Transport Phenomena in Einstein-Bose and Fermi-Dirac Gases. II

Abstract

In this paper the general theory of transport phenomena in simple gases is concluded, and numerical values of the gas coefficients for heat conductivity and viscosity are obtained as a function of the temperature and density for the particular case of molecules acting as rigid elastic spheres. In the Introduction will be found a qualitative discussion of the principal results obtained and an interpretation of these results according to elementary considerations. In Section 1 the method of solution of the integral equations with which the formal theory of Part I was concluded is given together with the resulting general equations for the heat conductivity and viscosity coefficients. Since the integral equations can be solved only by a method of successive approximations, the expressions for the gas coefficients are in the form of infinite series the rapidity of convergence of which depends on a suitable choice of a complete set of auxiliary functions. In Section 2 all of the integrals appearing in the first two terms of the infinite series are evaluated. That only two terms are required is due to the fact that one is able to make an excellent choice of functions to represent the auxiliary set. In the evaluation of these integrals restriction is made in the application of the theory to small values of the degeneracy parameter $A$, since only terms in the zeroth and first power of $A$ are retained. This restriction is only slightly greater than that imposed by the fundamental postulates of the general theory which restrict its applicability to moderately rare gases. In Section 3 the final equations for the gas coefficients are applied to gases consisting of molecules which interact quantum-mechanically as rigid elastic spheres of diameters and masses associated with the gases helium and hydrogen.