Kelvin

This article is about the unit of temperature. For other uses, see Kelvin (disambiguation).

Kelvin temperature conversion formulae

	from Kelvin	to Kelvin
Celsius	[°C] = [K] − 273.15	[K] = [°C] + 273.15
Fahrenheit	[°F] = [K] × 9⁄5 − 459.67	[K] = ([°F] + 459.67) × 5⁄9
Rankine	[°R] = [K] × 9⁄5	[K] = [°R] × 5⁄9
For temperature intervals rather than specific temperatures, 1 K = 1 °C = 1.8 °F = 1.8 °R Comparisons among various temperature scales

The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units (SI) and is assigned the unit symbol K. 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 is defined as the fraction ¹⁄_273.16 of the thermodynamic temperature of the triple point of water (273.16 K (0.01 °C; 32.02 °F)). ^[1]

The Kelvin scale is named after the Belfast-born 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 typeset as a degree. The kelvin is the primary unit of measurement in the physical sciences, but is often used in conjunction with the degree Celsius, which has the same magnitude. Absolute zero at 0 K is −273.15 °C (−459.67 °F).

History

See also: Thermodynamic temperature#History and Properties of water#Physics and chemistry

1848

Lord Kelvin (William Thomson), 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. Thomson calculated that absolute zero was equivalent to −273 °C on the air thermometers of the time.^[2] This absolute scale is known today as the Kelvin thermodynamic temperature scale. Thomson’s value of "−273" was the 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.

1954

Resolution 3 of the 10th 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.^[3]

1967/1968

Resolution 3 of the 13th CGPM renamed the unit increment of thermodynamic temperature "kelvin", symbol K, replacing "degree absolute", symbol °K.^[4] 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]

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 VSMOW.^[5]

Usage conventions

When reference is made to the unit kelvin (either a specific temperature or a temperature interval), kelvin is always spelled with a lowercase k unless it is the first word in a sentence.^[6] 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.

Until the 13th General Conference on Weights and Measures (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 (degree absolute), which was the unit’s official name from 1948 until 1954, was rather 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 name to simply "kelvin" (symbol K).^[7] The omission of "degree" indicates that it is not relative to an arbitrary reference point like the Celsius and Fahrenheit scales (although for some reason, 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). Because it is an absolute unit, the plural "kelvins" should be used for any quantity of temperature other than 1 kelvin (e.g. water freezes at 273.15 kelvins).

This SI unit is named after William Thomson, 1st Baron Kelvin. As with every SI unit whose name is derived from the proper name of a person, the first letter of its symbol is upper case (K). When an SI unit is spelled out in English, it should always begin with a lower case letter (kelvin), except where any word would be capitalized, such as at the beginning of a sentence or in capitalized material such as a title. Note that "degree Celsius" conforms to this rule because the "d" is lowercase. —Based on The International System of Units, section 5.2.

The kelvin symbol is always a roman, non-italic capital K. In the SI naming convention, all symbols named after a person are capitalized; in the case of the kelvin, capitalizing also distinguishes the symbol from the SI prefix "kilo", which has the lowercase k as its symbol. The admonition against italicizing the symbol K applies to all SI unit symbols; only symbols for variables and constants (e.g., P = pressure, and c = 299,792,458 m/s) are italicized in scientific and engineering papers. 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]

Unicode provides a compatibility character for the kelvin at U+212A (decimal 8490), for compatibility with CJK encodings that provide such a character (as such, in most fonts the width is the same as for fullwidth characters).

Use in conjunction with Celsius

In science and in engineering, the Celsius scale and the kelvin are often used simultaneously in the same article (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 Celsius temperatures and the magnitude of the degree Celsius is exactly equal to that of the kelvin.^[10] Notwithstanding that the official endorsement provided by Resolution 3 of the 13th CGPM states, "a temperature interval may also be expressed in degrees Celsius," the practice of simultaneously using both "°C" and "K" remains widespread throughout the scientific world as the use of SI prefixed forms of the degree Celsius (such as "µ°C" or "microdegrees Celsius") to express a temperature interval has not been widely adopted.^[4]

Proposed redefinition

In 2005 the CIPM embarked on a program to redefine, amongst others, the kelvin using a more rigorous basis than was in use. The current (2010) definition is unsatisfactory for temperatures below 20 K and above 1300 K.^[11] It is anticipated that the program will be completed in time for its adoption by the CGPM at its 2011 meeting. The committee proposes defining the kelvin as the temperature scale for which Boltzmann's constant is 1.3806505×10⁻²³ J/K exactly.^[12]

From a scientific point of view, this will link temperature to the rest of SI and result in a stable definition that is independent of any particular substance. From a practical point of view, the redefinition will pass unnoticed; water will still freeze at 0 °C (273.15 K).^[13]

Temperature conversion between units

See also

• Comparison of temperature scales
• International Temperature Scale of 1990
• Negative temperature
• Rankine scale
• Thermodynamic temperature
• Triple point

References

1. ^ ^{a b} "Resolution 4: Definition of the SI unit of thermodynamic temperature (kelvin)". Resolutions of the 13th CGPM. Bureau International des Poids et Mesures. 1967. http://www.bipm.fr/en/CGPM/db/13/4/. Retrieved 2008-02-06. 
2. ^ Thomson, William (October 1848). "On an Absolute Thermometric Scale". Philosophical Magazine. http://zapatopi.net/kelvin/papers/on_an_absolute_thermometric_scale.html. Retrieved 2008-02-06. 
3. ^ "Resolution 3: Definition of the thermodynamic temperature scale". Resolutions of the 10th CGPM. Bureau International des Poids et Mesures. 1954. http://www.bipm.fr/en/CGPM/db/10/3/. Retrieved 2008-02-06. 
4. ^ ^{a b} "Resolution 3: SI unit of thermodynamic temperature (kelvin)". Resolutions of the 13th CGPM. Bureau International des Poids et Mesures. 1967. http://www.bipm.fr/en/CGPM/db/13/3/. Retrieved 2008-02-06. 
5. ^ "Unit of thermodynamic temperature (kelvin)". SI Brochure, 8th edition. Bureau International des Poids et Mesures. 1967. pp. Section 2.1.1.5. http://www1.bipm.org/en/si/si_brochure/chapter2/2-1/2-1-1/kelvin.html. Retrieved 2008-02-06. 
6. ^ BIPM: SI brochure, Section 5.2
7. ^ Barry N. Taylor (2008) (.PDF). Guide for the Use of the International System of Units (SI). Special Publication 811. National Institute of Standards and Technology. http://physics.nist.gov/cuu/pdf/sp811.pdf. Retrieved 2011-03-05. 
8. ^ "SI Unit rules and style conventions". National Institute of Standards and Technology. September 2004. http://physics.nist.gov/cuu/Units/checklist.html. Retrieved 2008-02-06. 
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. http://www.bipm.org/en/si/si_brochure/chapter5/5-3-2.html#5-3-3. Retrieved 2008-02-06. 
10. ^ "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. http://www.bipm.org/en/si/si_brochure/chapter2/2-2/table3.html. Retrieved 2008-02-06. 
11. ^ J. Fischer1 et al (2007-05-02). "Report to the CIPM on the implications of changing the definition of the base unit Kelvin". International Committee for Weights and Measures (CIPM). http://www.bipm.org/wg/CCT/TG-SI/Allowed/Documents/Report_to_CIPM_2.pdf. Retrieved 2010-02-23. 
12. ^ Ian Mills (29 September 2010). "Draft Chapter 2 for SI Brochure, following redefinitions of the base units". CCU. http://www.bipm.org/utils/en/pdf/si_brochure_draft_ch2.pdf. Retrieved 2011-01-01. 
13. ^ "Updating the definition of the kelvin". International Bureau for Weights and Measures (BIPM). http://www.bipm.org/wg/CCT/TG-SI/Allowed/Documents/Updating_the_definition_of_the_kelvin2.pdf. Retrieved 2010-02-23. 

External links

• Bureau International des Poids et Mesures (2006). The International System of Units (SI) Brochure. 8th Edition. International Committee for Weights and Measures. http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf. Retrieved 2008-02-06.