Entropy balance in a multi-component system of gases derived by Grad's method

Abstract

The entropy balance equation (and consequently also the Gibbs equation) for non-stationary processes in an N-component mixture of rarefied gases (or plasma), all at the same temperature, is derived from kinetic theory by use of Grad's method of moments. The entropy balance equation is presented for both the 12 N+1 and 19 N+1 third-order moment descriptions of the mixture. An expression for entropy production is deduced as a linear function of collision integrals. Explicit expressions for entropy production are obtained for the case of non-Maxwellian molecules (when collision integrals are linearized) and for Maxwellian molecules. For the case of Maxwellian molecules (with linearized collision integrals) a proof of the validity of σ ≧0 is given. It is shown also how to extend the Fourier, Fick and Navier-Stokes transport laws to the case of non-Maxwellian gases.