Kelvin

History

Precursors

During the 18th century, multiple temperature scales were developed, notably Fahrenheit and 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 defunct Newton and Réaumur scales) the melting point of ice served as such a starting point, with Celsius being defined (from the 1740s to the 1940s) by calibrating a thermometer such that:

• Water's freezing point is 0 °C.
• Water's boiling point is 100 °C.

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 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From 1787 to 1802, it was determined by Jacques Charles (unpublished), John Dalton, and Joseph Louis Gay-Lussac that, at constant pressure, ideal gases expanded or contracted their volume linearly (Charles's law) by about 1/273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. Extrapolation of this law suggested that a gas cooled to about −273 °C would occupy zero volume.

Lord Kelvin

First absolute scale

In 1848, William Thomson, who was later ennobled as Lord Kelvin, published a paper On an Absolute Thermometric Scale. The scale proposed in the paper turned out to be unsatisfactory, but the principles and formulas upon which the scale was based were correct. For example, in a footnote, Thomson derived the value of −273 °C for absolute zero by calculating the negative reciprocal of 0.00366—the coefficient of thermal expansion of an ideal gas per degree Celsius relative to the ice point. This derived value agrees with the currently accepted value of −273.15 °C, allowing for the precision and uncertainty involved in the calculation.

The scale was designed on the principle 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." Specifically, Thomson expressed the amount of work necessary to produce a unit of heat (the thermal efficiency) as \mu(t) (1 + E t)/E, where t is the temperature in Celsius, E is the coefficient of thermal expansion, and \mu(t) was "Carnot's function", a substance-independent quantity depending on temperature, motivated by an obsolete version of Carnot's theorem. The scale is derived by finding a change of variables T_{1848} = f(T) of temperature T such that dT_{1848} / dT is proportional to \mu.

When Thomson published his paper in 1848, he only considered Regnault's experimental measurements of \mu(t). That same year, James Prescott Joule suggested to Thomson that the true formula for Carnot's function was \mu(t) = J \frac{E}{1+E t}, where J is "the mechanical equivalent of a unit of heat", now referred to as the specific heat capacity of water, approximately 771.8 ftlbf/F/lb. Thomson was initially skeptical of the deviations of Joule's formula from experiment, stating "I think it will be generally admitted that there can be no such inaccuracy in Regnault's part of the data, and there remains only the uncertainty regarding the density of saturated steam". Thomson referred to the correctness of Joule's formula as "Mayer's hypothesis", on account of it having been first assumed by Mayer. Thomson arranged numerous experiments in coordination with Joule, eventually concluding by 1854 that Joule's formula was correct and the effect of temperature on the density of saturated steam accounted for all discrepancies with Regnault's data. Therefore, in terms of the modern Kelvin scale T, the first scale could be expressed as follows: T_{1848} = 100 \frac{\log(T / \text{273 K})}{\log(\text{373 K} / \text{273 K})} The parameters of the scale were arbitrarily chosen to coincide with the Celsius scale at 0° and 100 °C or 273 and 373 K (the melting and boiling points of water). On this scale, an increase of approximately 222 degrees corresponds to a doubling of Kelvin temperature, regardless of the starting temperature, and "infinite cold" (absolute zero) has a numerical value of negative infinity.

Modern absolute scale

Thomson understood that with Joule's proposed formula for \mu, the relationship between work and heat for a perfect thermodynamic engine was simply the constant J. In 1854, Thomson and Joule thus formulated a second absolute scale that was more practical and convenient, agreeing with air thermometers for most purposes. Specifically, "the numerical measure of temperature shall be simply the mechanical equivalent of the thermal unit divided by Carnot's function."

To explain this definition, consider a reversible Carnot cycle engine, where Q_\mathrm{H} is the amount of heat energy transferred into the system, Q_\mathrm{C} is the heat leaving the system, W is the work done by the system (Q_\mathrm{H} - Q_\mathrm{C}), t_\mathrm{H} is the temperature of the hot reservoir in degrees Celsius, and t_\mathrm{C} is the temperature of the cold reservoir in Celsius. The Carnot function is defined as \mu =W / Q_\mathrm{H}(t_\mathrm{H} - t_\mathrm{C}), and the absolute temperature as T_\mathrm{H} = J/\mu. One finds the relationship T_\mathrm{H}= J Q_\mathrm{H} (t_\mathrm{H}-t_\mathrm{C})/W. By supposing T_\mathrm{H}-T_\mathrm{C}=J (t_\mathrm{H}-t_\mathrm{C}), one obtains the general principle of an absolute thermodynamic temperature scale for the Carnot engine, Q_\mathrm{H} / T_\mathrm{H} = Q_\mathrm{C} / T_\mathrm{C}. The definition can be shown to correspond to the thermometric temperature of the ideal gas laws.

This definition by itself is not sufficient. Thomson specified that the scale should have two properties:

• The absolute values of two temperatures are to one another in the proportion of the heat taken in to the heat rejected in a perfect thermodynamic engine working with a source and refrigerator at the higher and lower of the temperatures respectively.
• The difference of temperatures between the freezing- and boiling-points of water under standard atmospheric pressure shall be called 100 degrees. (The same increment as the Celsius scale) Thomson's best estimates at the time were that the temperature of freezing water was 273.7 K and the temperature of boiling water was 373.7 K.

These two properties would be featured in all future versions of the Kelvin scale, although it was not yet known by that name. 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.

Triple point standard

In 1873, William Thomson's older brother James coined the term triple point 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 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. The triple point could be measured with ±0.0001 °C accuracy, while the melting point just to ±0.001 °C.

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 standardized Kelvin scale which defined the triple point as exactly 273.15 + 0.01 = 273.16 degrees Kelvin.

In 1967/1968, Resolution 3 of the 13th CGPM renamed the unit increment of thermodynamic temperature "kelvin", symbol K, replacing "degree Kelvin", symbol °K. The 13th CGPM also held in Resolution 4 that "The kelvin, unit of thermodynamic temperature, is equal to the fraction of the thermodynamic temperature of the triple point of water."

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.

2019 redefinition

The Boltzmann constant kB serves as the bridge in the relation , linking characteristic microscopic energies to the macroscopic temperature scale. In the International System of Units (SI), the kelvin has traditionally been treated as an independent base unit with its own dimension. By contrast, in fundamental physics it is common to adopt natural units by setting the Boltzmann constant equal to unity, so that temperature and energy share the same units.

In 2005, the CIPM began a programme to redefine the kelvin in terms of the Boltzmann constant, alongside exploring new definitions for several other SI base units in terms of fundamental constants. The motivation was to allow more accurate measurements at temperatures far away from the triple point of water, and to be independent from any particular substance or measurement. Originally slated for adoption in 2011 with the Boltzmann constant being , X to be determined, |access-date=1 January 2011 |url-status=dead |archive-url=https://web.archive.org/web/20110110104615/http://www.bipm.org/utils/en/pdf/si_brochure_draft_ch2.pdf |archive-date=10 January 2011 | access-date = 25 October 2011 | url-status = dead | archive-url = https://web.archive.org/web/20120209175127/http://www.bipm.org/utils/en/pdf/Press_release_resolution_1_CGPM.pdf | archive-date = 9 February 2012 |url-status=dead |archive-url=https://web.archive.org/web/20151013174929/http://www.bipm.org/cc/TGFC/Allowed/Minutes/CODATA_Minutes_14-BIPM-public.pdf |archive-date=13 October 2015

With this new definition, the kelvin now only depends on the Boltzmann constant and universal constants (see 2019 SI unit dependencies diagram), allowing the kelvin to be expressed as: : 1 kelvin = ≈ .

In practical terms, as was the goal, the change went largely unnoticed: the chosen value has enough accuracy and significant figures for continuity, ensuring that water still freezes at 0 °C to high precision. The difference lies in the status of reference points. Before the redefinition, the triple point of water was taken as exact, while the Boltzmann constant had a measured value of , with a relative standard uncertainty of . |doi-access=free |bibcode-access=free

On a deeper level, the kelvin is now defined in terms of the joule, making the separate existence of a temperature dimension theoretically unnecessary. The kelvin could have been redefined as a non-coherent derived SI unit, with . Yet, "for historical and especially practical reasons, the kelvin will continue to be a base unit of the SI".

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 appear reddish, whereas those above about appear bluish. Colour temperature is important in the fields of image projection and photography, where a colour temperature of approximately 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 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

Main article: Noise figure

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 Johnson–Nyquist noise of resistors (which produces an associated kTC noise when combined with 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

Main article: Orders of magnitude (temperature)

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:

Orthography

According to SI convention, the kelvin is never referred to nor written as a degree. The word "kelvin" is not capitalized when used as a unit. It may be in plural form as appropriate (for example, "it is 283 kelvins outside", as for "it is 50 degrees Fahrenheit" and "10 degrees Celsius"). The unit's symbol K is a capital letter, per the SI convention to capitalize symbols of units derived from the name of a person. It is common convention to capitalize Kelvin when referring to Lord Kelvin or the Kelvin scale.

The unit symbol K is encoded in Unicode at code point . However, this is a compatibility character provided for compatibility with legacy encodings. The Unicode standard recommends using instead; that is, a normal capital K. "Three letterlike symbols have been given canonical equivalence to regular letters: , , and . In all three instances, the regular letter should be used."

Notes

References

Bibliography

References

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