A Statistical Theory of Liquids. III

Abstract

In the present paper the author incorporates the dissipative processes of heat conduction and viscosity into his theory. In order to do that, he generalizes first the procedures of statistical mechanics in such a way that they might describe processes involving molecular flow. This is achieved in close analogy to Boltzmann's treatment for gases: Boltzmann's integro-differential equation is replaced by Gibbs' principle of "conservation of density-in-phase," and the solution is sought in form of a power series which modifies (slightly) the canonical ensemble. Finally the anisotropic distribution function in real space is obtained by integrating the multidimensional distribution function with regard to all coordinates and moments except those of one particle.Section I gives the introduction and Section II the general outline of the theory. In Section III heat conduction is treated in form of the linear problem. The potential is smoothed out by making it dependent on the position of the center of mass only. With this simplification an asymptotic solution can be found which yields the time-dependent temperature gradient and heat current, and thereby the coefficient of heat conduction. In Section IV viscosity is treated in a similar way, and Section V treats the averaging processes involved in the evaluation of physical quantities. Finally, in Section VI, the coefficients of heat conduction and viscosity are calculated numerically for ten liquids from the potentials previously determined. The agreement is (with a few exceptions) about as good as might be anticipated from such a rigorous test. Thus, the same potentials, with their four available constants, have served now to calculate ten independent physical constants with a fair accuracy.