Ideal gas thermometer

T) = T. (17), so that absolute thermodynamic temperatures are equal to the gas temperatures measured with an ideal gas thermometer. 

It is not possible to construct an ideal gas thermometer. Instead, a real gas thermometer must be used under conditions where the real gas behaves as an ideal gas. This is done by extrapolating the pV product to zero pressure (where all gases behave ideally), and equation (1.9) becomes... 

The ability to measure temperature and temperature differences accurately and reproducibly is essential to the experimental study of thermodynamics. A thermometer constructed with an ideal gas as its working fluid yields temperatures that correspond to the fundamental thermodynamic temperature scale. However, such thermometers are extremely difficult to use, are not amenable to miniaturization, and are very expensive. Therefore, other means to measure temperatures that reproduce the ideal gas or thermodynamic temperature scale (Kelvin) have had to be developed. The international temperature scale represents a method to determine temperatures over a wide range with measuring devices that are easier to use than the ideal gas thermometer. The goal is to make temperature measurements that correspond to the thermodynamic temperature as accurately as possible. 

Techniques for accurate and reproducible measurement of temperature and temperature differences are essential to all experimental studies of thermodynamic properties. Ideal gas thermometers give temperatures that correspond to the fundamental thermodynamic temperature scale. These, however, are not convenient in most applications and practical measurement of temperature is based on the definition of a temperature scale that describes the thermodynamic temperature as accurately as possible. The analytical equations describing the latest of the international temperature scales, the temperature scale of 1990 (ITS-90) [1, 2]... 

It will be seen in Chapter VII ( 18k) that it is possible to develop an absolute temperature scale, also independent of the nature of the thermometric substance, based on the second law of thermodynamics. This is sometimes called the Kelvin scale, in honor of its originator. Lord Kelvin (William Thomson). Actually, the thermodynamic scale can be shown to be identical with the absolute ideal gas scale, as defined above hence, temperatures on the latter, as well as the former, scale are represented by the symbol K. The ice point is consequently 273.16 K. It may be noted, incidentally, that the thermodynamic derivation of the absolute temperature scale provides a more definite interpretation of the absolute zero, i.e., the lowest limit of temperature, than is possible by means of the ideal gas thermometer. ... 

The product of PV for a low-density gas is said to be a thermometric property in that to each value of FV there corresponds only a single value of temperature. The ideal gas thermometer is not convenient to use. however, because of both its mechanical construction (see Fig. 1.4-3) and the manipulation required to make a measurement. Therefore, common thermometers make use of thermometric properties of other materials—for example, the single-valued relation between temperature and the specific volume of liquid mercury (Problem 1.2) or the electrical resistance of platinum wire. There are two steps in the construction of thermometers based on these other thermometric propenies first, fabrication of the device, such as sealing liquid mercury in an otherwise evacuated tube and second, the calibration of the thermometric indi-... 

Figure 1.4-3 A simplified diagram of a con-, stant-volume ideal gas thermometer. In this hose thermometer the product PV for a gas at various temperatures is found by measuring the pressure P at constant volume. For each measurement the mercury reservoir is raised or lowered until the mercury column at the left touches an index mark. The pressure of the gas in the bulb is then equal to the atmospheric pressure plus the pressure due to the height of the mercury column.

If the arbitrary constant C is set equal to (nR) where n is the number of moles in the system and R is the gas constant per mole, then the thermod5mamic temperature T= 0-g where 0jg is the temperature measured by the ideal-gas thermometer depending on the equation of state... 

The absolute temperature is defined in that way that at the triple point of water T = 273.16 K. If the physical unit of the temperature is K, then this means the unit of the entropy is Any other temperature can be accessed using the ideal gas thermometer. 

The existence of the absolute temperature T (applicable in all the universe) which may be identified with the empirical temperature of the ideal gas thermometer b = T and is therefore positive (and increasing with physiological hotness ) and measurable in Kelvins. 

From results (1.28) we can see that absolute temperature [introduced, after aU, within a positive constant, cf. (1.27)] is proportional to the empirical temperature of the ideal gas thermometer T = c-. Arbitrary universal constant c may be chosen usually c = 1 and we can identify the absolute temperature with empirical temperature of ideal gas thermometer... 

Here d 2 is the heat exchanged in the process (may be their sum at different places and instants) where their absolute temperature has the same value T. We recall that T are identified with (positive) empirical temperature z of the ideal gas thermometer (1.30). 

Following [98, 99] we sketch this procedure in simplified form used in Rems. 10, 16 (using existence of the density of heat distribution rf). Similarly as in Rem. 10 we consider oo in our step approximation components of heat distribution are nowdg for each temperature d of ideal gas thermometer. Proof in this Sect. 1.4 then needs the infinite dimensional space with such vectors of heat distribution. Using (nonnegative) heat absorbed andemitted given now by Eq. (a) from... 

Again absolute temperature may be identified with empirical temperature of ideal gas thermometer (1.30) admitting of course, that the Carnot cycle may be introduced for any two empirical temperatures jl. 

The ideal gas thermometer realized by limitation (A.l) may be looked upon as a thermometer filled by ideal gas which is defined by... 

The Carnot cycle is an abstract construction because of ideal gas, namely this was used for obtaining temperature -d of the ideal gas thermometer in Kelvins (see (A.l)) and, through result (A.9) below, for obtaining the absolute temperature (1.30), see Sect. 1.4." Also the balance of energy (1.5) contains only the volume work w (because the (macroscopic) kinetic and potential energy may be neglected, see Rem. 9... 

Equality (A.9) is important for identification of empirical temperature of ideal gas thermometer 1) with the absolute temperature T (see deduction of (1.30) in Sect. 1.4). In most parts of this book, we use this absolute temperature T. Therefore, e.g., the state equation of ideal gas (A.3) may be written as... 

Gas Thermometry. If the equation of state, i.e., the function relating pressure, volume, and temperature, of a gas is known, the gas can be used to measure temperature. If one of the variables is held constant and a second is measured, the third can be calculated from the equation of state. In thermometry, it has been found most advantageous to hold the volume of a fixed amount of gas constant and measure the pressure. The temperature of the gas is then determined. When properly corrected, such a constant-volume gas temperature very closely approximates an ideal gas thermometer, and is used to fix points on the absolute temperature scale. 

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