Kelvin

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 = 9⁄5 °F = 9⁄5 °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 (exactly 0.01 °C or 32.018 °F).

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 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. Subtracting 273.16 K from the temperature of the triple point of water (0.01 °C) makes absolute zero (0 K) equivalent to −273.15 °C (−459.67 °F).

History

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. 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 kelvin.

1967/1968

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

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.

Usage conventions

This SI unit is named after William Thomson, 1st Baron Kelvin. As with every International System of Units (SI) unit whose name is derived from the proper name of a person, the first letter of its symbol is upper case (K). However, when an SI unit is spelled out in English, it should always begin with a lower case letter (kelvin), except in a situation where any word in that position 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. 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" ). 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").

Before 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 unit name to simply "kelvin" (symbol K). 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 Celsius

In science and in engineering, degrees Celsius and kelvins 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. 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.

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. 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.

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 (32 °F, 273.15 K).

Practical uses

Colour temperature

The kelvin is often used in the measure of the colour temperature of light sources. Colour temperature is based upon the principle that a black body radiator emits light whose colour depends on the temperature of the radiator. Black bodies with 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.

Kelvin as a measure of noise

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.

Temperature conversion between units