# Temperature Scale

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## temperature scale

[′tem·prə·chər ‚skāl]
(thermodynamics)
An assignment of numbers to temperatures in a continuous manner, such that the resulting function is single valued; it is either an empirical temperature scale, based on some convenient property of a substance or object, or it measures the absolute temperature.

## Temperature Scale

any system of comparable numerical values of temperature. Temperature is not a directly measurable quantity; its value is determined from the temperature change of some conveniently measurable physical property of a thermometric substance. Once the thermometric substance and property have been selected, the reference point and the size of the temperature unit, the degree, must be defined. Empirical temperature scales are determined in this manner. Two fundamental temperatures, corresponding to equilibrium points of one-component systems (fixed points), are usually specified in a temperature scale. The distance between these points is called the fundamental temperature interval. Such points as the triple point of water, the boiling points of water, hydrogen, and oxygen, and the freezing points of silver and gold are used as fixed points. The size of the unit interval (temperature unit) is taken as a given fraction of the fundamental interval, and one of the fixed points is adopted as the reference point of the temperature scale. An empirical temperature scale based on any thermometric property x can be defined in this way. If it is assumed that the relation between x and the temperature t is linear, then the temperature is t = n(x – x0)/(xn – x0). where x0 and xn are the numerical values of the property x at the initial and end points of the fundamental interval, (xn – x0)/n is the size of a degree, and n is the number of graduations in the fundamental interval.

In the Celsius scale, for example, the freezing point of water, or the melting point of ice, is taken as the reference point, and the fundamental interval between the freezing and boiling points of water is divided into 100 equal parts (n = 100).

A temperature scale is thus a system of consecutive temperature values that are linearly related to the values of the physical quantity being measured, which should be a single-valued and monotonic function of temperature. In the general case, temperature scales may differ in the thermometric property, which may be the thermal expansion of bodies or the change in the electrical resistance of conductors with temperature, or in the thermometric substance, which may be a gas, liquid, or solid; temperature scales may also depend on the fixed points. In the simplest case, temperature scales differ in the numerical values adopted for identical fixed points. Thus, in the Celsius scale (°C), the Reaumur scale (°R), and the Fahrenheit scale (°F), different values of temperature are assigned to the melting point of ice and the boiling point of water at normal pressure. The relation for converting a temperature from one scale to another is

n°C = 0.8n°R = (1.8n + 32)°F

Direct conversion for temperature scales differing in fundamental temperatures is impossible without additional experimental data. Temperature scales that differ in the thermometric property or substance are essentially different. An unlimited number of noncoincident empirical temperature scales is possible, since all thermometric properties are nonlinearly related to temperature and the degree of nonlinearity differs for different properties and substances. The temperature measured on an empirical temperature scale is called the relative temperature, for example, the mercury or platinum temperature, and its unit is called the relative degree. Gas scales, in which gases serve as the thermometric substance, have a special place among empirical temperature scales and include the nitrogen, hydrogen, and helium scales. These temperature scales are less dependent than others on the gas used and, by introducing corrections, can be related to the Avogadro theoretical gas temperature scale, which is valid for an ideal gas. A scale whose absolute zero corresponds to the temperature at which the numerical value of the physical property is x = 0 is called an absolute empirical temperature scale. For example, in the Avogadro scale, absolute zero corresponds to zero pressure of an ideal gas. The temperatures t(x) (on an empirical temperature scale) and T(x) (on an absolute empirical temperature scale) are related by the equation T(x) = t(x) + T0(x), where T0(x) is absolute zero on the empirical scale; the introduction of absolute zero is an extrapolation and does not presuppose reaching this temperature.

The fundamental shortcoming of empirical temperature scales—their dependence on the thermometric substance—is absent in a thermodynamic temperature scale based on the second law of thermodynamics. In determining the absolute thermodynamic temperature scale, or the Kelvin scale, the Carnot cycle is used as the basis. If an engine that completes the Carnot cycle absorbs heat Q1 at temperature T1 and gives off heat Q2 at temperature T2. then the relation T1/T2 = Q1/Q2 is independent of the properties of the working substance and makes it possible to determine the absolute temperature from the measurable quantities Q1 and Q2. Initially the fundamental interval of this scale was defined by the melting point of ice and the boiling point of water at atmospheric pressure, the unit of absolute temperature corresponded to 1/100 of the fundamental interval, and the melting point of ice was adopted as the reference point. In 1954 the Tenth General Conference on Weights and Measures established a thermodynamic temperature scale with one fixed point, the triple point of water, whose temperature was set at 273.16°K exactly, corresponding to 0.01°C. The temperature Tin the absolute thermodynamic temperature scale is measured in degrees kelvin (°K). The thermodynamic temperature scale in which the temperature t = 0°C is adopted for the melting point of ice is called the Celsius scale. The relations between temperatures expressed in the Celsius scale and the absolute thermodynamic temperature scale are

T°K = t°C + 273.15°K, n°K = n°C

so that the size of the units in these scales is the same. In the United States and some other countries, where temperature is commonly measured on the Fahrenheit scale, the Rankine absolute temperature scale is also used. The relation between the degree Kelvin and the degree Rankine is n°K = 1.8n°Ra. On the Rankine scale the melting point of ice corresponds to 491.67°Ra, and the boiling point of water, to 671.67°Ra.

Any empirical temperature scale can be related to the thermodynamic temperature scale by introducing corrections that allow for the nature of the relation between thermometric property and thermodynamic temperature. The thermodynamic temperature scale is not realized directly, namely, by putting a thermometric substance through the Carnot cycle, but by means of other processes associated with the thermodynamic temperature. In a broad range of temperatures, from approximately the boiling point of helium to the freezing point of gold, the thermodynamic temperature scale coincides with the Avogadro scale, so that the thermodynamic temperature is determined from the gas temperature, which is measured with a gas thermometer. At lower temperatures the thermodynamic temperature scale is realized on the basis of the temperature dependence of the magnetic susceptibility of paramagnetics, and at higher temperatures, on the basis of measurements of the intensity of blackbody radiation. It is extremely difficult to realize the thermodynamic temperature scale even by means of the Avogadro scale. For this reason, the International Practical Temperature Scale, which coincides with the thermodynamic temperature scale to a degree of accuracy that is experimentally attainable, was adopted in 1927. All instruments for temperature measurements are graduated according to the International Practical Temperature Scale.

### REFERENCES

Popov, M. M. Termometriia i kalorimetriia, 2nd ed. Moscow, 1954.
Gordov, A. N. Temperaturnye shkaly, Moscow, 1966.
Burdun, G. D. Spravochnik po Mezhdunarodnoi sisteme edinits. Moscow, 1971.
GOST 8.157–75: Shkaly temperaturnye prakticheskie.

D. I. SHAREVSKAIA

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