Heat Conductivity of Polyatomic and Polar Gases and Gas Mixtures

Abstract

A theory is presented which can be used for the practical calculation of the heat conductivity of polyatomic and polar gases and gas mixtures. For pure gases, the results are based on the Wang Chang—Uhlenbeck equations and involve no approximations, provided that a suitable definition of an internal diffusion coefficient is employed. This is compared with the known results for a gas of rough spheres, and found to hold to all orders of approximation. Approximations enter for real gases only in obtaining numerical estimates of internal diffusion coefficients and relaxation times. The result is essentially the same as that of Mason and Monchick. For mixtures, the results are based on the formal kinetic theory recently obtained by Monchick, Yun, and Mason. A brief digression on sound absorption and dispersion in mixtures is made in order to identify the cross relaxation times in the formulas. Two assumptions are required for mixtures to obtain usable formulas: neglect of ``complex collisions,'' and no correlation between internal energy states and relative velocities (or equal differential cross sections for all scattering channels). With these assumptions plus suitable definitions of internal diffusion coefficients and relaxation times, a usable formula for the heat conductivity is obtained. This formula is further simplified to include only first-order correction terms, and rearranged so that the heat conductivities of the pure components are automatically given correctly. Comparison with experimental results for a number of different types of mixtures showed that the calculated results were rather insensitive to inelastic collision corrections, provided they were forced to go through the correct end points. It was concluded that for most purposes a theory neglecting inelastic effects in the mixture would be adequate, but that inelastic effects must be included in calculations for the pure components.