# Kelvin

Physical unit
Unit name Kelvin
Unit symbol ${\ displaystyle \ mathrm {K}}$
Physical quantity (s) Absolute temperature , temperature difference
Formula symbol ${\ displaystyle T, \, \ Delta T, \, \ Delta \ vartheta}$
dimension ${\ displaystyle {\ mathsf {\ Theta}}}$
system International system of units
In SI units Base unit
Named after Lord Kelvin

The Kelvin (unit symbol: K ) is the SI base unit of thermodynamic temperature and at the same time the legal temperature unit in the EU , Switzerland and almost all other countries. The Kelvin is mainly used in science and technology to indicate temperatures and temperature differences.

The Kelvin scale is shifted by exactly 273.15 K compared to degrees Celsius (° C): A temperature of 0 ° C corresponds to 273.15 K; the absolute zero point is 0 K (= −273.15 ° C). The numerical value of a temperature difference in the two units Kelvin and degrees Celsius is the same.

The Kelvin was named after William Thomson, later Lord Kelvin , who introduced the thermodynamic temperature scale at the age of 24. Until 1967 the unit name was degrees Kelvin , the unit symbol was ° K.

## definition

Thermometer with Kelvin and with degrees Celsius . (Sint Stefans Church, Nijmegen , Netherlands )

The Kelvin is defined by the Boltzmann constant . This was set to the value as part of the redefinition of the International System of Units 2019 . With this definition, the Kelvin is defined independently of materials and normals, but depends via the Joule on the basic units meter , kilogram and second (also defined via natural constants) and thus ultimately on the three natural constants , and . Previously, the Kelvin was defined by the temperature at the triple point (solid / liquid / gaseous) of water. ${\ displaystyle k _ {\ mathrm {B}}}$${\ displaystyle k _ {\ mathrm {B}} = 1.380 \, 649 \ cdot 10 ^ {- 23} \, \ mathrm {J} / \ mathrm {K}}$${\ displaystyle k _ {\ mathrm {B}}}$${\ displaystyle \ Delta \ nu _ {\ mathrm {Cs}}}$${\ displaystyle h}$

The zero point of the Kelvin scale (T = 0 K) lies in the absolute zero point . However, according to Nernst's heat law, this temperature is neither measurable nor achievable.

## Relation to the degree Celsius

The Celsius scale of temperature is defined in such a way that the temperature measured in degrees Celsius is shifted by exactly 273.15 compared to the temperature in Kelvin:

${\ displaystyle \ mathrm {\ left \ {T \ right \} {} _ {K} = \ left \ {\ vartheta \ right \} _ {^ {\ circ} C} +273 {,} 15}}$
${\ displaystyle \ mathrm {\ left \ {\ vartheta \ right \} {} _ {^ {\ circ} C} = \ left \ {T \ right \} _ {K} -273 {,} 15}}$

Through this definition it was achieved that the difference between two temperature values ​​measured in Kelvin and degrees Celsius are numerically the same and can be used equally.

${\ displaystyle {\ frac {\ Delta \, T} {1 \, \ mathrm {K}}} = {\ frac {\ Delta \, \ vartheta} {1 \, ^ {\ circ} \ mathrm {C} }}}$.

With this definition, the freezing and boiling points of water under normal conditions (101.325  kPa pressure) are almost exactly 0 ° C (273.15 K) and 100 ° C (373.15 K).

## history

The absolute temperature scale with the value 0 at absolute zero was proposed by William Thomson (the 1st Baron Kelvin ). The divisions of this temperature scale initially had the designation ° A (for absolute). It was defined in such a way that temperature differences had the same numerical value as on the Celsius scale, which in turn was defined using the freezing point (0 ° C) and boiling point (100 ° C) of water. The absolute scale and the Celsius scale were thereby shifted by a fixed value. (Another absolute temperature scale is the Rankine scale , which is based on the Fahrenheit scale .)

In 1948 the 9th  General Conference on Weights and Measures (CGPM) determined that an absolute thermodynamic scale should have the triple point of water as the only fundamental fixed point. Above all, the strong dependence of the boiling point on the air pressure made temperature calibration using the previous fixed points difficult. The triple point, however, was easily and clearly reproducible. According to the new definition, the zero point of the Celsius scale (then called the centesimal scale in English ) should be exactly 0.01 degrees below. In anticipation of the future name of the unit, the symbol ° K was specified for "Degree Absolute".

In 1954 the Kelvin was defined by the CGPM in the form valid until 2019. and declared to be the basic unit. The name was initially "Degrees Kelvin (° K)" and was changed in 1967 to "Kelvin (K)". Since then the definition has been:

"The Kelvin, the unit of thermodynamic temperature, is the 273.16-th part of the thermodynamic temperature of the triple point of the water." .

With the definition of 1954 the degree Celsius got a new definition. These definitions lasted until May 19, 2019. Only in 2007 was it added that it should be (of course chemically pure) water with the isotopic composition of standard ocean water . The steadily decreasing uncertainties when measuring the temperature of the water triple point made it possible to determine the influence of the isotope composition on the triple point of the water (order of magnitude of about 10 mK).

Since the triple point temperature for calibrating temperature measuring instruments for other temperature ranges was unwieldy, the ITS-90 ("International Temperature Scale of 1990") was created in 1990 . It records several reference values ​​distributed over a large temperature range, for example well-defined melting points; the triple point of the water is also the central point of reference here.

With the redefinition of the International System of Units in 2019, the Kelvin was redefined with reference to natural constants by setting the Boltzmann constant k B to a fixed value. The long-planned redefinition became possible after k B could be measured with a sufficiently high degree of accuracy.

## Thermodynamic temperature

The temperature measured in Kelvin is linked by this definition with the thermal energy of a body or system and is called thermodynamic temperature . For an ideal gas , as long as the number of degrees of freedom does not change, its heat energy is proportional to the temperature. From an atomistic point of view , one can then say that on the Kelvin scale, the mean kinetic energy of the particles (atoms or molecules) is proportional to the temperature, i.e. double the kinetic energy corresponds to double the temperature. Another correlation is derived from the Maxwell-Boltzmann distribution : a doubling of the temperature on the Kelvin scale leads to an increase in the particle speed in the square mean by the factor ( root 2 ). ${\ displaystyle {\ sqrt {2}} \ approx 1 {,} 4142}$

## Color temperature

The color temperature is also given in Kelvin. It is important in photography and for characterizing light sources . The color temperature indicates the spectral radiance distribution of a black body (see Stefan-Boltzmann's law ), which has the temperature = color temperature. In the case of incandescent lamps with wavelength-dependent emissivity and non-thermal light sources, the color temperature deviates from the temperature of the lamp.

According to Wien's law of displacement , the wavelength shift of the spectral radiation maximum is proportional to the temperature change in Kelvin.

Ratio pyrometers use this relationship to measure the temperature of a body for its emission-independent temperature measurement. The prerequisite is that the reception area is a "gray" radiator, i. This means that it has the same emissivity at both reception wavelengths.

## Temperature and energy

It is often important to know whether an energetic barrier can be overcome solely on the basis of thermal fluctuations. The probability of overcoming the barrier is given by the Boltzmann distribution : ${\ displaystyle \ Delta E}$

${\ displaystyle W (E) \ propto \ exp \ left (- {\ frac {\ Delta E} {k _ {\ mathrm {B}} T}} \ right)}$

where is the Boltzmann constant . A barrier is in fact never overcome, with it is easily overcome and with the barrier is practically not perceived. ${\ displaystyle k _ {\ mathrm {B}}}$${\ displaystyle \ Delta E \ gg k _ {\ mathrm {B}} T}$${\ displaystyle \ Delta E = k _ {\ mathrm {B}} T}$${\ displaystyle \ Delta E \ ll k _ {\ mathrm {B}} T}$

For the sake of simplicity, energies are therefore often given in Kelvin or temperatures in energetic units such as joules or electron volts (eV). The conversion factors are then:

${\ displaystyle {\ begin {array} {rcll} 1 \, \ mathrm {K} & {\ hat {=}} & 8 {,} 61735 \ cdot 10 ^ {- 5} \, \ mathrm {eV} \\ 1 \, \ mathrm {eV} & {\ hat {=}} & 1 {,} 16045 \ cdot 10 ^ {4} \, \ mathrm {K} \\ 1 \, \ mathrm {K} & {\ hat { =}} & 1 {,} 38066 \ cdot 10 ^ {- 23} \, \ mathrm {J} \\ 1 \, \ mathrm {J} & {\ hat {=}} & 7 {,} 24290 \ cdot 10 ^ {22} \, \ mathrm {K} \\\ end {array}}}$

This should be illustrated using the example of the hydrogen molecule :

• At what temperature does the hydrogen molecule rotate?
The rotational energy for hydrogen is , where is the rotational constant and the rotational quantum number. To convert the molecule from the non-rotating state ( ) to the slowest rotating state ( ), you need the energy . This corresponds to 175 K. Hydrogen rotates considerably at room temperature.${\ displaystyle E = B \ cdot J \ cdot (J + 1)}$${\ displaystyle B}$${\ displaystyle J}$${\ displaystyle J = 0}$${\ displaystyle J = 1}$${\ displaystyle \ Delta E = E_ {J = 1} -E_ {J = 0} = 2 \ cdot B = 2 {,} 42 \ cdot 10 ^ {- 21} \, \ mathrm {J}}$
• At what temperature do the hydrogen atoms vibrate against each other?
The energy that is needed to produce hydrogen in the first oscillation state to convey is: . Hydrogen molecules only begin to oscillate at very high temperatures of approx. 6000 K.${\ displaystyle \ Delta E = 8 {,} 26 \ cdot 10 ^ {- 20} \, \ mathrm {J}}$

## symbol

The symbol for the unit of measurement is the capital letter " K ". The Unicode standard in the Unicode block "Letter-like symbols" also contains the symbol , but only for reasons of compatibility. The Unicode Consortium expressly advises against its use. U+212A KELVIN SIGN

## Prefixes

SI prefixes for multiples (kilo-, mega-, ...) are uncommon for temperatures in Kelvin . MK, µK and nK are used for fractions of the Kelvin.

## Comparison with other scales

### conversion

Temperatures in Kelvin can be exactly converted using a numerical equation as follows:

 Degree Celsius : ${\ displaystyle \ left \ {t \ right \} _ {\ mathrm {^ {\ circ} C}} = \ left \ {T \ right \} _ {\ mathrm {K}} -273 {,} 15}$ ${\ displaystyle \ left \ {T \ right \} _ {\ mathrm {K}} = \ left \ {t \ right \} _ {\ mathrm {^ {\ circ} C}} +273 {,} 15}$ Fahrenheit degree : ${\ displaystyle \ left \ {t \ right \} _ {\ mathrm {^ {\ circ} F}} = \ left \ {T \ right \} _ {\ mathrm {K}} \ cdot {\ tfrac {9 } {5}} - 459 {,} 67}$ ${\ displaystyle \ left \ {T \ right \} _ {\ mathrm {K}} = (\ left \ {t \ right \} _ {\ mathrm {^ {\ circ} F}} +459 {,} 67 ) \ cdot {\ tfrac {5} {9}}}$ Rankine degree : ${\ displaystyle \ left \ {t \ right \} _ {\ mathrm {^ {\ circ} Ra}} = \ left \ {T \ right \} _ {\ mathrm {K}} \ cdot {\ tfrac {9 } {5}}}$ ${\ displaystyle \ left \ {T \ right \} _ {\ mathrm {K}} = \ left \ {t \ right \} _ {\ mathrm {^ {\ circ} Ra}} \ cdot {\ tfrac {5 } {9}}}$

### Fixed points

Fixed points of common temperature scales
Kelvin ° Celsius ° Fahrenheit ° Rankine ° Réaumur
Boiling point of water at normal pressure  373.150K 100,000 ° C 212,000 ° F 671.670 ° Ra 80,000 ° Ré
" Human body temperature " according to Fahrenheit 308.70 5  K 35, 555  ° C 96,000 ° F 555.670 ° Ra 28, 444  ° Ré
Triple point of water 273.160K 0.010 ° C 32.018 ° F 491.688 ° Ra 0.008 ° Ré
Freezing point of water at normal pressure 273.150K 0.000 ° C 32,000 ° F 491.670 ° Ra 0.000 ° Ré
Cold mixture of water, ice and NH 4 Cl 255.37 2  K −17, 777  ° C 0.000 ° F 459.670 ° Ra −14, 222  ° Ré
absolute zero 0 K −273.150 ° C −459.670 ° F 0 ° Ra −218.520 ° Ré

The fixed points with which the scales were originally defined are highlighted in color and converted exactly into the other scales. Today they have lost their role as fixed points and are only approximate. Only the absolute zero point still has exactly the specified values.

## Individual evidence

1. a b The Kelvin. PTB, February 20, 2019, accessed on April 13, 2019 .
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3. Thermometry: SI base unit (kelvin). In: bipm.org. Bureau International des Poids et Mesures , accessed October 21, 2019 .
4. ^ Resolution 3 of the 9th CGPM (1948). In: bipm.org. Bureau International des Poids et Mesures , accessed August 8, 2019 .
5. ^ Resolution 7 of the 9th CGPM (1948). In: bipm.org. Bureau International des Poids et Mesures , accessed August 17, 2019 .
6. ^ Resolution 3 of the 10th CGPM (1954). In: bipm.org. Bureau International des Poids et Mesures , accessed August 8, 2019 .
7. ^ Resolution 6 of the 10th CGPM (1954). In: bipm.org. Bureau International des Poids et Mesures , accessed August 8, 2019 .
8. ^ Resolution 3 of the 13th CGPM (1967). In: bipm.org. Bureau International des Poids et Mesures , accessed on July 11, 2020 .
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13. Unicode Consortium: The Unicode Standard, Version 10.0. (PDF) 2017, p. 785 , accessed on February 26, 2018 (English).