Kelvin

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Kelvin
CelsiusKelvinThermometer.jpg
Thermometer with markings in Celsius and in kelvins
General information
Unit systemInternational system of units (SI)
Unit ofTemperature
SymbolK
Named afterWilliam Thomson, 1st Baron Kelvin
Conversions
x K in ...... is equal to ...
   SI units   x − 273.15 °C
   Imperial/US units   1.8 ( x − 273.15) + 32 °F
   Imperial/US absolute scale   1.8 x °Ra

The kelvin, symbol K, is the SI base unit of temperature,[1][2][3][4] named after the Belfast-born and University of Glasgow based engineer and physicist William Thomson, 1st Baron Kelvin (1824–1907). The Kelvin scale is an absolute thermodynamic temperature scale, meaning it uses absolute zero as its null point.

The Kelvin scale was developed by shifting the starting point of the much older Celsius scale down from the melting point of water to absolute zero, and its increments still closely approximate the historic definition of a degree Celsius, but since 2019 the scale has been defined by fixing the Boltzmann constant k to 1.380649×10−23 J⋅K−1.[1] Hence, one kelvin is equal to a change in the thermodynamic temperature T that results in a change of thermal energy kT by 1.380649×10−23 J. The temperature in Celsius is now defined as the temperature in kelvins minus 273.15,[2] meaning that a change or difference in temperature has exactly the same value when expressed in kelvins as in Celsius, that absolute zero is exactly 0 K and −273.15 °C, and that pure water freezes very close to 273.15 K and boils close to 373.15 K at standard atmospheric pressure.

The kelvin is the primary unit of temperature for engineering and the physical sciences, while in most countries Celsius remains the dominant scale outside of these fields and in the United States the Fahrenheit scale (also now defined using the kelvin[5][6]) is still widespread.

Unlike the degree Fahrenheit and degree Celsius, the kelvin dates to the mid 19th century rather than the early to mid 18th and is never referred to nor written as a degree, nor typically capitalised except when abbreviated to K, e.g. "It's 50 degrees Fahrenheit outside" vs "It's 10 degrees Celsius outside" vs "It's 283 kelvins outside".[7]

History[edit]

Precursors[edit]

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,[8] most notably Fahrenheit and centigrade (later Celsius). These scales predated much of the modern science of thermodynamics, including the scientific consensus in favour of atomic theory and the kinetic theory of gases that underpin the concept of absolute zero. Instead, they chose defining points inside the range of human experience at the time that could be easily and reasonably accurately reproduced, but did not necessarily have any deep significance in thermal physics. In the case of the Celsius scale (and the long since defunct Newton scale and Réaumur scale) the melting point of water served as such a semi-arbitrary starting point, with Celsius being defined, from the 1740s up until the 1940s, by calibrating a thermometer such that:

This referring to pure water at a set pressure designed to approximate the natural air pressure at sea level. An implication of this was that an increment of 1 °C was equal to an increment of 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.

Lord Kelvin[edit]

Lord Kelvin, the namesake of the unit of measure

In October 1848, William Thomson, a 24-year-old professor of Natural Philosophy at the University of Glasgow, published a paper On an Absolute Thermometric Scale.[9][10][11] 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.

Within a decade, Thomson had abandoned caloric theory and superseded the 1848 scale with a new one[10][12] 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.[13]

Triple point standard[edit]

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[14] to describe the combination of temperature and pressure at which the solid, liquid, and gas phases of a substance were capable of coexisting in thermodynamic equilibrium. While any two phases could coexist along a range of temperature-pressure combinations (e.g. the boiling point of water can be affected quite dramatically by raising or lowering the pressure), the triple point condition for a given substance can occur only at 1 pressure and only at 1 temperature. By the 1940s, the triple point of water had been experimentally measured to be about 0.6% of standard atmospheric pressure and very close to 0.01 °C per the historical definition of Celsius then in use.

In 1948, the Celsius scale was recalibrated by assigning the triple point temperature of water the value of 0.01 °C exactly and allowing the melting point at standard atmospheric pressure to have an empirically determined value (and the actual melting point at ambient pressure to have a fluctuating value) close to 0 °C. This was justified on the grounds that the triple point was judged to give a more accurately reproducible reference temperature than the melting point.[15]

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"[16][17]

In 1967/1968, Resolution 3 of the 13th CGPM renamed the unit increment of thermodynamic temperature "kelvin", symbol K, replacing "degree Kelvin", symbol °K.[7][18] Furthermore, feeling it useful to more explicitly define the magnitude of the unit increment, the 13th CGPM also held in Resolution 4 that "The kelvin, unit of thermodynamic temperature, is equal to the fraction 1/273.16 of the thermodynamic temperature of the triple point of water."[4][19][20]

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.

Hydrogen has 2 stable isotopes (and one trace radioisotope) and oxygen has 3 stable isotopes. In 2005, noting that the triple point could be influenced by the isotopic ratio of the hydrogen and oxygen making up a water sample and that this was "now one of the major sources of the observed variability between different realizations of the water triple point", the International Committee for Weights and Measures (CIPM), a committee of the CGPM, affirmed that for the purposes of delineating the temperature of the triple point of water, the definition of the kelvin would refer to water having the isotopic composition specified for Vienna Standard Mean Ocean Water:[4][21][22]

  • 0.000 155 76 moles of 2H per mole of 1H
  • 0.000 379 9 moles of 17O per mole of 16O
  • 0.002 005 2 moles of 18O per mole of 16O

2019 redefinition[edit]

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.[23] 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.[24]

The redefinition was further postponed in 2014, pending more accurate measurements of Boltzmann's constant in terms of the current definition,[25] but was finally adopted at the 26th CGPM in late 2018, with a value of k = 1.380649×10−23 J⋅K−1.[26][23][1][2][4][27]

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.[2] Thus, this definition depends only on universal constants, and not on any physical artifacts as practiced previously, such as the International Prototype of the Kilogram, whose mass diverged over time from the original value. The challenge was to avoid degrading the accuracy of measurements close to the triple point. For practical purposes, the redefinition was unnoticed; water still freezes at 273.15 K (0 °C),[2][28] 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.[29] Afterward, the Boltzmann constant is exact and the uncertainty is transferred to the triple point of water, which is now 273.1600(1) K.

For legal metrology purposes, the new definition officially came into force on 20 May 2019, the 144th anniversary of the Metre Convention.[27][1][2][4]

Post-2019 definition[edit]

Ludwig Boltzmann, namesake of the Boltzmann constant

Interpretation[edit]

The post-2019 definition is based on fixing the value of the Boltzmann constant k, expressed in SI units, at 1.380649×10−23 joules per kelvin.[1] This constant appears in (some formulations of) the ideal gas law, which links the pressure, P, of an ideal gas, its volume, V, its temperature, T, and the number of gas particles making it up, N, via the relationship:

  • P V = N k T

Substituting in the defined value of k gives:

  • P V = N T × 1.380649×10−23 J/K

Which can be rearranged to give:

  • T/K = 1023/1.380649 × P V/J N

Or:

  • T (K) = 1023/1.380649 × P V/N (J)

Where T (K) is the numerical value of the temperature expressed in kelvins, and P V/N (J) is the numerical value of the product of the pressure and the average volume per gas particle expressed in joules. It is worth emphasising that in dimensional analysis terms the product of a pressure and a volume is an energy. This can be seen by considering that pressure, volume, and energy have the dimensions force/length2, length3 and force × length, respectively. Another context where this relationship becomes intuitive is in the case of a pump or a water turbine, where the minimum energy demand and maximum energy available, respectively, is given by the volume of fluid passing through the component multiplied by the pressure differential across it. The above temperature equation holds exactly for an ideal gas, a hypothetical substance composed of point particles affected only by elastic collisions with their container, but is closely approximated by a real gas that is well above its boiling or sublimation point and well below its critical pressure. Using the metric prefix system this can be given as:

Because the average kinetic energy per degree of freedom is P V/N/2 and gas particles have 3 translational degrees of freedom, the temperature in kelvins is also related to the mean kinetic energy per degree of freedom by:

  • T (K) = 1/6.903245 × KE/Degree of freedom (yJ)

And to the mean translational kinetic energy by:

  • T (K) = KETranslational (yJ)/20.709735

Expressed in terms of the SI defining constants 1 kelvin is:

  • 1 K = 1.380649×10−23/9192631770 × 6.62607015×10−34 h ΔνCs/k = 2.761298×1017/121822045942277331 h ΔνCs/k2.266665264601 h ΔνCs/k

Where h is the Planck constant and ΔνCs is the caesium-133 hyperfine transition frequency.[3] Because the term h ΔνCs is equal to the photon energy of the caesium-133 hyperfine transition radiation, ΔECs, and 1/k is equal to N T/P V for an ideal gas:

  • 1 K = 2.761298×1017/121822045942277331 ΔECs N T/P V

Which can be rearranged to give:

  • T/K = 121822045942277331/2.761298×1017 P V/N ΔECs

Or:

  • T (K) = 121822045942277331/2.761298×1017 P V/N ΔECs0.441176743482 P V/N ΔECs

Expressed in terms of mean kinetic energy, this becomes:

  • T (K) = 121822045942277331/1.380649×1017 KE per degree of freedom/ΔECs0.882353486964 KE per degree of freedom/ΔECs

And:

  • T (K) = 40607348647425777/1.380649×1017 KETranslational/ΔECs0.294117828988 KETranslational/ΔECs

Implications[edit]

Although the kelvin is an SI base unit, its only use in fundamental physics is the Boltzmann constant. This allows a natural unit definition kB = 1 that makes kelvins and joules different units for the same dimension, 1 K = 1.380649×10−23 J.[30] Such a definition is already in use in some textbooks.[31] However, such a definition is unlikely to have a practical use in an experiment due to the large orders of magnitude involved.[32]

Several physical constants are defined in terms of the Boltzmann constant and other SI defining constants, for example the universal gas constant, R, is defined as the product of the Boltzmann constant, k, and the Avogadro constant, NA. Prior to 2019, its value in SI units could only be empirically estimated, with a small but inevitable degree of experimental uncertainty. After 2019, the kelvin was redefined by giving an exact value to the Boltzmann constant and the mole was redefined by assigning an exact value to the Avogadro constant, meaning the value of the universal gas constant in SI units could be calculated exactly as:

  • R = k × NA = 1.380649×10−23 J K−1 × 6.02214076×1023 mol−1 = 8.31446261815324 J K−1 mol−1

Similarly, the Stefan-Boltzmann constant, σ, not to be confused with the Boltzmann constant, relates the temperature of a black body to the rate at which thermal energy is electromagnetically radiated from its surface and is equal to:

  • σ = 2 π5 k4/15 h3 c2

Where h is the Planck constant, whose value now defines the kilogram, and c is the speed of light, whose value now defines the metre (and had been implicit in the definition of the metre since 1983).[33] The exact value of σ in SI units is therefore:

  • σ = 2 π5 k4/15 h3 c2 = 2 π5 (1.380649×10−23 J/K)4/15 (6.62607015×10−34 J s)3 (299,792,458 m/s)2 = 5,454,781,984,210,512,994,952,000,000 π5/29,438,455,734,650,141,042,413,712,126,365,436,049 W m−2 K−45.6703744191844288×10−8 W m−2 K−4

The second radiation constant in Planck's law, c2, is equal to:

Which means its exact value in SI units is:

  • c2 = 6.62607015×10−34 J s × 299,792,458 m/s/1.380649×10−23 J/K = 2.72115870842319 m K/189.130.014387768775 m K

1 kelvin[edit]

The Boomerang Nebula, the only known natural environment with a temperature close to 1 kelvin

1 kelvin is the approximate temperature of the Boomerang Nebula, the coldest known natural environment in the universe.[35] Because 1 K is colder than the effective temperature of the cosmic microwave background (about 2.7 K[36]), it cannot be reached simply by moving a previously warm object far away from point sources of heat (e.g. stars) and requires additional cooling mechanisms, such as evaporative cooling, laser cooling, or adiabatic cooling to achieve in the current universe, though in the far future the ongoing expansion of the universe may cause the average temperature of the universe to drop below 1 K. Temperatures significantly colder than 1 K are not known to occur in nature, but have been produced in laboratories[37] and, from the perspective of an external observer, black holes may appear to have temperatures extremely close to absolute zero when not feeding. Their effective temperature, T, due to Hawking radiation is given by:

  • T = c3 ħ/8 π M G k

Where c is the speed of light in a vacuum, ħ is the reduced Planck constant, M is the black hole's mass, and G is the gravitational constant,[38] hence:

  • T(299,792,458 m/s)3 × 6.62607015×10−34 J s/(2 π)/8 π M × 6.674×10−11 m3 kg−1 s−2 × 1.380649×10−23 J/K 1.2269×1023 kg K/M

Which means a black hole of mass 1.2269×1023 kg, about 1.67 times the mass of the moon,[39] would have an effective temperature of ≈ 1 K. Black holes known to actually exist in nature have significantly larger masses (and lower effective temperatures) than this, being at least several solar masses.

At a temperature of 1 K (and a pressure of 1 standard atmosphere) the overwhelming majority of substances are solids,[40] including nitrogen[41] and the even more volatile neon[42] and hydrogen.[43] An exception is helium whose most common isotope, helium-4, exists in an exotic liquid-like state known as a superfluid characterised by a total absence of viscosity,[40] while the much rarer helium-3 isotope remains a "normal" liquid.[40] At 1 K some common metals, including lead and mercury are superconductors, losing all electrical resistance.[44][45][46]

A black body at 1 K radiates energy at a rate of about 56.7 nW per square metre[33] with a peak wavelength of about 2.9 mm,[47] in the microwave spectrum. A heat pump attempting to extract heat from an refrigeration chamber at 1 K and vent it into an ambient environment at 20 °C, would require a minimum of 292.15 joules of mechanical work to draw out 1 joule of thermal energy.

Usage conventions[edit]

Degrees[edit]

Before the 13th CGPM in 1967–1968, the unit kelvin was termed a "degree", the same as with the other temperature scales at the time. It was distinguished from the other scales with either the adjective suffix "Kelvin" ("degree Kelvin") or with "absolute" ("degree absolute") and its symbol was °K. The latter term (degree absolute), which was the unit's official name from 1948 until 1954, was ambiguous since it could also be interpreted as referring to the Rankine scale. Before the 13th CGPM, the plural form was "degrees absolute". The 13th CGPM changed the unit name to simply "kelvin" (symbol: K).[7][48] The omission of "degree" indicates that it is not relative to an arbitrary reference point like the Celsius and Fahrenheit scales (although the Rankine scale continued to use "degree Rankine"), but rather an absolute unit of measure which can be manipulated algebraically (e.g., multiplied by two to indicate twice the amount of "mean energy" available among elementary degrees of freedom of the system).[citation needed]

Pluralisation[edit]

The preferred plural form of kelvin is not explicitly stated in the SI Brochure or in the mise en pratique[1] for the kelvin. The 8th edition of the Brochure (written before the 2019 redefinition) refers to the kelvin in plural as "kelvins":

"A difference or interval of temperature may be expressed in kelvins or in degrees Celsius, the numerical value of the temperature difference being the same."[49]

However in the 9th edition (written after the redefinition) this was changed to:

"A difference or interval of temperature may be expressed in kelvin or in degrees Celsius, the numerical value of the temperature difference being the same in either case."[2]

The US based National Institute of Standards and Technology recommends the use of "kelvins":

"The kelvin unit is not expressed in degrees like Celsius or Fahrenheit are. It is used by itself to describe temperature. For example, 'mercury loses all electrical resistance at a temperature of 4.2 kelvins.'"[4]

The style guide for CERN, however, specifically says to always use "kelvin", even when plural.[50]

The US based Merriam-Webster dictionary recommends "kelvins"[51]

Capitalisation[edit]

When writing the name of the unit out in full it is uncapitalised, except in contexts where most words would be capitalised (e.g. at the start of a sentence or as part of a title) however, when abbreviated to a symbol, K, it is always capitalised. In the SI an uncapitalised (and unitalicised) letter k would indicate the kilo- prefix:

″The kelvin is the SI base unit of temperature.″

Alex: ″What units do you want me to record this in?″ Billie: ″Kelvins!″

″The sample was chilled to 50 K."

″Tay traveled 100 km from Poughkeepsie to Manhattan.″

This somewhat unintuitive convention is in fact in line with other SI units named after people, such as the newton, watt, and tesla, symbols N, W, and T respectively.[2] When reference is made to the "Kelvin scale", Kelvin references a person, not an SI unit, and is therefore capitalized.

Spacing[edit]

As with most other SI unit symbols (angle symbols, e.g., 45° 3′ 4″, are the exception) there is a space between the numeric value and the kelvin symbol (e.g., "99.987 K").[52]

Relation to Celsius and other temperature scales[edit]

Kelvin temperature conversion formulae
from kelvins to kelvins
Celsius [°C] = [K] − 273.15 [K] = [°C] + 273.15
Fahrenheit [°F] = [K] × 95 − 459.67 [K] = ([°F] + 459.67) × 59
Rankine [°R] = [K] × 95 [K] = [°R] × 59
For temperature intervals rather than specific temperatures,
1 K = 1 °C = 95 °F = 95 °R
Comparisons among various temperature scales

The size of a degree Celsius (historically defined as 1/100 of the temperature difference between the melting and boiling points of water, see history section for more details), was the template for the size of the kelvin and the convention that the Kelvin and Celsius scales have the same size increments remains in place today,[2] meaning that a change in temperature or a difference in temperature necessarily has the same numerical value when expressed in kelvins as it does when expressed in degrees Celsius:

  • ΔT (K) = ΔT (°C)

However while the Kelvin scale takes absolute zero as its starting point, the modern iteration of the Celsius scale takes 273.15 K as its starting point, this being a close approximation of the melting point of water at standard atmospheric pressure, indeed, the 9th edition of the SI Brochure defines the temperature in Celsius such that:

  • T (°C) = T (K) − 273.15

So, for example, "It is 10 °C colder outside the house than inside" and "It is 10 K colder outside the house than inside" are exactly equivalent statements, while "It is 10 °C outside" and "It is 10 K outside" describe very different situations! This convention makes conversion between °C and K relatively straightforward, but has the downside that neither the melting nor boiling points of water have round values when expressed in kelvins, being approximately 273.15 K and 373.15 K respectively.

As the melting and boiling points of water were historically 180 degrees apart on the Fahrenheit scale (32 °F and 212 °F, respectively) a temperature interval of 1 K (and of 1 °C) is equal to an interval of 1.8 °F. Absolute zero in °F is:

  • Absolute zero = (−273.15 × 1.8 + 32) °F = −459.67 °F

Hence:

  • T (K) = T (°F) + 459.67/1.8
  • T (°F) = 1.8 × T (K) − 459.67

Colour temperature[edit]

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 5778 K.

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[edit]

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.

Units derived from the kelvin[edit]

The International System of Units (SI) is based on seven SI base units (the second, metre, kilogram, kelvin, ampere, mole, and candela) representing seven fundamental types of physical quantity, or "dimensions" (time, length, mass, temperature, electrical current, amount of substance, and luminous intensity respectively), with all other SI units defined using these seven basic building blocks.[2] These SI derived units can either be given special names, e.g., tesla, volt, lux, etc., or left as bare descriptions, e.g. metre per second. The only SI unit with a special name derived from the kelvin is the degree Celsius, which is also the only SI unit derived from another by offsetting, rather than by multiplication or division. Some commonly used units derived from the kelvin without special names are:

Dimension Unit Symbol In SI base units
Thermal mass/Heat capacity Joule per kelvin J/K kg m2 s−2 K−1
Specific heat capacity Joule per kilogram kelvin J/(kg·K) m2 s−2 K−1
Volumetric heat capacity Joule per cubic metre kelvin J/(m3·K) kg m−1 s−2 K−1
Molar heat capacity Joule per kelvin mole J/(K·mol) kg m2 s−2 mol−1 K−1
Thermal conductivity Watt per metre kelvin W/(m·K) kg m s−3 K−1
Thermal transmittance (U-value) Watt per square metre kelvin W/(m2·K) kg s−3 K−1
R-value Square metre kelvin per watt m2 K/W K kg−1 s3
Coefficient of thermal expansion Inverse kelvin or percent per kelvin 1/K K−1

Many of these are of interest in the engineering of heating, ventilation, and air conditioning systems and of building insulation. Coefficient of thermal expansion is an important consideration in structural engineering.

Multiples[edit]

SI multiples of kelvin (K)
Submultiples Multiples
Value SI symbol Name Value SI symbol Name
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
Common multiples are in bold face.

Like other SI units, the kelvin can modified by adding a prefix that multiplies it by a power of 10.[2]

Yoctokelvin[edit]

A yoctokelvin (yK) is one septillionth of a kelvin (10−24 K) and the smallest unit of temperature defined in the International System of Units. It is a little more than the temperature increase that would result from adding 1 joule of thermal energy to the Indian Ocean, assuming properties similar to those of pure water.[53]

Zeptokelvin[edit]

A zeptokelvin (zK) is one sextillionth of a kelvin (10−21 K). It is somewhat less than the temperature increase that would result from adding 1 joule of thermal energy to the Baltic Sea, assuming properties similar to those of pure water.[53]

Attokelvin[edit]

An attokelvin (aK) is one quintillionth of a kelvin (10−18 K). It is the approximate effective temperature of an extremely massive 61.7 billion solar mass supermassive black hole, only a little less massive than the black hole Ton 618,[38] and the approximate temperature increase that would result from adding 1 joule of thermal energy to Lake Toba, the largest lake in Indonesia.

Femtokelvin[edit]

A femtokelvin (fK) is one quadrillionth of a kelvin (10−15 K). It is the approximate effective temperature of a 61.7 million solar mass supermassive black hole.

Picokelvin[edit]

A picokelvin (pK) is one trillionth of a kelvin (10−12 K).

Nanokelvin[edit]

A nanokelvin (nK) is one billionth of a kelvin (10−9 K). It is the approximate effective temperature of a fairly large 61.7 solar mass stellar-mass black hole. NASA's Cold Atom Laboratory can chill small numbers of atoms down to below 1 nanokelvin.[37]

Microkelvin[edit]

A microkelvin (μK) is one millionth of a kelvin (10−6 K).

Millikelvin[edit]

A millikelvin (mK) is one thousandth of a kelvin (0.001 K or 10−3 K).

Centikelvin[edit]

A centikelvin (cK) is one hundredth of a kelvin (0.01 K or 10−2 K).

Decikelvin[edit]

A decikelvin (dK) is one tenth of a kelvin (0.1 K or 10−1 K).

Decakelvin[edit]

A decakelvin (daK) is ten kelvins (10 K or 101 K). The main components of air, nitrogen and oxygen, boil at 77 K[41] and 90 K[54] respectively under 1 atmosphere of pressure.

Hectokelvin[edit]

A hectokelvin (hK) is one hundred kelvins (100 K or 102 K). Air temperatures recorded occurring naturally on Earth (excluding, e.g. wildfires, volcanoes, and meteorite impacts) range from 184 K at Vostok Station in Antarctica to 330 K at Furnace Creek in Death Valley.[55] Yakutsk in Russia's Sakha Republic has a daily average low in January of 229 K.[56] Ice melts at 273.15 K. Kuwait City has a daily average high in July and August of 320 K.[57] Water boils at 373.15 K at 1 atmosphere. The average surface temperature on Venus in 737 K.[58]

Kilokelvin[edit]

A kilokelvin (kK) is one thousand kelvins (1000 K or 103 K). Iron melts at 1811 K, or 1.8 kK.[59] The temperature at the surface of the Sun is about 5800 K, or 5.8 kK.[60]

Megakelvin[edit]

A megakelvin (MK) is one million kelvins (106 K). The temperature at the centre of the Sun is about 15.7 MK.[60]

Gigakelvin[edit]

A gigakelvin (GK) is one billion kelvins (109 K).

Terakelvin[edit]

A terakelvin (TK) is one trillion kelvins (1012 K).

Petakelvin[edit]

A petakelvin (PK) is one quadrillion kelvins (1015 K).

Exakelvin[edit]

An exakelvin (EK) is one quintillion kelvins (1018 K).

Zettakelvin[edit]

A zettakelvin (ZK) is one sextillion kelvins (1021 K).

Yottakelvin[edit]

A yottakelvin (YK) is one septillion kelvins (1024 K) and the largest unit of temperature defined in the SI. It corresponds to a mean translational kinetic energy of 20.709735 joules, the same order of magnitude as the Oh-My-God particle. The Planck temperature is approximately 141,680,000 yottakelvins.[61]

Unicode character[edit]

The symbol 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."[62]

See also[edit]

References[edit]

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External links[edit]