# TEMPERATURE

The temperature of an object or fluid is that property which determines the direction of the flow of heat from that body or fluid to an adjacent body or fluid with which it is in contact. Thus, heat flows from a body or fluid of higher temperature to a body or fluid of lower temperature. Temperature is one of the main parameters of state which defines the thermal state of the system. The temperature of all parts of the system in thermodynamic equilibrium is the same. Based on the molecular-kinetic approach, the temperature of a system characterizes the intensity of thermal motion of atoms, molecules and other particles forming the system.

For instance, for a system described by the laws of classical statistical physics the mean kinetic energy of thermal motion of particles is directly proportional to the absolute temperature of the system. In this regard we can say that the temperature characterizes the thermal motions within a body.

In thermodynamics the reciprocal of the derivative of the entropy S of a body with respect to its energy E is called the absolute temperature T:

(1) Temperature, like entropy, is a purely statistical quantity and makes sense only for macroscopic bodies. According to the second law of thermodynamics, energy is transferred from bodies with higher temperature to bodies with lower temperature. The absolute temperature is always positive, T > 0. The least absolute temperature possible is the absolute zero. At absolute zero, the translatory and rotary motion of atoms and molecules comes to an end, and they are in a state of the so-called "zero vibrations" rather than in a state of rest. By Nernst theorem the entropy of any body becomes zero at absolute zero temperature. Absolute zero is unattainable. The entropy S is a dimensionless quantity and from Eq. (1) it follows that temperature has the dimensions of energy and can be measured in Joules. The ratio Joules/Kelvins (K) called Boltzmann’s constant k is equal to k = 1.38 × 10−23 Joules/K.

Actually, the temperature is usually measured in arbitrary units, degrees (Celsius degree, °C, Fahrenheit, °F, Réaumur, °R) or in "Kelvins" whose value is determined by the corresponding temperature scales.

Temperature scales are systems of sequentially numbered values corresponding to various temperatures. The temperature can be determined by measuring any quantity dependent on it and it is convenient to measure a physical property of a certain, so-called thermometric substance (for instance, the volume or pressure of a gas, the resistance of a conductor). To realize a temperature scale, we must select its origin and the dimension of the temperature unit (degree). For this purpose, we usually use two reference points — temperatures of transition of a substance from one agregate state to another. Such temperature scales are called "practical." The first practical temperature scale was suggested by Fahrenheit in 1724, in which one of the reference points was the temperature of a human body, accepted by Fahrenheit to be equal to 96 degrees (°F), the second, the temperature of ice melting, equal to 32 degrees (°F). A liquid mercury thermometer served as an interpolation device.

More accurate practical temperature scales were suggested by Celsius and Réaumur. In these scales the temperatures of melting of ice and boiling of water at atmosphere pressure were used as reference points. The temperature interval between these points in Celsius’ scale (°C) was divided by 100, and in Réaumur’s scale (°R) by 80 equal parts. In Fahrenheit's temperature scale, this temperature interval is equal to 180 (°F). In the absolute Kelvin (K) and Rankine (R) temperature scales, where the origin of scale is the absolute zero, the temperature interval is equal to 100 and 180 temperature units, respectively. The principle of constructing temperature scales suggested by Fahrenheit (the reference points and interpolation device) is used in the international temperature scales. For instance, the international temperature scale of 1927, ITS-27, was realized using two points (0°C and 100°C), the unit of temperature is the degree Celsius (°C); in the ITS-90, one point, the temperature of the triple point of water, 273.16 K, was used; the unit of temperature is the Kelvin (K). The main interpolation device is a platinum resistance thermometer.

The so-called thermodynamic temperature scale, which is independent of the particular properties of a thermometric substance, can be realized on the basis of the second law of thermodynamics, by determining the ratio of temperatures from the ratio of temperatures in Carnot’s cycle. In practice, to construct such a scale, relations are used which, whilst not contradicting the second law of thermodynamics, relate the thermodynamic temperature to some additive physical quantity which can be measured accurately enough. The most widespread are:

• the gas thermometer based on the gas law

(2) where R is the universal gas constant, and p, , T are the pressure, molar volume and temperature of a working substance in an ideal gas state;

• the acoustic thermometer based on measuring the velocity of sound, C, in a gas

(3) where γ = cp/cv is the specific heat ratio (for an ideal gas γ = const), and is the molecular weight of the working substance;

• the radiation thermometer based on measuring the total energy of heat radiation E(T) emitted by a blackbody at temperature T

(4) where σ is the Stefan-Boltzmann constant;

• the thermal noise thermometer based on measuring the root- mean-square of voltage noise in current flow through a resistance Ω (ohm) at a temperature T (Nyquist’s equation)

(5) where Δf is the band width (Hz).

Presently the most exact values of thermodynamic temperature in a wide range of values can be obtained using the gas thermometer; however, near 4 K and above 200 K the noise and radiation thermometers approach the gas thermometer in accuracy. In 1848, J. Thomson (Lord Kelvin) proved that the temperatures determined from Carnot’s cycle and by the gas thermometer are identical and represent the thermodynamic or absolute temperature. With the assumption for a dimension of a temperature unit made by Celsius, Thomson determined the value of temperature of ice melting on a new scale, −273.15 K.

Since 1960, the unit of thermodynamic temperature (K) was determined as 1/273.16 of the temperature of the triple point of water, −273.16 K. When using a gas thermometer of constant volume ( = const) relation (2) for determining the unknown temperature Tx takes the form

(6) where T0 = 273.16 K, p0 is the pressure of the working substance at a temperature Tx. In the ITS-90 the basic unit of temperature T90 is the Kelvin (K). The measurements allowed for measuring temperature in °C (t90) are defined as #### REFERENCES

Quinn, T. I. (1983) Temperature, London, Academic Press.

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