In carrying out various types of thermodynamic calculations, an accurate and assured knowledge of the heat capacities of the substances involved is often essential. Frequently, a t least one of the constituents in such considerations is a gas and, due to inherent experimental difficulties, the literature is generally lacking in reliable values for the specific heats of gases2 The latter observation is particularly true for data taken either at very high or at very low temperatures. Yet, frequently, it is in these more extreme temperature regions that a more exact knowledge of the heat capacity curves assumes greatest interest and importance.Moreover, until quite recently no adequate quantitative theory had been proposed to account for the heat capacities of molecules containing more than one atom. The most useful guide had been the principle of the Equipartition of Energy, enunciated by Boltzmann. This principle was derived by application of statistical methods to a classical energy distribution among the various degrees of freedom associated with the translational, rotational and vibrational motions of the molecules. For monatomic gases the Equipartition Principle yields correct specific heats,4 but its inadequacy to account correctly for the magnitudes, as well as the variations, in the specific heats of more complex gases constituted one of the original arguments in favor of quantum theory.'The approach to a correct solution of the more general problem was made, independently, by Kemble5 and by Reiche.6 These authors attempted to calculate the rotational portion of the heat capacity of hydrogen on the basis of what was then known concerning rotational quantization in molecules. By considering the diatomic molecule as a rigid rotator, Reiche obtained the well-known equation for CR, the molar rotational heat capacity, which takes the form7 d2 In Q doP CR = u'R -(1) Presented March 31, 1931, as part of the Symposium on "Applications of Quantum Theory to (2) The low temperature measurements on hydrogen, made by Cornish and Eastman [THIS (3) Boltzmann, Sitzb. Akod. Wi'iss. Wicn., 58 (1861). (4) Except at high temperatures, where all monatomic gases will rise above the equipartition value ( 5 ) Kemble, Phys. Rea., 11, 156 (1918). (6) Reiche, Ann. Physik, 68, 657 (1919).(7) Here R is the molar gas constant: T, the absolute temperature; k, the gas constant per molecule: I , the moment of inertia: Pm the statistical weight of the rotational state possessing the quantum number "m"; and the summation is over ail values of "m" from m&&mum to OD.
Chemistry," Indianapolis Meeting of the American Chemical Society.JotrRNAL., 60,627 (1928) ] are a noteworthy exception.due to electronic excitation.