Specific heat of gases

General.—It is a question of fundamental importance for the applications of thermodynamics, and of my Heat Theorem in particular, whether we know the value of the integral 

Before going into details I should like to refer briefly to two results which are of importance for our purposes — 

All gases, at sufficiently low temperatures and under sufficiently low pressures, behave like monatomic gases as regards their specific heats, i.e. their molecular heat at constant volume converges towards the value fR. 

If we suppose a gas of finite concentration to be cooled at constant volume, avoiding any condensation, it passes into a state totally different from the ordinary gaseous state 

There are a number of relationships concerning the specific heats of gases that are of significant use to the process modeller. The specific heat, c, is defined as the amount of heat that must be supplied to raise the temperature of unit mass of a substance by one degree  

It is possible to express the principal specific heats in terms of the thermodynamic variables we have introduced previously. The first law of thermodynamics may be written 

Thus the specific heat at constant volume is found by substituting from (3.11) into (3.9) to give 

In fact, specific internal energy is dependent solely on temperature for an ideal gas, and so the constant-volume subscript, v, may be dropped  

For the case when the pressure is kept constant during the heating process, we begin by noting the definition of specific enthalpy, namely  

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In statistical mechanics (e.g. the theory of specific heats of gases) a degree of freedom means an independent mode of absorbing energy by movement of atoms. Thus a mon-... 

The specific heat of gases at constant pressure is calculated using the principle of corresponding states. The for a mixture in the gaseous state is equal to the sum of the C g of the ideal gas and a pressure correction term ... 

CpfC Ratios of Specific Heats of Gases at 1-atm Pressure.. 2-183... 

The method has been applied by Eucken to determine specific heats of gases (e.g., H2) at constant volume by enclosing them in small metallic vessels. 

Fig. 1.1 Specific heats of gases at constant volume as a function of temperature.

Thus, one obtains the specific heats of gases composed of monatomic, diatomic, and polyatomic molecules as follows ... 

J.R. Partington W.G. Shilling Specific Heats of Gases , E. Benn Ltd, London... 

Or, Explain specific heat of gases at constant volume (Meerut 2004)... 

The calculation of the flame temperature for a combustible gas like hydrogen, carbon monoxide, or methane at first sight appears to be a simple problem since the apparently necessary data are only the heat of combustion and the specific heats of the products. Such calculations always yield very high results much above those recorded by direct experimental measurements. The discrepancy is probably due to a combination of several causes. On account of the temperature of the flame the products are partially dissociated,1 so that combustion is not complete m the flame. The specific heat of gases increases with rise m temperature, so that the value obtained at the ordinary temperature for the specific heat is too low. In addition to these two causes, another contributory factor is the loss of heat by radiation, which may be very considerable even m nou-lummous flames, whilst the general presence of an excess of the supporter of combustion and the non-instantaneous character of the combustion also detract from the accuracy of the calculation.2... 

Variation in specific heats of gases under the special conditions, which render the theoretical calculations uncertain. 

The value of Cp is usually known, and thus can be calculated. Brandt calculated c for the liquid. Donath s calculations of specific heats of gases from the variation of latent heat of evaporation with temperature, apart from the use of an incorrect equation, are subject to large influences of experimental errors, and the method is unsatisfactory. Hooks and Kerze described a nomogram for dependence of latent heat on temperature based on the equation ... 

Equations (3) and (4) were deduced by Planck. It has been proposed to use them to calculate specific heats of gases and vapours. 

The supposed differences between chemical constants determined from vapour pressures (7/) and from chemical equilibrium data from the Nernst Heat Theorem Jn found by Eucken, Karwat, and Fried, are illusory, and due to inaccuracies in the experiments made in Eucken s laboratory, The supposed constant differences between the calorimetric and optical values (from moments of inertia found from band spectra. or otherwise) listed, with a theoretical explanation, by Eucken, Karwat, and Fried, are also illusory for the same reason. The relation between the spectroscopic and calorimetric entropies, as found from experimental results meriting confidence, is fully discussed in 70.11 and 26-29.IV. Apart from the incorrect data used by Eucken, Karwat, and Fried, 11 their method of extrapolation of specific heats of gases to 0°K. is much cruder than they suspected. 12... 

In general, the specific heat of gases rises with the temperature. The more complex the molecule, and the larger the value of the specific heat at 0°, the more rapid is the increase with the temperature. It has been found of late that the specific heat Cp of certain gases increases as the temperature is lowered to near the condensation point. Thus, Scheel and Heuse found for air ... 

We shall show in the next paragraph that the vapour pressure constants play an important part in the calculation of chemical equilibria in gases. The first problem which Nernst had to solve after the discovery of his theorem was therefore the calculation of at least the approximate value of C for as many simple substances as possible. For this purpose he made use of the theorem of corresponding states, and assumed further that the specific heat of solid and liquid bodies diminishes to a small but finite value (viz. nx 1 5, where n is the number of atoms in the molecule) as the temperature is lowered. On the evidence of the measurements published up to that time he also assumed that the molecular specific heat of gases and vapours is a linear function of the temperature which approaches the value 3-5-l-7ixl-5 at very low temperatures. In this way he arrived at the vapour pressure formula... 

The vacuum calorimeter described by Schwers and me has been further developed recently in a few respects by Gunther (107), who used it for many important measurements reference may therefore be made to the description given by Gunther for a more detailed account. The vacuum calorimeter has been used by Eucken (105) with marked success to determine the specific heats of gases at constant volume, and also for the measurement of heats of evaporation, heats of fusion, and heats of transformation at low temperatures (cf. also Chapter V). 

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