The heat capacity of a perfect gas. Chemical constants

The heat capacities of perfect gases are very closely related to their molecular structures. The exact relations have been derived on the basis of statistical mechanics but here we shall give only a general account of the problem. More detailed accounts will be found in the standard works on statistical mechanics.  

We shall limit ourselves to the case where the mean energy of each molecule is equal to the sum of the energies of translation, of rotation and of vibration. The heat capacity at constant volume (c/. 10.5) will also be composed of three terms arising from these three kinds of motion. The contribution from the translational motion is f R per mole, and that from rotation is JR or fR depending upon whether the molecule is linear or not. This last statement is only exact if the rotational motion may be treated by classical, as opposed to quantum, mechanics. This is a good approximation even at low temperatures except for very light molecules such as Hg and HD. Finally the contribution from vibration of the atoms in a molecule relative to one another is the sum of the contributions from the various modes of vibration. Each mode of vibration is characterized by a fundamental frequency vj which is independent of the temperature. It is convenient to relate the fundamental frequency to a characteristic temperature (0j) defined by 

The contribution of each vibration to the specific heat increases with increasing temperature and may be written in the form RP where 

Fowler and Guggenheim [20], chap. III. Mayer and Mayer [34], chap. V to VIII. 

P is a universal function called the Planck-Einstein function, of which an abbreviated table is given in table 10.1. 

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