Heat Capacity Curves of the Simpler Gases. I. Heat Capacity, Entropy and Free Energy of Gaseous Nitric Oxide from Near Zero Absolute to 5000°K.¹

Abstract

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.

A Mollier Diagram for the Internal-combustion Engine.

“…In recent years the technique of calculating the specific heats of gases over a temperature range extending down to absolute zero has been perfected; the calculations have been carried out for a number of gases, and the results have been published in a series of papers by Johnston and his coworkers (1,4,5,6,7,8), and in papers by Kassel (9) and Gordon (2), all of which appeared in the years 1933, 1934, and 1935. Knowledge of the specific heats permits the calculation of entropies; the results of these calculations are given in the papers mentioned.…”

“…For the first step, if the value of pc is chosen not greatly different from the initial pressure p0, the value of c to be found will be small and will be denoted by A'c. Equation 3 may then be written: (4) in which (EPxPc)[v. indicates the average energy of burned gas at the pressure pc which burned at pressures varying from p0 to pc. If the step is small and/or if the relation connecting c and pc is substantially linear, (EpxPc)*y-is the average value of EPxPe as obtained from figure 6 between px = po and px = pc along the curve for the value of pc chosen.…”

The specific heat of gases at high temperatures

“…It is, therefore, of great interest to compare these "spectroscopic values" with those obtained in the present investigation and, as this has been done, it is necessary to give the source of the spectroscopic values that have been used. During the last few years Giauque (1930 a, b;Gia uque and Overstreet 1932;Clayton and Giauque 1932), Johnston and their co-workers Chapman 1933; Walker 1933 a, b, 1935; Lewis and von Elbe 1933 a, b;Johnston and Dawson 1933;Giauque and Clayton 1933;Gordon 1934;Johnston and Davis 1934;D avis and Johnston 1934;Kassel 1934) have published their spectroscopic determinations of the molecular heat at constant pressure of such gases as hydrogen (Davis and Johnston 1934), carbon monoxide (Johnston and Davis 1934), nitrogen (Johnston and Davis 1934), oxygen (Johnston and Walker 1935), nitric oxide (Johnston and Chapman 1933 ), OH (Johnston and Dawson 1933), carbon dioxide (Kassel 1934), nitrous oxide (Kassel 1934) and water vapour (Gordon 1934), the temperatures extending in many cases up to 5000° C (abs. ).…”