S. Boguslavskii. Foundations of Molecular Physics and the Application of Statistics to the Calculation of Thermodynamic Potentials. Moscow, 1917. [Master’s dissertation; edition copied on a typewriter].

As the author indicates in the preface: “the present work is devoted to the question of the kinetic interpretation and calculation of thermodynamic functions.” It is assumed here that all thermodynamic functions are certain mean values of molecular velocity and coordinates. After setting forth the proposition on the virial, there are given, for periodic motions, such functions as possess the properties of thermodynamic functions, as was discovered by Boltzmann’s works on the mechanical interpretation of the second law and by Helmholtz’s works devoted to the statics of monocyclic systems. The author then examines in detail the replacement of the time average by the statistical average and, after expounding the principles of statistical mechanics, gives its application to the calculation of thermodynamic potentials. The applications concern the free energy of a solid dielectric, the free energy of a monatomic gas, the potential of a dielectric and of a monatomic gas, the potential of a diatomic gas, the specific heat of a paramagnetic gas, and certain magnetic and electrical phenomena. In contrast to the usual theory of gases, which regards the absolute temperature as proportional to the vis viva, the author takes the temperature \(T\) to be equal to \(\frac{1}{\tau}\), where

\(\tau\)—the period of oscillation of the molecule; the entropy \(\eta=\int_{0}^{\tau} 2w\,dt\), where \(w\) is the kinetic energy of the system.

P. Lazarev.