Kelvin

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kelvin
CelsiusKelvinThermometer.jpg
Thermometer with markings in degrees Celsius and in kelvins
General information
Unit system SI
Unit of temperature
SymbolK
Named after William Thomson, 1st Baron Kelvin
Conversions
x K in ...... corresponds to ...
    Celsius    (x − 273.15) °C
    Fahrenheit    (1.8x − 459.67) °F
    Rankine    1.8x °Ra

The kelvin, symbol K, is a unit of measurement for temperature. [1] 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. [2] The kelvin is the base unit of temperature in the International System of Units (SI), used alongside its prefixed forms. [2] [3] [4] It is named after the Belfast-born and University of Glasgow-based engineer and physicist William Thomson, 1st Baron Kelvin (1824–1907). [5]

Contents

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. [1] [5] This relationship remains accurate, but the Celsius, Fahrenheit, and Rankine scales are now defined in terms of the Kelvin scale. [2] [6] [7] 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. [5] In the United States, outside of the physical sciences, the Fahrenheit scale predominates, with the kelvin or Rankine scale employed for absolute temperature. [6]

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. Melting ice thermometer.jpg
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] 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. 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, [9] [10] and Joseph Louis Gay-Lussac [11] 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. This suggested that the volume of a gas cooled at about −273 °C would reach zero.

Lord Kelvin

Lord Kelvin, the namesake of the unit of measure. Baron Kelvin 1906.jpg
Lord Kelvin, the namesake of the unit of measure.

In 1848, William Thomson, who was later ennobled as Lord Kelvin, published a paper On an Absolute Thermometric Scale. [12] [13] [14] Using the soon-to-be-defunct caloric theory, he proposed an "absolute" scale based on the following parameters:

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

"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:

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

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. [15]

Within a decade, Thomson had abandoned caloric theory and superseded the 1848 scale with a new one [13] [16] based on the 2 features that would characterise all future versions of the Kelvin 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. [lower-alpha 1]

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. Phase-diag2.svg
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 [17] 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 [18] 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. [19] The triple point could be measured with ±0.0001 °C accuracy, while the melting point just to ±0.001 °C. [18]

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. [20] [21]

In 1967/1968, Resolution 3 of the 13th CGPM renamed the unit increment of thermodynamic temperature "kelvin", symbol K, replacing "degree Kelvin", symbol °K. [22] [23] [24] 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] [25] [26]

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. [4] [27] [28]

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. Unit relations in the new SI.svg
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. [29] 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. [30]

The redefinition was further postponed in 2014, pending more accurate measurements of the Boltzmann constant in terms of the current definition, [31] but was finally adopted at the 26th CGPM in late 2018, with a value of k = 1.380649×10−23 J⋅K−1. [32] [29] [1] [2] [4] [33]

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. 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] [34] 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. [35] 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. [33] [1] [2] [4]

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:

SI multiples of kelvin (K)
SubmultiplesMultiples
ValueSI symbolNameValueSI symbolName
10−1 KdKdecikelvin101 KdaKdecakelvin
10−2 KcKcentikelvin102 KhKhectokelvin
10−3 KmKmillikelvin103 KkKkilokelvin
10−6 KμKmicrokelvin106 KMKmegakelvin
10−9 KnKnanokelvin109 KGKgigakelvin
10−12 KpKpicokelvin1012 KTKterakelvin
10−15 KfKfemtokelvin1015 KPKpetakelvin
10−18 KaKattokelvin1018 KEKexakelvin
10−21 KzKzeptokelvin1021 KZKzettakelvin
10−24 KyKyoctokelvin1024 KYKyottakelvin
10−27 KrKrontokelvin1027 KRKronnakelvin
10−30 KqKquectokelvin1030 KQKquettakelvin

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"). [36] [37] [38] The unit symbol K is a capital letter. [22] It is common convention to capitalize Kelvin when referring to Lord Kelvin [5] or the Kelvin scale. [39]

The unit symbol K is encoded in Unicode at code point U+212AKELVIN SIGN. However, this is a compatibility character provided for compatibility with legacy encodings. The Unicode standard recommends using U+004BKLATIN CAPITAL LETTER K instead; that is, a normal capital K. "Three letterlike symbols have been given canonical equivalence to regular letters: U+2126OHM SIGN, U+212AKELVIN SIGN, and U+212BANGSTROM SIGN. In all three instances, the regular letter should be used." [40]

See also

Notes

  1. For example, Encyclopaedia Britannica editions from the 1920s and 1950s, one example being the article "Planets".

Related Research Articles

<span class="mw-page-title-main">Absolute zero</span> Lowest theoretical temperature

Absolute zero is the lowest limit of the thermodynamic temperature scale; a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as zero kelvin. The fundamental particles of nature have minimum vibrational motion, retaining only quantum mechanical, zero-point energy-induced particle motion. The theoretical temperature is determined by extrapolating the ideal gas law; by international agreement, absolute zero is taken as −273.15 degrees on the Celsius scale, which equals −459.67 degrees on the Fahrenheit scale. The corresponding Kelvin and Rankine temperature scales set their zero points at absolute zero by definition.

<span class="mw-page-title-main">Fahrenheit</span> Temperature scale

The Fahrenheit scale is a temperature scale based on one proposed in 1724 by the European physicist Daniel Gabriel Fahrenheit (1686–1736). It uses the degree Fahrenheit as the unit. Several accounts of how he originally defined his scale exist, but the original paper suggests the lower defining point, 0 °F, was established as the freezing temperature of a solution of brine made from a mixture of water, ice, and ammonium chloride. The other limit established was his best estimate of the average human body temperature, originally set at 90 °F, then 96 °F.

<span class="mw-page-title-main">Kilogram</span> Metric unit of mass

The kilogram is the base unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially. It means 'one thousand grams'.

<span class="mw-page-title-main">Metre Convention</span> 1875 international treaty

The Metre Convention, also known as the Treaty of the Metre, is an international treaty that was signed in Paris on 20 May 1875 by representatives of 17 nations: Argentina, Austria-Hungary, Belgium, Brazil, Denmark, France, Germany, Italy, Peru, Portugal, Russia, Spain, Sweden and Norway, Switzerland, Ottoman Empire, United States of America, and Venezuela.

The Rankine scale is an absolute scale of thermodynamic temperature named after the University of Glasgow engineer and physicist Macquorn Rankine, who proposed it in 1859.

<span class="mw-page-title-main">International System of Units</span> Modern form of the metric system

The International System of Units, internationally known by the abbreviation SI, is the modern form of the metric system and the world's most widely used system of measurement. Coordinated by the International Bureau of Weights and Measures it is the only system of measurement with an official status in nearly every country in the world, employed in science, technology, industry, and everyday commerce.

<span class="mw-page-title-main">SI base unit</span> One of the seven units of measurement that define the Metric System

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<span class="mw-page-title-main">Triple point</span> Thermodynamic point where three matter phases exist

In thermodynamics, the triple point of a substance is the temperature and pressure at which the three phases of that substance coexist in thermodynamic equilibrium. It is that temperature and pressure at which the sublimation, fusion, and vaporisation curves meet. For example, the triple point of mercury occurs at a temperature of −38.8 °C (−37.8 °F) and a pressure of 0.165 mPa.

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<span class="mw-page-title-main">Thermodynamic temperature</span> Measure of absolute temperature

Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics.

<span class="mw-page-title-main">Boltzmann constant</span> Physical constant relating particle kinetic energy with temperature

The Boltzmann constant is the proportionality factor that relates the average relative thermal energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, and in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used in calculating thermal noise in resistors. The Boltzmann constant has dimensions of energy divided by temperature, the same as entropy. It is named after the Austrian scientist Ludwig Boltzmann.

The molar gas constant is denoted by the symbol R or R. It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per amount of substance, rather than energy per temperature increment per particle. The constant is also a combination of the constants from Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. It is a physical constant that is featured in many fundamental equations in the physical sciences, such as the ideal gas law, the Arrhenius equation, and the Nernst equation.

The term degree is used in several scales of temperature, with the notable exception of kelvin, primary unit of temperature for engineering and the physical sciences. The degree symbol ° is usually used, followed by the initial letter of the unit; for example, "°C" for degree(Souvik) Celsius. A degree can be defined as a set change in temperature measured against a given scale; for example, one degree Celsius is one-hundredth of the temperature change between the point at which water starts to change state from solid to liquid state and the point at which it starts to change from its liquid to gaseous state.

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<span class="mw-page-title-main">International Temperature Scale of 1990</span> Practical temperature scale

The International Temperature Scale of 1990 (ITS-90) is an equipment calibration standard specified by the International Committee of Weights and Measures (CIPM) for making measurements on the Kelvin and Celsius temperature scales. It is an approximation of thermodynamic temperature that facilitates the comparability and compatibility of temperature measurements internationally. It defines fourteen calibration points ranging from 0.65 K to 1357.77 K and is subdivided into multiple temperature ranges which overlap in some instances. ITS-90 is the most recent of a series of International Temperature Scales adopted by the CIPM since 1927. Adopted at the 1989 General Conference on Weights and Measures, it supersedes the International Practical Temperature Scale of 1968 and the 1976 "Provisional 0.5 K to 30 K Temperature Scale". The CCT has also published several online guidebooks to aid realisations of the ITS-90. The lowest temperature covered by the ITS-90 is 0.65 K. In 2000, the temperature scale was extended further, to 0.9 mK, by the adoption of a supplemental scale, known as the Provisional Low Temperature Scale of 2000 (PLTS-2000).

<span class="mw-page-title-main">Celsius</span> Scale and unit of measurement for temperature

The degree Celsius is the unit of temperature on the Celsius scale, one of two temperature scales used in the International System of Units (SI), the other being the closely related Kelvin scale. The degree Celsius can refer to a specific temperature on the Celsius scale or to a difference or range between two temperatures. It is named after the Swedish astronomer Anders Celsius (1701–1744), who proposed the first version of it in 1742. The unit was called centigrade in several languages for many years. In 1948, the International Committee for Weights and Measures renamed it to honor Celsius and also to remove confusion with the term for one hundredth of a gradian in some languages. Most countries use this scale.

<span class="mw-page-title-main">Temperature</span> Physical quantity of hot and cold

Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making up a substance.

Scale of temperature is a methodology of calibrating the physical quantity temperature in metrology. Empirical scales measure temperature in relation to convenient and stable parameters or reference points, such as the freezing and boiling point of water. Absolute temperature is based on thermodynamic principles: using the lowest possible temperature as the zero point, and selecting a convenient incremental unit.

<span class="mw-page-title-main">2019 redefinition of the SI base units</span> Definition of the units kg, A, K and mol

In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artifacts such as the standard kilogram. Effective 20 May 2019, the 144th anniversary of the Metre Convention, the kilogram, ampere, kelvin, and mole are now defined by setting exact numerical values, when expressed in SI units, for the Planck constant, the elementary electric charge, the Boltzmann constant, and the Avogadro constant, respectively. The second, metre, and candela had previously been redefined using physical constants. The four new definitions aimed to improve the SI without changing the value of any units, ensuring continuity with existing measurements. In November 2018, the 26th General Conference on Weights and Measures (CGPM) unanimously approved these changes, which the International Committee for Weights and Measures (CIPM) had proposed earlier that year after determining that previously agreed conditions for the change had been met. These conditions were satisfied by a series of experiments that measured the constants to high accuracy relative to the old SI definitions, and were the culmination of decades of research.

<span class="mw-page-title-main">History of the metric system</span> History of the metric system measurement standards

The history of the metric system began during the Age of Enlightenment with measures of length and weight derived from nature, along with their decimal multiples and fractions. The system became the standard of France and Europe within half a century. Other measures with unity ratios were added, and the system went on to be adopted across the world.

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  30. "General Conference on Weights and Measures approves possible changes to the International System of Units, including redefinition of the kilogram" (PDF) (Press release). Sèvres, France: General Conference on Weights and Measures. 2011-10-23. Archived (PDF) from the original on 2012-02-09. Retrieved 2011-10-25.
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  32. "2018 CODATA Value: Boltzmann constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 2019-05-20. Retrieved 2019-05-20.
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  34. "Updating the definition of the kelvin" (PDF). International Bureau for Weights and Measures (BIPM). Archived (PDF) from the original on 2008-11-23. Retrieved 2010-02-23.
  35. Newell, D B; Cabiati, F; Fischer, J; Fujii, K; Karshenboim, S G; Margolis, H S; de Mirandés, E; Mohr, P J; Nez, F; Pachucki, K; Quinn, T J; Taylor, B N; Wang, M; Wood, B M; Zhang, Z; et al. (Committee on Data for Science and Technology (CODATA) Task Group on Fundamental Constants) (2018-01-29). "The CODATA 2017 values of h, e, k, and NA for the revision of the SI". Metrologia. 55 (1): L13–L16. Bibcode:2018Metro..55L..13N. doi: 10.1088/1681-7575/aa950a .
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  37. "Definition of KELVIN". www.merriam-webster.com. Retrieved 2023-08-21.
  38. CERN English Language Style Guide (PDF). CERN. 2022. p. 64.
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