Thekelvin (symbol:K) is thebase unit fortemperature in theInternational System of Units (SI). TheKelvin scale is anabsolutetemperature scale that starts at the lowest possible temperature (absolute zero), taken to be 0 K.[1][2][3][4] By definition, theCelsius scale (symbol °C) and the Kelvin scale have the exact same magnitude; that is, a rise of 1 K is equal to a rise of 1 °C and vice versa, and any temperature in degrees Celsius can be converted to kelvin by adding 273.15.[1][5]
The 19th century British scientistLord Kelvin first developed and proposed the scale.[5] It was often called the "absolute Celsius" scale in the early 20th century.[6] The kelvin was formally added to the International System of Units in 1954, defining 273.16 K to be thetriple point of water. The Celsius,Fahrenheit, andRankine scales were redefined in terms of the Kelvin scale using this definition.[2][7][8] The2019 revision of the SI now defines the kelvin in terms of energy by setting theBoltzmann constant; every 1 K change ofthermodynamic temperature corresponds to a change in thethermal energy,kBT, ofexactly1.380649×10−23joules.[2]
An ice water bath offered a practicalcalibration point forthermometers (shown here in Celsius) before the physical nature of heat was well understood.
During the 18th century,multiple temperature scales were developed,[9] notablyFahrenheit and centigrade (later Celsius). These scales predated much of the modern science ofthermodynamics, includingatomic theory and thekinetic 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 defunctNewton andRéaumur scales) the melting point of ice served as such a starting point, with Celsius being defined (from the1740s to the1940s) by calibrating a thermometer such that:
This definition assumes pure water at a specificpressure chosen to approximate the natural air pressure at sea level. Thus, an increment of 1 °C equals1/100 of the temperature difference between the melting and boiling points. The same temperature interval was later used for the Kelvin scale.
From 1787 to 1802, it was determined byJacques Charles (unpublished),John Dalton,[10][11] andJoseph Louis Gay-Lussac[12] that, at constant pressure, ideal gases expanded or contracted their volume linearly (Charles's law) by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 °C and 100 °C. Extrapolation of this law suggested that a gas cooled to about −273 °C would occupy zero volume.
In 1848, William Thomson, who was laterennobled asLord Kelvin, published a paperOn an Absolute Thermometric Scale.[13] The scale proposed in the paper turned out to be unsatisfactory, but the principles and formulas upon which the scale was based were correct.[14] For example, in a footnote, Thomson derived the value of −273 °C for absolute zero by calculating the negative reciprocal of 0.00366—thecoefficient of thermal expansion of an ideal gas per degree Celsius relative to the ice point.[15] This derived value agrees with the currently accepted value of −273.15 °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 bodyA at the temperatureT° of this scale, to a bodyB at the temperature(T − 1)°, would give out the same mechanical effect, whatever be the numberT."[16] Specifically, Thomson expressed the amount of work necessary to produce a unit of heat (thethermal efficiency) as, where is the temperature in Celsius, is the coefficient of thermal expansion, and was "Carnot's function", a substance-independent quantity depending on temperature,[17] motivated by an obsolete version ofCarnot's theorem.[14][18] The scale is derived by finding a change of variables of temperature such that is proportional to.
Thermometer showing temperature in kelvin and degrees Celsius
When Thomson published his paper in 1848, he only considered Regnault's experimental measurements of.[19] That same year,James Prescott Joule suggested to Thomson that the true formula for Carnot's function was[20]where is "the mechanical equivalent of a unit of heat",[21] now referred to as thespecific heat capacity of water, approximately 771.8 foot-pounds force per degree Fahrenheit per pound (4,153 J/K/kg).[22] 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".[23] Thomson referred to the correctness of Joule's formula as "Mayer's hypothesis", on account of it having been first assumed by Mayer.[24] 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.[25] Therefore, in terms of the modern Kelvin scale, the first scale could be expressed as follows:[18]The parameters of the scale were arbitrarily chosen to coincide with the Celsius scale at 0° and 100 °C or 273 and 373 K (the melting and boiling points of water).[26] On this scale, an increase of approximately 222 degrees corresponds to a doubling of Kelvin temperature, regardless of the starting temperature, and "infinite cold" (absolute zero) has a numerical value of negativeinfinity.[27]
Thomson understood that with Joule's proposed formula for, the relationship between work and heat for a perfect thermodynamic engine was simply the constant.[28] In 1854, Thomson and Joule thus formulated a second absolute scale that was more practical and convenient, agreeing with air thermometers for most purposes.[29] Specifically, "the numerical measure of temperature shall be simply the mechanical equivalent of the thermal unit divided by Carnot's function."[30]
To explain this definition, consider a reversibleCarnot cycle engine, where is the amount of heat energy transferred into the system, is the heat leaving the system, is the work done by the system (), is the temperature of the hot reservoir in degrees Celsius, and is the temperature of the cold reservoir in Celsius. The Carnot function is defined as, and the absolute temperature as. One finds the relationship. By supposing, one obtains the general principle of an absolute thermodynamic temperature scale for the Carnot engine,. The definition can be shown to correspond to the thermometric temperature of theideal gas laws.[31]
This definition by itself is not sufficient. Thomson specified that the scale should have two properties:[32]
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 K and the temperature of boiling water was 373.7 K.[33]
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 "absoluteCelsius" 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.[6]
A typicalphase 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 thecritical point, beyond which further increases in temperature and pressure produce asupercritical fluid.
In 1873, William Thomson's older brotherJames coined the termtriple point[34] to describe the combination of temperature andpressure at which the solid, liquid, and gasphases of a substance were capable of coexisting inthermodynamic equilibrium. While any two phases could coexist along a range of temperature-pressure combinations (e.g. theboiling 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% ofstandard 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[35] and allowing themelting point at standard atmospheric pressure to have an empirically determined value (and the actual melting point at ambient pressure to have afluctuating 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.[36] The triple point could be measured with ±0.0001 °C accuracy, while the melting point just to ±0.001 °C.[35]
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 10thGeneral 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.[37][38]
In 1967/1968, Resolution 3 of the 13th CGPM renamed the unit increment of thermodynamic temperature "kelvin", symbol K, replacing "degree Kelvin", symbol °K.[39][40][41] The 13th CGPM also held in Resolution 4 that "The kelvin, unit of thermodynamic temperature, is equal to the fraction1/273.16 of the thermodynamic temperature of the triple point of water."[4][42][43]
Afterthe 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", theInternational 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 forVienna Standard Mean Ocean Water.[4][44][45]
2019 SI unit dependencies. The kelvin (K) is now fixed in terms of the Boltzmann constant (kB) and thejoule. The joule is not shown because it is aderived unit defined by the metre (m), second (s), and kilogram (kg). Those SI base units are themselves defined by theuniversal constants of thespeed of light (c), thecaesium-133 hyperfine transition frequency (ΔνCs) and thePlanck constant (h). Black arrows trace the dependencies from these constants to the kelvin.
TheBoltzmann constantkB serves as the bridge in the relationE =kBT, linking characteristic microscopic energies to the macroscopic temperature scale.[46] In the International System of Units (SI), the kelvin has traditionally been treated as an independent base unit with its own dimension. By contrast, in fundamental physics it is common to adoptnatural units by setting the Boltzmann constant equal tounity, so that temperature and energy share the same units.[46][47]
In 2005, theCIPM began a programme to redefine the kelvin in terms of the Boltzmann constant, alongside exploring new definitions for several otherSI base units in terms of fundamental constants. The motivation was to allow more accurate measurements at temperatures far away from the triple point of water, and to be independent from any particular substance or measurement.[48] Originally slated for adoption in 2011 with the Boltzmann constant being1.38065X×10−23 J/K,X to be determined,[49] concerns arose about maintaining the precision of the triple point, and the redefinition was postponed until such time as more accurate measurements could be made, with these experiments taking several years in some cases.[50][51] Ultimately, the kelvin redefinition became part of the larger2019 revision of the SI. In late 2018, the 26th General Conference on Weights and Measures (CGPM) adopted the value ofkB = 1.380649×10−23 J⋅K−1[52][49][1][2][4][53] and the new definition officially came into force on 20 May 2019, the 144th anniversary of theMetre Convention.[53][1][2][4]
With this new definition, the kelvin now only depends on the Boltzmann constant anduniversal constants (see 2019 SI unit dependencies diagram), allowing the kelvin to be expressed as:[2]
In practical terms, as was the goal,[48] the change went largely unnoticed: the chosen value has enough accuracy andsignificant figures for continuity, ensuring that water still freezes at 0 °C to high precision.[54] The difference lies in the status of reference points. Before the redefinition, the triple point of water was taken as exact, while the Boltzmann constant had a measured value of1.38064903(51)×10−23 J/K, with a relative standard uncertainty of3.7×10−7.[55] Afterward, the Boltzmann constant was exact and the uncertainty is transferred to the triple point of water, which is now273.1600(1) K.[a]
On a deeper level, the kelvin is now defined in terms of the joule, making the separate existence of a temperature dimension theoretically unnecessary. The kelvin could have been redefined as a non-coherent derived SI unit, with1 K =1.380649×10−23 J.[46][57] Yet, "for historical and especially practical reasons, the kelvin will continue to be a base unit of the SI".[58]
The kelvin is often used as a measure of thecolour temperature of light sources. Colour temperature is based upon the principle that ablack body radiator emits light with a frequency distribution characteristic of its temperature. Black bodies at temperatures below about4000 K appear reddish, whereas those above about7500 K appear bluish. Colour temperature is important in the fields of image projection and photography, where a colour temperature of approximately5600 K is required to match "daylight" film emulsions.
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.
According to SI convention, the kelvin is never referred to nor written as adegree. 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").[5][63][64][65] The unit's symbol K is a capital letter,[39] per the SI convention to capitalize symbols of units derived from the name of a person.[66] It is common convention to capitalize Kelvin when referring to Lord Kelvin[5] or the Kelvin scale.[67]
The unit symbol K is encoded inUnicode at code pointU+212AKKELVIN SIGN. However, this is acompatibility character provided for compatibility with legacy encodings. The Unicode standard recommends usingU+004BKLATIN CAPITAL LETTER K instead; that is, a normal capitalK. "Three letterlike symbols have been given canonical equivalence to regular letters:U+2126ΩOHM SIGN,U+212AKKELVIN SIGN, andU+212BÅANGSTROM SIGN. In all three instances, the regular letter should be used."[68]
^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."
^Westphal, Wilhelm Heinrich (1952)."Nox, Dunkelleuchtdichte, Skot". In Westphal, Wilhelm H. (ed.).Physikalisches Wörterbuch (in German) (1 ed.). Berlin / Göttingen / Heidelberg, Germany:Springer-Verlag OHG. pp. 125, 271, 389.doi:10.1007/978-3-662-12706-3.ISBN978-3-662-12707-0. Retrieved2023-03-16. pp. 271, 389:Dunkelleuchtdichte. [...] Unter Zugrundelegung dieser Empfindlichkeitskurve hat man 1940 in Deutschland die Dunkelleuchtdichte mit der EinheitSkot (sk) so festgesetzt, daß bei einem Licht der Farbtemperatur 2360 °K 1 sk = 10−3 asb gilt. 1948 ist von derInternationalen Beleuchtungskommission (IBK) die Bezugstemperatur auf 2046 °K, die Erstarrungstemperatur desPlatins, 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 Skot festgesetzt worden, um eine Verwendung der Dunkelleuchtdichte im Gebiet des gemischtenZapfen- undStäbchensehens 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 derDeutschen Lichttechnischen Gesellschaft [de] geschaffen wurde. Für diesen Anschluß wurde die Strahlung desschwarzen Körpers beiT = 2360 °K, d.h. eine Strahlung der FarbtemperaturT1 = 2360 °K vereinbart. Eine Lichtquelle strahlt mit der Dunkelleuchtdichte 1 sk, wenn sie photometrisch gleich einer Strahlung der FarbtemperaturT2 = 2360 °K und der Leuchtdichte von 10−3 asb (Apostilb) ist. Bei der FarbtemperaturT1 = 2360 °K gilt also die Relation: 1 sk = 10−3 asb = 10−7/π sb.{{cite book}}:ISBN / Date incompatibility (help)
^Kittel, Charles; Kroemer, Herbert (1980).Thermal physics (2nd ed.). San Francisco: W. H. Freeman. p. 41.ISBN0716710889.We prefer to use a more natural temperature scale ... the fundamental temperature has the units of energy.
^Fellmuth, B.; Fischer, J.; Machin, G.; Picard, S.; Steur, P. P. M.; Tamura, O.; White, D. R.; Yoon, H. (2016-03-28)."The kelvin redefinition and its mise en pratique".Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.374 (2064).doi:10.1098/rsta.2015.0037.
^Prša, Andrej; Harmanec, Petr; Torres, Guillermo; Mamajek, Eric; Asplund, Martin; Capitaine, Nicole; Christensen-Dalsgaard, Jørgen; Depagne, Éric; Haberreiter, Margit; Hekker, Saskia; Hilton, James; Kopp, Greg; Kostov, Veselin; Kurtz, Donald W.; Laskar, Jacques; Mason, Brian D.; Milone, Eugene F.; Montgomery, Michele; Richards, Mercedes; Schmutz, Werner; Schou, Jesper; Stewart, Susan G. (2016)."NOMINAL VALUES FOR SELECTED SOLAR AND PLANETARY QUANTITIES: IAU 2015 RESOLUTION B3*†".The Astronomical Journal.152 (2): 41.arXiv:1605.09788.doi:10.3847/0004-6256/152/2/41.
^"NIST Guide to the SI | Chapter 9: Rules and Style Conventions for Spelling Unit Names",NIST SP 811, 2016-01-28,A derived unit is usually singular in English, for example, the value 3 m2·K/W is usually spelled out as 'three square meter kelvin per watt', and the value 3 C·m2/V is usually spelled out as 'three coulomb meter squared per volt'. However, a 'single' unit may be plural; for example, the value 5 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 kPa is spelled out as 'five-tenths kilopascal'.
