# Kelvin

The kelvin, symbol K, is a unit of measurement for temperature. The Kelvin scale is an absolute scale, which is defined such that 0 K is absolute zero and a change of thermodynamic temperature T by 1 kelvin corresponds to a change of thermal energy kT by 1.380649×10−23 J. The Boltzmann constant k = 1.380649×10−23 J⋅K−1 was exactly defined in the 2019 redefinition of the SI base units such that the triple point of water is 273.16±0.0001 K. The kelvin is the base unit of temperature in the International System of Units (SI), used alongside its prefixed forms. It is named after the Belfast-born and University of Glasgow-based engineer and physicist William Thomson, 1st Baron Kelvin (1824–1907).

kelvin Thermometer with markings in degrees Celsius and in kelvins
General information
Unit systemSI
Unit oftemperature
SymbolK
Named afterWilliam Thomson, 1st Baron Kelvin
Conversions
x K in ...... corresponds to ...
Celsius   (x − 273.15) °C
Fahrenheit   (1.8 x − 459.67) °F
Rankine   1.8 x °Ra

Historically, the Kelvin scale was developed from the Celsius scale, such that 273.15 K was 0 °C (the approximate melting point of ice) and a change of one kelvin was exactly equal to a change of one degree Celsius. This relationship remains accurate, but the Celsius, Fahrenheit, and Rankine scales are now defined in terms of the Kelvin scale. The kelvin is the primary unit of temperature for engineering and the physical sciences, while in most countries the Celsius scale remains the dominant scale outside of these fields. In the United States, outside of the physical sciences, the Fahrenheit scale predominates, with the kelvin or Rankine scale employed for absolute temperature.

## History

### Precursors An ice water bath offered a practical calibration point for thermometers in a time before the physical nature of heat was well understood.

During the 18th century, multiple temperature scales were developed, 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 water served as such a starting point, with Celsius being defined, from the 1740s up until the 1940s, by calibrating a thermometer such that

This definition assumes pure water at a specific pressure chosen to approximate the natural air pressure at sea level. Thus an increment of 1 °C equals 1/100 of the temperature difference between the melting and boiling points. This temperature interval would go on to become the template for the kelvin.[citation needed]

### Charles's law

From 1787 to 1802, it was determined by Jacques Charles (unpublished), John Dalton, and Joseph Louis Gay-Lussac 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° and 100° C. This suggested that the volume of a gas cooled at about −273 °C would reach zero.

### Lord Kelvin

In 1848, William Thomson, who was later ennobled as Lord Kelvin, 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:

• The melting point of water is 0 degrees.
• The boiling point of water is 100 degrees.

"The arbitrary points which coincide on the two scales are 0° and 100°"

• Any two heat engines whose heat source and heat sink are both separated by the same number of degrees will, per Carnot's theorem, be capable of producing the same amount of mechanical work per unit of "caloric" passing through.

"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."

As 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:

• Efficiency ≤ 1 − absolute temperate of heat sink/absolute temperature of heat source

It 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, T, on the 1848 scale is related to the absolute temperature of the melting point of water, Tmpw, and the absolute temperature of the boiling point of water, Tbpw, by

• T (1848 scale) = 100 (ln T/Tmpw) / (ln Tbpw/Tmpw)

On 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 coefficient of thermal expansion of an ideal gas per degree Celsius relative to the ice point, giving a remarkable consistency to the currently accepted value.[citation needed]

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:

• Absolute zero is the null point.
• Increments have the same magnitude as they do in the Celsius scale.

In 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.[a]

### Triple point standard 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, beyond which further increases in temperature and pressure produce a supercritical fluid.

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 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 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. The triple point could be measured with ±0.0001 °C accuracy, while the melting point just to ±0.001 °C.

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 273.15 + 0.01 = 273.16 degrees Kelvin.

In 1967/1968, Resolution 3 of the 13th CGPM renamed the unit increment of thermodynamic temperature "kelvin", symbol K, replacing "degree Kelvin", symbol °K. The 13th CGPM also held in Resolution 4 that "The kelvin, unit of thermodynamic temperature, is equal to the fraction 1/273.16 of the thermodynamic temperature of the triple point of water."

After 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.

### 2019 redefinition The kelvin is now fixed in terms of the Boltzmann constant and the joule, itself defined by the caesium-133 hyperfine transition frequency and the Planck constant. Both k and kB are accepted shorthand for the Boltzmann constant.

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 1.3806505×10−23 J/K. 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 the Boltzmann constant in terms of the current definition, but was finally adopted at the 26th CGPM in late 2018, with a value of k = 1.380649×10−23 J⋅K−1.

For 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. 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 1.38064903(51)×10−23 J/K, with a relative standard uncertainty of 3.7×10−7. Afterward, the Boltzmann constant is exact and the uncertainty is transferred to the triple point of water, which is now 273.1600(1) K.

The new definition officially came into force on 20 May 2019, the 144th anniversary of the Metre Convention.

## Practical uses

### Colour temperature

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 4000 K appear reddish, whereas those above about 7500 K appear bluish. Colour temperature is important in the fields of image projection and photography, where a colour temperature of approximately 5600 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 5772 K  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, "warmer" colours.

### Kelvin as a unit of noise temperature

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.

## Derived units and SI multiples

The only 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:

Submultiples Multiples Value SI symbol Name Value 10−1 K dK decikelvin 101 K daK decakelvin 10−2 K cK centikelvin 102 K hK hectokelvin 10−3 K mK millikelvin 103 K kK kilokelvin 10−6 K µK microkelvin 106 K MK megakelvin 10−9 K nK nanokelvin 109 K GK gigakelvin 10−12 K pK picokelvin 1012 K TK terakelvin 10−15 K fK femtokelvin 1015 K PK petakelvin 10−18 K aK attokelvin 1018 K EK exakelvin 10−21 K zK zeptokelvin 1021 K ZK zettakelvin 10−24 K yK yoctokelvin 1024 K YK yottakelvin 10−27 K rK rontokelvin 1027 K RK ronnakelvin 10−30 K qK quectokelvin 1030 K QK quettakelvin

## Orthography

According to SI convention, the kelvin is never referred to nor written as a degree. The word "kelvin" is not capitalised when used as a unit. It is pluralised as appropriate (for example, "it is 283 kelvins outside", in contrast with "it is 50 degrees Fahrenheit" or "10 degrees Celsius"). The unit symbol K is a capital letter. It is common convention to capitalize Kelvin when referring to Lord Kelvin or the Kelvin scale.

The unit symbol K is encoded in Unicode at code point U+212A KELVIN SIGN. However, this is a compatibility character provided for compatibility with legacy encodings. The Unicode standard recommends using U+004B K LATIN CAPITAL LETTER K instead; that is, a normal capital K. "Three letterlike symbols have been given canonical equivalence to regular letters: U+2126 OHM SIGN, U+212A KELVIN SIGN, and U+212B ANGSTROM SIGN. In all three instances, the regular letter should be used."