Kelvin

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Kelvin
Unit system SI base unit
Unit of Temperature
SymbolK
Named after William Thomson, 1st Baron Kelvin

The Kelvin scale is an absolute thermodynamic temperature scale using as its null point absolute zero, the temperature at which all thermal motion ceases in the classical description of thermodynamics. The kelvin (symbol: K) is the base unit of temperature in the International System of Units (SI).

An absolute scale is a system of measurement that begins at a minimum, or zero point, and progresses in only one direction. An absolute scale differs from an arbitrary, or "relative," scale, which begins at some point selected by a person and can progress in both directions. An absolute scale begins at a natural minimum, leaving only one direction in which to progress.

Thermodynamic temperature absolute measure of temperature

Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics.

Scale of temperature is a way to measure temperature quantitatively. Empirical scales measure the quantity of heat in a system in relation to a fixed parameter, a thermometer. They are not absolute measures, that is why scales vary. Absolute temperature is thermodynamic temperature because it is directly related to thermodynamics. It is the Zeroth Law of Thermodynamics that leads to a formal definition of thermodynamic temperature.

Contents

Until 2018, the kelvin was defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water (exactly 0.01 °C or 32.018 °F). [1] In other words, it was defined such that the triple point of water is exactly 273.16 K.

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 curve, fusion curve and the vaporisation curve meet. For example, the triple point of mercury occurs at a temperature of −38.83440 °C and a pressure of 0.2 mPa.

On 16 November 2018, a new definition was adopted, in terms of a fixed value of the Boltzmann constant. For legal metrology purposes, the new definition will officially come into force on 20 May 2019 (the 130th anniversary of the Metre Convention). [2]

The Boltzmann constant is a physical constant relating the average relative kinetic energy of particles in a gas with the temperature of the gas and occurs in Planck's law of black-body radiation and in Boltzmann's entropy formula. It was introduced by Max Planck, but named after Ludwig Boltzmann.

Metre Convention

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. The treaty created the International Bureau of Weights and Measures (BIPM), an intergovernmental organization under the authority of the General Conference on Weights and Measures (CGPM) and the supervision of the International Committee for Weights and Measures (CIPM), that coordinates international metrology and the development of the metric system.

The Kelvin scale is named after the Belfast-born, Glasgow University engineer and physicist William Thomson, 1st Baron Kelvin (1824–1907), who wrote of the need for an "absolute thermometric scale". Unlike the degree Fahrenheit and degree Celsius, the kelvin is not referred to or written as a degree. The kelvin is the primary unit of temperature measurement in the physical sciences, but is often used in conjunction with the degree Celsius, which has the same magnitude. The definition implies that absolute zero (0 K) is equivalent to −273.15 °C (−459.67 °F).

William Thomson, 1st Baron Kelvin British physicist and engineer

William Thomson, 1st Baron Kelvin, was a Scots-Irish mathematical physicist and engineer who was born in Belfast in 1824. At the University of Glasgow he did important work in the mathematical analysis of electricity and formulation of the first and second laws of thermodynamics, and did much to unify the emerging discipline of physics in its modern form. He worked closely with mathematics professor Hugh Blackburn in his work. He also had a career as an electric telegraph engineer and inventor, which propelled him into the public eye and ensured his wealth, fame and honour. For his work on the transatlantic telegraph project he was knighted in 1866 by Queen Victoria, becoming Sir William Thomson. He had extensive maritime interests and was most noted for his work on the mariner's compass, which previously had limited reliability.

Fahrenheit unit of temperature

The Fahrenheit scale is a temperature scale based on one proposed in 1724 by Dutch–German–Polish physicist Daniel Gabriel Fahrenheit (1686–1736). It uses the degree Fahrenheit as the unit. Several accounts of how he originally defined his scale exist. The lower defining point, 0 °F, was established as the freezing temperature of a solution of brine made from equal parts of ice, water and salt. Further limits were established as the melting point of ice (32 °F) and his best estimate of the average human body temperature. The scale is now usually defined by two fixed points: the temperature at which water freezes into ice is defined as 32 °F, and the boiling point of water is defined to be 212 °F, a 180 °F separation, as defined at sea level and standard atmospheric pressure.

Celsius Scale and unit of measurement for temperature

The Celsius scale, also known as the centigrade scale, is a temperature scale used by the International System of Units (SI). As an SI derived unit, it is used by all countries except the United States, the Bahamas, Belize, the Cayman Islands and Liberia. It is named after the Swedish astronomer Anders Celsius (1701–1744), who developed a similar temperature scale. The degree Celsius (°C) can refer to a specific temperature on the Celsius scale or a unit to indicate a difference between two temperatures or an uncertainty. Before being renamed to honor Anders Celsius in 1948, the unit was called centigrade, from the Latin centum, which means 100, and gradus, which means steps.

History

Lord Kelvin, the namesake of the unit Lord Kelvin photograph.jpg
Lord Kelvin, the namesake of the unit

In 1848, William Thomson, who later was made Lord Kelvin, wrote in his paper, On an Absolute Thermometric Scale, of the need for a scale whereby "infinite cold" (absolute zero) was the scale's null point, and which used the degree Celsius for its unit increment. Kelvin calculated that absolute zero was equivalent to −273 °C on the air thermometers of the time. [3] This absolute scale is known today as the Kelvin thermodynamic temperature scale. Kelvin's value of "−273" was the negative reciprocal of 0.00366—the accepted expansion coefficient of gas per degree Celsius relative to the ice point, giving a remarkable consistency to the currently accepted value.

In 1954, Resolution 3 of the 10th General Conference on Weights and Measures (CGPM) gave the Kelvin scale its modern definition by designating the triple point of water as its second defining point and assigned its temperature to exactly 273.16 kelvins. [4]

The General Conference on Weights and Measures is the supreme authority of the International Bureau of Weights and Measures, the inter-governmental organization established in 1875 under the terms of the Metre Convention through which Member States act together on matters related to measurement science and measurement standards. The CGPM is made up of delegates of the governments of the Member States and observers from the Associates of the CGPM. Under its authority, the International Committee for Weights and Measures executes an exclusive direction and supervision of the BIPM.

In 1967/1968, Resolution 3 of the 13th CGPM renamed the unit increment of thermodynamic temperature "kelvin", symbol K, replacing "degree Kelvin", symbol °K. [5] 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." [1]

In 2005, the Comité International des Poids et Mesures (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 thermodynamic temperature scale would refer to water having an isotopic composition specified as Vienna Standard Mean Ocean Water. [6]

In 2018, Resolution A of the 26th CGPM adopted a significant redefinition of SI base units which included redefining the Kelvin in terms of a fixed value for the Boltzmann constant of 1.380649×10−23 J/K.

Usage conventions

When spelled out or spoken, the unit is pluralised using the same grammatical rules as for other SI units such as the volt or ohm (e.g. "the triple point of water is exactly 273.16 kelvins" [7] ). When reference is made to the "Kelvin scale", the word "kelvin"—which is normally a noun—functions adjectivally to modify the noun "scale" and is capitalized. 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"). [8] [9]

Before the 13th CGPM in 1967–1968, the unit kelvin was called 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). [10] 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).

Use in conjunction with degrees Celsius

A thermometer calibrated in degrees Celsius (left) and kelvins (right). CelsiusKelvinThermometer.jpg
A thermometer calibrated in degrees Celsius (left) and kelvins (right).

In science and engineering, degrees Celsius and kelvins are often used simultaneously in the same article, where absolute temperatures are given in degrees Celsius, but temperature intervals are given in kelvins. E.g. "its measured value was 0.01028 °C with an uncertainty of 60 µK."

This practice is permissible because the degree Celsius is a special name for the kelvin for use in expressing relative temperatures, and the magnitude of the degree Celsius is exactly equal to that of the kelvin. [11] Notwithstanding that the official endorsement provided by Resolution 3 of the 13th CGPM states "a temperature interval may also be expressed in degrees Celsius", [5] the practice of simultaneously using both °C and K is widespread throughout the scientific world. The use of SI prefixed forms of the degree Celsius (such as µ°C or microdegree Celsius) to express a temperature interval has not been widely adopted.

2019 redefinition

In 2005 the CIPM embarked on a programme to redefine the kelvin (along with the other SI units) using a more experimentally rigorous methodology. In particular, the committee proposed redefining the kelvin such that Boltzmann's constant takes the exact value 1.3806505×10−23 J/K. [12] The committee had hoped that the programme 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 programme. [13]

The redefinition was further postponed in 2014, pending more accurate measurements of Boltzmann's constant in terms of the current definition, [14] but was finally adopted at the 26th CGPM in late 2018, with a value of k = 1.380649×10−23 J/K. [12] [15]

From a scientific point of view, the main advantage is that this will allow 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 challenge was to avoid degrading the accuracy of measurements close to the triple point. From a practical point of view, the redefinition will pass unnoticed; water will still freeze at 273.15 K (0 °C), [16] and the triple point of water will continue 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. [15] Afterward, the Boltzmann constant is exact and the uncertainty is transferred to the triple point of water, which is now 273.1600(1) K.

Practical uses

Kelvin temperature conversion formulae
from kelvinsto 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

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 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

In 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.

Unicode character

The symbol 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." [17]

See also

Notes and references

  1. 1 2 "Resolution 4: Definition of the SI unit of thermodynamic temperature (kelvin)". Resolutions of the 13th CGPM. Bureau International des Poids et Mesures. 1967. Archived from the original on 15 June 2007. Retrieved 6 February 2008.
  2. Draft Resolution A "On the revision of the International System of units (SI)" to be submitted to the CGPM at its 26th meeting (2018) (PDF)
  3. Lord Kelvin, William (October 1848). "On an Absolute Thermometric Scale". Philosophical Magazine. Archived from the original on 1 February 2008. Retrieved 6 February 2008.
  4. "Resolution 3: Definition of the thermodynamic temperature scale". Resolutions of the 10th CGPM. Bureau International des Poids et Mesures. 1954. Archived from the original on 23 June 2007. Retrieved 6 February 2008.
  5. 1 2 "Resolution 3: SI unit of thermodynamic temperature (kelvin)". Resolutions of the 13th CGPM. Bureau International des Poids et Mesures. 1967. Archived from the original on 21 April 2007. Retrieved 6 February 2008.
  6. "Unit of thermodynamic temperature (kelvin)". SI Brochure, 8th edition. Bureau International des Poids et Mesures. 1967. pp. Section 2.1.1.5. Archived from the original on 26 September 2007. Retrieved 2008-02-06.
  7. "Rules and style conventions for expressing values of quantities". SI Brochure, 8th edition. Bureau International des Poids et Mesures. 1967. pp. Section 2.1.1.5. Archived from the original on 16 July 2012. Retrieved 27 August 2012.
  8. "SI Unit rules and style conventions". National Institute of Standards and Technology. September 2004. Archived from the original on 5 February 2008. Retrieved 6 February 2008.
  9. "Rules and style conventions for expressing values of quantities". SI Brochure, 8th edition. Bureau International des Poids et Mesures. 1967. pp. Section 5.3.3. Archived from the original on 23 September 2015. Retrieved 13 December 2015.
  10. Barry N. Taylor (2008). "Guide for the Use of the International System of Units (SI)" (.PDF). Special Publication 811. National Institute of Standards and Technology. Archived (PDF) from the original on 3 June 2016. Retrieved 5 March 2011.
  11. "Units with special names and symbols; units that incorporate special names and symbols". SI Brochure, 8th edition. Bureau International des Poids et Mesures. 2006. pp. Section 2.2.2, Table 3. Archived from the original on 18 June 2007. Retrieved 27 June 2016.
  12. 1 2 Ian Mills (29 September 2010). "Draft Chapter 2 for SI Brochure, following redefinitions of the base units" (PDF). CCU. Archived (PDF) from the original on 10 January 2011. Retrieved 1 January 2011.
  13. "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. 23 October 2011. Archived (PDF) from the original on 9 February 2012. Retrieved 25 October 2011.
  14. Wood, B. (3–4 November 2014). "Report on the Meeting of the CODATA Task Group on Fundamental Constants" (PDF). BIPM. p. 7. Archived (PDF) from the original on 13 October 2015. [BIPM director Martin] Milton responded to a question about what would happen if ... the CIPM or the CGPM voted not to move forward with the redefinition of the SI. He responded that he felt that by that time the decision to move forward should be seen as a foregone conclusion.
  15. 1 2 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) (29 January 2018). "The CODATA 2017 values of h, e, k, and NA for the revision of the SI". Metrologia. 55 (1). doi: 10.1088/1681-7575/aa950a .
  16. "Updating the definition of the kelvin" (PDF). International Bureau for Weights and Measures (BIPM). Archived (PDF) from the original on 23 November 2008. Retrieved 23 February 2010.
  17. "22.2". The Unicode Standard, Version 8.0 (PDF). Mountain View, CA, USA: The Unicode Consortium. August 2015. ISBN   978-1-936213-10-8. Archived (PDF) from the original on 6 December 2016. Retrieved 6 September 2015.

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