Entropy Production and Variation Principle in The Kinetic Theory of Rigid-Sphere Gas Mixture

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The balance equations and the fluxes of thermodynamical variables are obtained on the basis of the modified Boltzmann equation for a multicomponent rigid-sphere gas. The kinetic expression of entropy balance is obtained in terms of the H-theorem, the correction to the entropy due to imperfectness of the gas being added. The correction is calculated from the equation of state, which is derived from the momentum transport equation. The entropy balance is also formulated thermodynamically with the aid of the Gibbs relation. By the use of these two expressions a variational problem, concerning the entropy production rate can be set up. The solution of this problem leads to the first approximation equation for singlet distribution function, which is identical with Enskog’s one apart from the terms independent of the energy dissipation.

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