, between 0&nbsp;°C and 100&nbsp;°C. Extrapolation of this law suggested that a gas cooled to about −273&nbsp;°C would occupy zero volume.

=== Lord Kelvin ===
[[File:Baron Kelvin 1906.jpg|thumb|upright|[[William Thomson, 1st Baron Kelvin|Lord Kelvin]], the namesake of the unit of measure.]]

==== First absolute scale ====
In 1848, William Thomson, who was later [[Nobility|ennobled]] as [[Lord Kelvin]], published a paper ''On an Absolute Thermometric Scale''.{{sfn|Thomson|1882|pp=100–106}} The scale proposed in the paper turned out to be unsatisfactory, but the principles and formulas upon which the scale was based were correct.<ref name="Magie">{{cite book |last1=Magie |first1=William Francis |title=A Source Book In Physics |date=1935 |page=237 |url=https://archive.org/details/in.ernet.dli.2015.449479/page/n251/mode/2up}}</ref> For example, in a footnote, Thomson derived the value of −273&nbsp;°C for absolute zero by calculating the negative reciprocal of 0.00366—the [[Thermal expansion#Isobaric expansion in ideal gases|coefficient of thermal expansion]] of an ideal gas per degree Celsius relative to the ice point.<ref>{{harvnb|Thomson|1882|p=104}}: "If we push the strict principle of graduation, stated above, sufficiently far, we should arrive at a point corresponding to the volume of air being reduced to nothing, which would be marked as −273° of the scale (−100/·366, if ·366 be the coefficient of expansion); and therefore −273° of the air-thermometer is a point which cannot be reached at any finite temperature, however low."</ref> This derived value agrees with the currently accepted value of −273.15&nbsp;°C, allowing for the precision and uncertainty involved in the calculation.

The scale was designed on the principle that "a unit of heat descending from a body {{mvar|A}} at the temperature {{mvar|T}}° of this scale, to a body {{mvar|B}} at the temperature {{nowrap|({{mvar|T}} − 1)°}}, would give out the same mechanical effect, whatever be the number {{mvar|T}}."{{sfn|Thomson|1882|p=104}} Specifically, Thomson expressed the amount of work necessary to produce a unit of heat (the [[thermal efficiency]]) as <math>\mu(t) (1 + E t)/E</math>, where <math>t</math> is the temperature in Celsius, <math>E</math> is the coefficient of thermal expansion, and <math>\mu(t)</math> was "Carnot's function", a substance-independent quantity depending on temperature,{{sfn|Thomson|1882|p=187}} motivated by an obsolete version of [[Carnot's theorem (thermodynamics)|Carnot's theorem]].<ref name="Magie"/>{{sfn|Thomson|1882|p=106}} The scale is derived by finding a change of variables <math>T_{1848} = f(T)</math> of temperature <math>T</math> such that <math>dT_{1848} / dT</math> is proportional to <math>\mu</math>.
[[File:CelsiusKelvinThermometer.jpg|thumb|Thermometer showing temperature in kelvin and degrees Celsius]]
When Thomson published his paper in 1848, he only considered Regnault's experimental measurements of <math>\mu(t)</math>.{{sfn|Thomson|1882|p=193}} That same year, [[James Prescott Joule]] suggested to Thomson that the true formula for Carnot's function was{{sfn|Thomson|1882|p=212}}
<math display="block">\mu(t) = J \frac{E}{1+E t},</math>
where <math>J</math> is "the mechanical equivalent of a unit of heat",{{sfn|Thomson|1882|p=186}} now referred to as the [[specific heat capacity]] of water, approximately {{convert|771.8|ftlbf/F/lb|J/K/kg}}.{{sfn|Thomson|1882|p=192}} Thomson was initially skeptical of the deviations of Joule's formula from experiment, stating "I think it will be generally admitted that there can be no such inaccuracy in Regnault's part of the data, and there remains only the uncertainty regarding the density of saturated steam".{{sfn|Thomson|1882|pp=214–215}} Thomson referred to the correctness of Joule's formula as "[[Julius von Mayer|Mayer]]'s hypothesis", on account of it having been first assumed by Mayer.{{sfn|Thomson|1882|p=213}} Thomson arranged numerous experiments in coordination with Joule, eventually concluding by 1854 that Joule's formula was correct and the effect of temperature on the density of saturated steam accounted for all discrepancies with Regnault's data.{{sfn|Thomson|1882|p=388}} Therefore, in terms of the modern Kelvin scale <math>T</math>, the first scale could be expressed as follows:{{sfn|Thomson|1882|p=106}}
<math display="block">T_{1848} = 100 \times \frac{\log(T / \text{273 K})}{\log(\text{373 K} / \text{273 K})}</math>
The parameters of the scale were arbitrarily chosen to coincide with the Celsius scale at 0° and 100&nbsp;°C or 273 and 373 K (the melting and boiling points of water).<ref>{{harvnb|Thomson|1882|p=105}}: "The arbitrary points which coincide on the two scales are 0° and 100°"</ref> On this scale, an increase of approximately 222&nbsp;degrees corresponds to a doubling of Kelvin temperature, regardless of the starting temperature, and "infinite cold" ([[absolute zero]]) has a numerical value of negative [[infinity]].<ref>{{cite journal |last1=Saslow |first1=WM |title=A History of Thermodynamics: The Missing Manual. |journal=Entropy |date=7 January 2020 |volume=22 |issue=1 |doi=10.3390/e22010077|doi-access=free |pmid=33285852|pmc=7516509 |bibcode=2020Entrp..22...77S |at=eqn. (36)}}</ref>

==== Modern absolute scale ====

Thomson understood that with Joule's proposed formula for <math>\mu</math>, the relationship between work and heat for a perfect thermodynamic engine was simply the constant <math>J</math>.{{sfn|Thomson|1882|p=190|loc=formula (7)|}} In 1854, Thomson and Joule thus formulated a second absolute scale that was more practical and convenient, agreeing with air thermometers for most purposes.{{sfn|Thomson|1882|pp=106,232–236}} Specifically, "the numerical measure of temperature shall be simply the mechanical equivalent of the thermal unit divided by Carnot's function."{{sfn|Thomson|1882|p=234}}

To explain this definition, consider a reversible [[Carnot cycle]] engine, where <math>Q_H</math> is the amount of heat energy transferred into the system, <math>Q_C</math> is the heat leaving the system, <math>W</math> is the work done by the system (<math>Q_H - Q_C</math>), <math>t_H</math> is the temperature of the hot reservoir in Celsius, and <math>t_C</math> is the temperature of the cold reservoir in Celsius. The Carnot function is defined as <math>\mu =W / Q_H / (t_H - t_C)</math>, and the absolute temperature as <math>T_H = J/\mu</math>. One finds the relationship <math>T_H= J \times Q_H \times (t_H-t_C)/W</math>. By supposing <math>T_H-T_C=J \times (t_H-t_c)</math>, one obtains the general principle of an absolute thermodynamic temperature scale for the Carnot engine, <math>Q_H / T_H = Q_C / T_C</math>. The definition can be shown to correspond to the thermometric temperature of the [[ideal gas law]]s.<ref>{{cite book |last1=Wang |first1=Lin-Shu |title=A treatise of heat and energy |date=2020 |publisher=Springer |location=Cham |isbn=9783030057466 |page=77}}</ref>

This definition by itself is not sufficient. Thomson specified that the scale should have two properties:{{sfn|Thomson|1882|p=235}}
* The absolute values of two temperatures are to one another in the proportion of the heat taken in to the heat rejected in a perfect thermodynamic engine working with a source and refrigerator at the higher and lower of the temperatures respectively.
* The difference of temperatures between the freezing- and boiling-points of water under standard atmospheric pressure shall be called 100 degrees. (The same increment as the Celsius scale) Thomson's best estimates at the time were that the temperature of freezing water was 273.7&nbsp;K and the temperature of boiling water was 373.7&nbsp;K.{{sfn|Thomson|1882|p=236}}

These two properties would be featured in all future versions of the Kelvin scale, although it was not yet known by that name. In the early decades of the 20th century, the Kelvin scale was often called the "absolute [[Celsius scale|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.<ref name="absoluteC">''Encyclopaedia Britannica'' editions from the 1920s and 1950s, the article "Planets".</ref>

=== Triple point standard ===
[[Image:Phase-diag2.svg|thumb|upright=1.5|A typical [[phase diagram]]. The solid green line applies to most substances; the dashed green line gives the anomalous behavior of water. The boiling line (solid blue) runs from the triple point to the [[Critical point (thermodynamics)|critical point]], beyond which further increases in temperature and pressure produce a [[supercritical fluid]].]]
In 1873, William Thomson's older brother [[James Thomson (engineer)|James]] coined the term ''[[triple point]]''<ref>{{Cite journal|last=Thomson|first=James|date=1873|title=A quantitative investigation of certain relations between the gaseous, the liquid, and the solid states of water-substance|journal=Proceedings of the Royal Society of London|url=https://babel.hathitrust.org/cgi/pt?id=hvd.32044106377062&view=1up&seq=48|volume=22|page=28|bibcode=1873RSPS...22...27T |issn=0370-1662|quote=and consequently that the three curves would meet or cross each other in one point, which I have called the ''triple point''.}}</ref> to describe the combination of temperature and [[pressure]] at which the solid, liquid, and gas [[Phase (matter)|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 a single pressure and only at a single temperature. By the 1940s, the triple point of water had been experimentally measured to be about 0.6% of [[standard atmosphere (unit)|standard atmospheric pressure]] and very close to 0.01&nbsp;°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&nbsp;°C exactly<ref name=":0">{{Cite journal |last=Swinton |first=F. L. |date=September 1967 |title=The triplet point of water |url=https://pubs.acs.org/doi/abs/10.1021/ed044p541 |journal=Journal of Chemical Education |language=en |volume=44 |issue=9 |pages=541 |doi=10.1021/ed044p541 |bibcode=1967JChEd..44..541S |issn=0021-9584}}</ref> 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 [[Low-pressure area|fluctuating]] value) close to 0&nbsp;°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.<ref name="CGPM 9 res 3 (1948)">{{cite web |title=Resolution 3 of the 9th CGPM (1948) |url=https://www.bipm.org/en/committees/cg/cgpm/9-1948/resolution-3 |publisher=BIPM |access-date=21 February 2022}}</ref> The triple point could be measured with ±0.0001&nbsp;°C accuracy, while the melting point just to ±0.001&nbsp;°C.<ref name=":0" />

In 1954, with absolute zero having been experimentally determined to be about −273.15&nbsp;°C per the definition of °C then in use, Resolution&nbsp;3 of the 10th [[General Conference on Weights and Measures]] (CGPM) introduced a new internationally standardized Kelvin scale which defined the triple point as exactly 273.15 + 0.01 = 273.16 degrees Kelvin.<ref name="CGPM 10 res 3 (1954)">{{cite web |title=Resolution 3 of the 10th CGPM (1954) |url=https://www.bipm.org/en/committees/cg/cgpm/10-1954/resolution-3 |publisher=BIPM |access-date=21 February 2022}}</ref><ref name=res310>{{cite web |title=Resolution 3: Definition of the thermodynamic temperature scale |work=Resolutions of the 10th CGPM |publisher=Bureau International des Poids et Mesures |url=http://www.bipm.fr/en/CGPM/db/10/3/ |year=1954 |access-date=2008-02-06 |url-status=dead |archive-url=https://web.archive.org/web/20070623215318/http://www.bipm.fr/en/CGPM/db/10/3/ |archive-date=23 June 2007}}</ref>

In 1967/1968, Resolution&nbsp;3 of the 13th CGPM renamed the unit increment of thermodynamic temperature "kelvin", symbol K, replacing "degree Kelvin", symbol {{not a typo|°K}}.<ref name="CGPM 13 res 3 (1967)" /><ref name=res313>{{cite web |title=Resolution 3: SI unit of thermodynamic temperature (kelvin) |work=Resolutions of the 13th CGPM |url=http://www.bipm.fr/en/CGPM/db/13/3/ |publisher=Bureau International des Poids et Mesures |year=1967 |access-date=2008-02-06 |url-status=dead |archive-url=https://web.archive.org/web/20070421013852/http://www.bipm.fr/en/CGPM/db/13/3/ |archive-date=21 April 2007}}</ref><ref name="Westphal_1952"/> The 13th CGPM also held in Resolution&nbsp;4 that "The kelvin, unit of thermodynamic temperature, is equal to the fraction {{sfrac|273.16}} of the thermodynamic temperature of the triple point of water."<ref name="NIST SI redefinition" /><ref name="CGPM 13 res 4 (1967)">{{cite web |title=Resolution 4 of the 13th CGPM (1967) |url=https://www.bipm.org/en/committees/cg/cgpm/13-1967/resolution-4 |publisher=BIPM |access-date=21 February 2022}}</ref><ref name="res413">{{cite web|url=https://www.bipm.org/en/CGPM/db/13/4/|title=Resolution 4: Definition of the SI unit of thermodynamic temperature (kelvin)|year=1967|work=Resolutions of the 13th CGPM|publisher=Bureau International des Poids et Mesures|archive-url=https://web.archive.org/web/20070615125646/http://www.bipm.fr/en/CGPM/db/13/4/|archive-date=15 June 2007|url-status=dead |access-date=2008-02-06}}</ref>

After [[metre#Speed of light definition|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.

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]].<ref name="NIST SI redefinition" /><ref name="CGPM 23 res 10 (2007)">{{cite web |title=Resolution 10 of the 23rd CGPM (2007) |url=https://www.bipm.org/en/committees/cg/cgpm/23-2007/resolution-10 |publisher=BIPM |access-date=21 February 2022}}</ref><ref name=sib2115>{{cite web|title=Unit of thermodynamic temperature (kelvin) |work=SI Brochure, 8th edition |at=Section 2.1.1.5 |url=http://www1.bipm.org/en/si/si_brochure/chapter2/2-1/2-1-1/kelvin.html |publisher=Bureau International des Poids et Mesures |year=1967 |access-date=2008-02-06 |url-status=dead |archive-url=https://web.archive.org/web/20070926215600/http://www1.bipm.org/en/si/si_brochure/chapter2/2-1/2-1-1/kelvin.html |archive-date=26 September 2007 }}</ref>

=== 2019 redefinition ===
{{main|2019 revision of the SI}}
[[File:Unit relations in the new SI black arrows to K.svg|thumb|280x280px|2019 SI unit dependencies. The kelvin (K) is now fixed in terms of the Boltzmann constant ({{math|''k''<sub>B</sub>}}) and the [[joule]]. The joule is not shown because it is a [[SI derived unit|derived unit]] defined by the metre (m), second (s), and kilogram (kg). Those SI base units are themselves defined by the [[Physical constant|universal constants]] of the [[speed of light]] (''{{mvar|c}}''), the [[Caesium standard|caesium-133 hyperfine transition frequency]] ({{math|Δ''ν''<sub>Cs</sub>}}) and the [[Planck constant]] (''{{mvar|h}}''). Black arrows trace the dependencies from these constants to the kelvin.]]
In 2005, the [[International Committee for Weights and Measures|CIPM]] began a programme to redefine the kelvin (along with other [[SI base units]]) using a more experimentally rigorous method. In particular, the committee proposed [[2019 revision of the SI#Kelvin|redefining the kelvin]] such that the [[Boltzmann constant]] ({{math|''k''<sub>B</sub>}}) would take the exact value {{val|1.3806505|e=-23|u=J|up=K}}.<ref name="draft">
{{cite web
|url=http://www.bipm.org/utils/en/pdf/si_brochure_draft_ch2.pdf
|title=Draft Chapter 2 for SI Brochure, following redefinitions of the base units
|author=Ian Mills
|publisher=CCU
|website=BIPM
|date=29 September 2010
|access-date=2011-01-01
|url-status=dead
|archive-url=https://web.archive.org/web/20110110104615/http://www.bipm.org/utils/en/pdf/si_brochure_draft_ch2.pdf
|archive-date=10 January 2011
}}</ref> The committee hoped 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 part of a [[2019 revision of the SI|larger program]].<ref>
{{cite press release
| url = http://www.bipm.org/utils/en/pdf/Press_release_resolution_1_CGPM.pdf
| title = General Conference on Weights and Measures approves possible changes to the International System of Units, including redefinition of the kilogram.
| publisher = [[General Conference on Weights and Measures]]
| location = Sèvres, France
| date = 23 October 2011
| access-date = 25 October 2011
| url-status = dead
| archive-url = https://web.archive.org/web/20120209175127/http://www.bipm.org/utils/en/pdf/Press_release_resolution_1_CGPM.pdf
| archive-date = 9 February 2012
}}</ref> A challenge was to avoid degrading the accuracy of measurements close to the triple point. The redefinition was further postponed in 2014, pending more accurate measurements of the Boltzmann constant in terms of the current definition,<ref>
{{Cite web
 |url=http://www.bipm.org/cc/TGFC/Allowed/Minutes/CODATA_Minutes_14-BIPM-public.pdf
 |title=Report on the Meeting of the CODATA Task Group on Fundamental Constants
 |date=3–4 November 2014
 |place=[[BIPM]]
 |first=B.
 |last=Wood
 |page=7
 |quote=[BIPM director Martin] Milton responded to a question about what would happen if ... the CIPM or the CGPM voted not to move forward with the redefinition of the SI. He responded that he felt that by that time the decision to move forward should be seen as a foregone conclusion.
 |url-status=dead
 |archive-url=https://web.archive.org/web/20151013174929/http://www.bipm.org/cc/TGFC/Allowed/Minutes/CODATA_Minutes_14-BIPM-public.pdf
 |archive-date=13 October 2015
}}</ref> but was finally adopted at the 26th CGPM in late 2018, with a value of {{math|''k''<sub>B</sub>}}&nbsp;=&nbsp;{{physconst|k|after=.}}<ref name="draft" /><ref name="MEP for kelvin 2019" /><ref name="SI Brochure 9" /><ref name="NIST SI redefinition" /><ref name="CGPM 26 res 1 (2018)" />

In fundamental physics, the mapping {{math|1={{var|E}}={{var|''k''<sub>B</sub>}}{{var|T}}}} which converts between the characteristic microscopic energy and the macroscopic temperature scale is often simplified by using [[natural units]] which set the Boltzmann constant to [[1|unity]]. This convention means that temperature and energy quantities have the same [[Dimension (physics)|dimensions]].<ref name=Kalinin/><ref>{{cite book |last1=Kittel |first1=Charles |last2=Kroemer |first2=Herbert |title=Thermal physics |date=1980 |publisher=W. H. Freeman |location=San Francisco |isbn=0716710889 |pages=41 |edition=2nd |quote=We prefer to use a more natural temperature scale ... the fundamental temperature has the units of energy.}}</ref> In particular, the SI unit kelvin becomes superfluous, being defined in terms of joules as {{math|1= 1 K = {{val|1.380649|e=-23|u=J}}}}.<ref>{{cite journal |last1=Mohr |first1=Peter J. |last2=Shirley |first2=Eric L. |last3=Phillips |first3=William D. |last4=Trott |first4=Michael |title=On the dimension of angles and their units |journal=Metrologia |date=1 October 2022 |volume=59 |issue=5 |pages=053001 |doi=10.1088/1681-7575/ac7bc2|arxiv=2203.12392|bibcode=2022Metro..59e3001M |doi-access=free|quote=The scientific community could have decided to have a unit system in which temperature is measured in joules, but we find it to be more convenient to measure temperature in kelvins.}}</ref> With this convention, temperature is always given in units of energy, and the kelvin unit is not explicitly needed in formulas.<ref name=Kalinin>{{cite journal | doi = 10.1007/s11018-005-0195-9 |last1=Kalinin |first1=M. |last2=Kononogov |first2=S. | title = Boltzmann's Constant, the Energy Meaning of Temperature, and Thermodynamic Irreversibility | journal = Measurement Techniques | pages = 632–636 | volume = 48 | issue = 7 | year = 2005|bibcode=2005MeasT..48..632K |s2cid=118726162 }}</ref>

For scientific purposes, the redefinition's main advantage is in allowing more accurate measurements at very low and very high temperatures, as the techniques used depend on the Boltzmann constant. Independence from any particular substance or measurement is also a philosophical advantage. The kelvin now only depends on the Boltzmann constant and [[Physical constant|universal constants]] (see 2019 SI unit dependencies diagram), allowing the kelvin to be expressed as:<ref name="SI Brochure 9" />

: 1&nbsp;kelvin = {{Nowrap|{{sfrac|{{val|1.380649|e=-23}}|({{val|6.62607015|e=-34}})({{val|9192631770}})}} {{Math|{{sfrac|{{gaps|[[Planck constant|''h'']]|[[Caesium standard|Δ''ν''<sub>Cs</sub>]]}}|[[Boltzmann constant|''k''<sub>B</sub>]]}}}}}} ≈ {{Nowrap|{{val|2.2666653}} {{Math|{{sfrac|{{gaps|''h''|Δ''ν''<sub>Cs</sub>}}|''k''<sub>B</sub>}}}}}}.

For practical purposes, the redefinition was unnoticed; enough digits were used for the Boltzmann constant to ensure that 273.16&nbsp;K has enough [[Significant figures|significant digits]] to contain the uncertainty of water's triple point<ref name="codata2017" /> and water still normally freezes at 0&nbsp;°C<ref>{{cite web |url=http://www.bipm.org/wg/CCT/TG-SI/Allowed/Documents/Updating_the_definition_of_the_kelvin2.pdf |title=Updating the definition of the kelvin |publisher=[[BIPM]] |access-date=2010-02-23 |url-status=dead |archive-url=https://web.archive.org/web/20081123043044/http://www.bipm.org/wg/CCT/TG-SI/Allowed/Documents/Updating_the_definition_of_the_kelvin2.pdf |archive-date=23 November 2008}}</ref> to a high degree of precision. But before the redefinition, the triple point of water was exact and the Boltzmann constant had a measured value of {{val|1.38064903|(51)|e=-23|u=J|up=K}}, with a relative standard uncertainty of {{val|3.7|e=-7}}.<ref name=codata2017>
{{cite journal
 |title=The CODATA 2017 values of ''h'', ''e'', ''k'', and ''N''<sub>A</sub> for the revision of the SI
 |collaboration=Committee on Data for Science and Technology (CODATA) Task Group on Fundamental Constants
 |first1=D B |last1=Newell |first2=F |last2=Cabiati |first3=J |last3=Fischer |first4=K |last4=Fujii
 |first5=S G |last5=Karshenboim |first6=H S |last6=Margolis |first7=E |last7=de Mirandés
 |first8=P J |last8=Mohr |first9=F |last9=Nez |first10=K |last10=Pachucki |first11=T J |last11=Quinn
 |first12=B N |last12=Taylor |first13=M |last13=Wang |first14=B M |last14=Wood |first15=Z |last15=Zhang
 |journal=Metrologia |volume=55 |issue=1 |pages=L13–L16
 |date=29 January 2018
 |doi=10.1088/1681-7575/aa950a |bibcode=2018Metro..55L..13N
 |doi-access=free |bibcode-access=free
}}</ref> Afterward, the Boltzmann constant is exact and the uncertainty is transferred to the triple point of water, which is now {{val|273.1600|(1)|u=K}}.{{efn|name=uncertainty|The absolute uncertainty can be calculated as {{math|273.16 × {{val|3.7|e=-7|u=K}}}}, which can be rounded to {{val|0.10|u=mK}} for all practical purposes.<ref>{{cite journal |last1=Fischer |first1=J |last2=Fellmuth |first2=B |last3=Gaiser |first3=C |last4=Zandt |first4=T |last5=Pitre |first5=L |last6=Sparasci |first6=F |last7=Plimmer |first7=M D |last8=de Podesta |first8=M |last9=Underwood |first9=R |last10=Sutton |first10=G |last11=Machin |first11=G |last12=Gavioso |first12=R M |last13=Madonna Ripa |first13=D |last14=Steur |first14=P P M |last15=Qu |first15=J |last16=Feng |first16=X J |last17=Zhang |first17=J |last18=Moldover |first18=M R |last19=Benz |first19=S P |last20=White |first20=D R |last21=Gianfrani |first21=L |last22=Castrillo |first22=A |last23=Moretti |first23=L |last24=Darquié |first24=B |last25=Moufarej |first25=E |last26=Daussy |first26=C |last27=Briaudeau |first27=S |last28=Kozlova |first28=O |last29=Risegari |first29=L |last30=Segovia |first30=J J |last31=Martín |first31=M C |last32=del Campo |first32=D |title=The Boltzmann project |journal=Metrologia |date=1 April 2018 |volume=55 |issue=2 |pages=R1–R20 |doi=10.1088/1681-7575/aaa790 |pmid=31080297|pmc=6508687|bibcode=2018Metro..55R...1F }}</ref>}}

The new definition officially came into force on 20 May 2019, the 144th anniversary of the [[Metre Convention]].<ref name="CGPM 26 res 1 (2018)">{{cite web |title=Resolution 1 of the 26th CGPM (2018) |url=https://www.bipm.org/en/committees/cg/cgpm/26-2018/resolution-1 |publisher=BIPM |access-date=21 February 2022}}</ref><ref name="MEP for kelvin 2019" /><ref name="SI Brochure 9" /><ref name="NIST SI redefinition" />

== Practical uses ==
[[File:Kelvin Temperature Chart Vertical tightened.svg|thumb|390x390px|[[Colour temperature]] (right) of various light sources (left)]]

=== Colour temperature ===
{{see also|Stefan–Boltzmann constant}}
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 {{val|4000|u=K}} appear reddish, whereas those above about {{val|7500|u=K}} appear bluish. Colour temperature is important in the fields of image projection and photography, where a colour temperature of approximately {{val|5600|u=K}} 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 {{val|5772|u=K}} [https://books.google.com/books?id=zT2HEAAAQBAJ&pg=PA216][https://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html][https://books.google.com/books?id=2QBBEAAAQBAJ&dq=5772+K&pg=PA51][https://arxiv.org/pdf/1605.09788.pdf#] as adopted by IAU 2015 Resolution B3.

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, [[Color theory#Warm vs. cool colors|"warmer" colours]].

=== Kelvin as a unit of noise temperature ===
{{main|Noise figure}}
For [[electronics]], the kelvin is used as an indicator of how [[electronic noise|noisy]] a circuit is in relation to an ultimate [[noise floor]], i.e. the [[noise temperature]]. The [[Johnson–Nyquist noise]] of [[resistors]] (which produces an associated [[Johnson–Nyquist noise#Thermal noise on capacitors|''kTC'' noise]] when combined with [[capacitors]]) is a type of thermal noise derived from the [[Boltzmann constant]] and can be used to determine the noise temperature of a [[Electrical network|circuit]] using the [[Friis formulas for noise]].

== Derived units and SI multiples ==
{{main|Orders of magnitude (temperature)}}
The only [[SI derived unit#Derived units with special names|SI derived unit with a special name]] derived from the kelvin is the degree Celsius. Like other SI units, the kelvin can also be modified by adding a [[metric prefix]] that multiplies it by a [[power of 10]]:
{{SI multiples
| unit=kelvin
| symbol=K
}}

== Orthography ==
According to SI convention, the kelvin is never referred to nor written as a [[Degree (temperature)|''degree'']]. The word "kelvin" is not capitalized when used as a unit. It may be in plural form as appropriate (for example, "it is 283 kelvins outside", as for "it is 50 degrees Fahrenheit" and "10 degrees Celsius").<ref name="plurals">{{citation |work=NIST SP 811 |title=NIST Guide to the SI {{!}} Chapter 9: Rules and Style Conventions for Spelling Unit Names |date=28 January 2016 |url=https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-9-rules-and-style-conventions-spelling-unit-names#97 |quote=A derived unit is usually singular in English, for example, the value 3&nbsp;m<sup>2</sup>·K/W is usually spelled out as 'three square meter kelvin per watt', and the value 3&nbsp;C·m<sup>2</sup>/V is usually spelled out as 'three coulomb meter squared per volt'. However, a 'single' unit may be plural; for example, the value 5&nbsp;kPa is spelled out as 'five kilopascals', although 'five kilopascal' is acceptable. If in such a single-unit case the number is less than one, the unit is always singular when spelled out; for example, 0.5&nbsp;kPa is spelled out as 'five-tenths kilopascal'. }}</ref><ref name="nist intro"/><ref>{{Cite web |title=Definition of KELVIN |url=https://www.merriam-webster.com/dictionary/kelvin |access-date=2023-08-21 |website=www.merriam-webster.com |language=en}}</ref><ref>{{Cite book |url=https://translation-council-support-group.web.cern.ch/sites/default/files/styles/large/CERN%20TM%20English%20language%20style%20guide.pdf |title=CERN English Language Style Guide |publisher=[[CERN]] |year=2022 |pages=64}}</ref> The unit's symbol K is a capital letter,<ref name="CGPM 13 res 3 (1967)">{{cite web |title=Resolution 3 of the 13th CGPM (1967) |url=https://www.bipm.org/en/committees/cg/cgpm/13-1967/resolution-3 |publisher=BIPM |access-date=2022-02-21}}</ref> per the SI convention to capitalize symbols of units derived from the name of a person.<ref>{{Cite journal |date=2010-01-13 |title=Writing with SI (Metric System) Units |url=https://www.nist.gov/pml/owm/writing-si-metric-system-units |journal=NIST |language=en}}</ref> It is common convention to capitalize Kelvin when referring to Lord Kelvin<ref name="nist intro"/> or the Kelvin scale.<ref>{{cite book |last1=Brady |first1=James E. |last2=Senese |first2=Fred |title=Chemistry, Student Study Guide: The Study of Matter and Its Changes |date=28 January 2008 |publisher=John Wiley & Sons |isbn=978-0-470-18464-6 |page=15 |url=https://books.google.com/books?id=zS1EX-e7kPQC&pg=PA15 |language=en}}</ref>

The unit symbol K is encoded in [[Unicode]] at code point {{unichar|212A|kelvin sign}}. However, this is a [[Unicode compatibility characters|compatibility character]] provided for compatibility with legacy encodings. The Unicode standard recommends using {{unichar|004B|latin capital letter [[k]]}} instead; that is, a normal capital [[K]]. "Three letterlike symbols have been given canonical equivalence to regular letters: {{unichar|2126|ohm sign}}, {{unichar|212A|kelvin sign}}, and {{unichar|212B|angstrom sign}}. In all three instances, the regular letter should be used."<ref>{{cite book|title=The Unicode Standard, Version 8.0|date=August 2015|publisher=The Unicode Consortium|location=Mountain View, CA, USA|isbn=978-1-936213-10-8|section=22.2|url=https://www.unicode.org/versions/Unicode8.0.0/ch22.pdf|access-date=6 September 2015|url-status=live|archive-url=https://web.archive.org/web/20161206230132/http://www.unicode.org/versions/Unicode8.0.0/ch22.pdf|archive-date=6 December 2016}}</ref>

== See also ==
{{Portal|Energy}}
* [[Comparison of temperature scales]]
* [[International Temperature Scale of 1990]]
* [[kT (energy)]] – product of the Boltzmann constant and temperature
* [[Negative temperature]]
* [[Outline of metrology and measurement]]

== Notes ==
{{notelist}}

== References ==
{{Reflist|refs=
<ref name="SI Brochure 9">{{cite web |title=SI Brochure: The International System of Units (SI) – 9th edition (updated in 2022) |url=https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf/2d2b50bf-f2b4-9661-f402-5f9d66e4b507 |publisher=BIPM |access-date=7 September 2022}}</ref>
<ref name="BIPM web page for kelvin">{{cite web |title=SI base unit: kelvin (K) |url=https://www.bipm.org/en/si-base-units/kelvin |publisher=BIPM |access-date=5 March 2022}}</ref>
<ref name="NIST SI redefinition">{{cite journal |title=A Turning Point for Humanity: Redefining the World's Measurement System |url=https://www.nist.gov/si-redefinition/turning-point-humanity-redefining-worlds-measurement-system |journal=NIST |date=12 May 2018 |access-date=21 February 2022}}</ref>
<ref name="MEP for kelvin 2019">{{cite web |last=BIPM |date=20 May 2019 |title=Mise en pratique for the definition of the kelvin in the SI |url=https://www.bipm.org/documents/20126/41489682/SI-App2-kelvin.pdf/cd36cb68-3f00-05fd-339e-452df0b6215e?version=1.5&t=1637237805352&download=false |access-date=18 February 2022 |website=BIPM.org}}</ref>
<ref name="nist intro">{{cite web |title=Kelvin: Introduction |url=https://www.nist.gov/si-redefinition/kelvin-introduction |website=NIST |access-date=2 September 2022 |language=en |date=14 May 2018}}</ref>
<ref name="NIST HB44 Appendix C">{{cite web |title=Handbook 44 – 2022 – Appendix C – General Tables of Units of Measurement |url=https://www.nist.gov/system/files/documents/2021/11/30/2022-HB44-Section-Appendix-C.pdf |website=nist.gov |publisher=NIST |access-date=21 February 2022}}</ref>
<ref name="Busting Myths about the Metric System">{{cite journal |author-last=Benham |author-first=Elizabeth |title=Busting Myths about the Metric System |url=https://www.nist.gov/blogs/taking-measure/busting-myths-about-metric-system |journal=NIST |date=6 October 2020 |publisher=Taking Measure (official blog of the NIST) |access-date=21 February 2022}}</ref>
<ref name="Dalton_1801_1">{{Cite journal |author-first=John |author-last=Dalton |date=1801 |url=https://books.google.com/books?id=3qdJAAAAYAAJ&pg=PA595 |title=Essay II. On the force of steam or vapour from water and various other liquids, both in vacuum and in air |journal=Memoirs of the Literary and Philosophical Society of Manchester |volume=5 part 2 |pages=550–574}}</ref>
<ref name="Dalton_1801_2">{{Cite journal |author-first=John |author-last=Dalton |date=1801 |url=https://books.google.com/books?id=3qdJAAAAYAAJ&pg=PA595 |title=Essay IV. On the expansion of elastic fluids by heat |journal=Memoirs of the Literary and Philosophical Society of Manchester |volume=5 part 2 |pages=595–602}}</ref>
<ref name="Gay-Lussac_1802">{{citation |author-last=Gay-Lussac |author-first=Joseph Louis |author-link=Joseph Louis Gay-Lussac |date=1802 |title=Recherches sur la dilatation des gaz et des vapeurs |journal=Annales de Chimie |volume=XLIII |page=137}}. [http://web.lemoyne.edu/~giunta/gaygas.html English translation (extract).]</ref>
<ref name="Westphal_1952">{{cite book |title=Physikalisches Wörterbuch |language=de |trans-title= |chapter=Nox, Dunkelleuchtdichte, Skot |author-first=Wilhelm Heinrich |author-last=Westphal |editor-first1=Wilhelm H. |editor-last1=Westphal |author-link=Wilhelm Heinrich Westphal |date=1952 |edition=1 |publisher=[[Springer-Verlag OHG]] |publication-place=Berlin / Göttingen / Heidelberg, Germany |isbn=978-3-662-12707-0 |doi=10.1007/978-3-662-12706-3 |pages=125, 271, 389 |chapter-url=https://books.google.com/books?id=QaCFBwAAQBAJ&pg=RA1-PA125 |access-date=2023-03-16 |quote-pages=271, 389 |quote=Dunkelleuchtdichte. [...] Unter Zugrundelegung dieser Empfindlichkeitskurve hat man 1940 in Deutschland die Dunkelleuchtdichte mit der Einheit [[Skot (unit)|Skot]] (sk) so festgesetzt, daß bei einem Licht der Farbtemperatur 2360&nbsp;{{not a typo|°[[Kelvin (unit)|K]]}} 1&nbsp;sk&nbsp;= 10<sup>−3</sup>&nbsp;asb gilt. 1948 ist von der [[Internationale Beleuchtungskommission|Internationalen Beleuchtungskommission]] (IBK) die Bezugstemperatur auf 2046&nbsp;{{not a typo|°K}}, die Erstarrungstemperatur des [[Platinum|Platin]]s, festgesetzt worden. Die Bezeichnung Skot wurde von der IBK nicht übernommen, dafür soll "skotopisches Stilb" gesagt werden. Als höchstzulässiger Grenzwert für die Dunkelleuchtdichte ist in Deutschland 10&nbsp;Skot festgesetzt worden, um eine Verwendung der Dunkelleuchtdichte im Gebiet des gemischten [[Photopic vision|Zapfen]]- und [[Scotopic vision|Stäbchensehen]]s zu vermeiden, da in diesem Bereich die photometrischen Maßgrößen wegen der allmählich gleitenden Augenempfindlichkeitskurve ihren Sinn verlieren. [...] Skot, abgek[ürzt] sk, Einheit für die Dunkelleuchtdichte, welche für zahlenmäßige Angaben und zum Anschluß der Dunkelleuchtdichte an die normale Leuchtdichte 1940 von der {{ill|German Lighting Society|de|Deutsche Lichttechnische Gesellschaft|lt=Deutschen Lichttechnischen Gesellschaft}} geschaffen wurde. Für diesen Anschluß wurde die Strahlung des [[Black body|schwarzen Körper]]s bei ''T''&nbsp;= 2360&nbsp;{{not a typo|°K}}, d.h. eine Strahlung der Farbtemperatur ''T''<sub>1</sub>&nbsp;= 2360&nbsp;{{not a typo|°K}} vereinbart. Eine Lichtquelle strahlt mit der Dunkelleuchtdichte 1&nbsp;sk, wenn sie photometrisch gleich einer Strahlung der Farbtemperatur ''T''<sub>2</sub>&nbsp;= 2360&nbsp;{{not a typo|°K}} und der Leuchtdichte von 10<sup>−3</sup>&nbsp;asb (Apostilb) ist. Bei der Farbtemperatur ''T''<sub>1</sub>&nbsp;= 2360&nbsp;{{not a typo|°K}} gilt also die Relation: 1&nbsp;sk&nbsp;= 10<sup>−3</sup>&nbsp;asb&nbsp;= 10<sup>−7</sup>/π sb. |trans-quote=}}</ref>
}}

== Bibliography ==
* {{cite web |author=Bureau International des Poids et Mesures |title=The International System of Units (SI) Brochure |version=9th Edition |publisher=International Committee for Weights and Measures |url=https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf |date=2019 |access-date=2022-04-28}}
* {{cite book |last1=Thomson |first1=William (Lord Kelvin) |title=Mathematical and physical papers: Volume I |date=1882 |publisher=Cambridge University Press |url=https://archive.org/details/mathematicalphys01kelv}}

== External links ==
{{wiktionary}}
* {{cite web |author-last=Thomson |author-first=William |title=On an Absolute Thermometric Scale founded on Carnot's Theory of the Motive Power of Heat, and calculated from Regnault's Observations |url=https://zapatopi.net/kelvin/papers/on_an_absolute_thermometric_scale.html |website=zapatopi.net |publisher=Philosophical Magazine|date=October 1848 |access-date=21 February 2022|archive-url=https://web.archive.org/web/20080201095927/http://zapatopi.net/kelvin/papers/on_an_absolute_thermometric_scale.html |archive-date=1 February 2008}}
* {{cite web |author-last=Thomson |author-first=William |title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam |url=https://zapatopi.net/kelvin/papers/on_the_dynamical_theory_of_heat.html |website=zapatopi.net |publisher=
Transactions of the Royal Society of Edinburgh|date=March 1851|access-date=5 May 2024}}

{{Scales of temperature}}
{{SI units}}
{{CGS units}}

[[Category:1848 introductions]]
[[Category:Scottish inventions]]
[[Category:SI base units]]
[[Category:William Thomson, 1st Baron Kelvin]]
[[Category:Scales of temperature]]
[[Category:Scales in meteorology]]