Kinetic Theory of Nonspherical Molecules. V

Abstract

A generalized Boltzmann equation for fluids composed of molecules with arbitrary internal degrees of freedom and which interact according to classical mechanics through arbitrary, noncentral pair‐additive forces is developed using techniques similar to those used by Hollinger and Curtiss. Several special cases are considered: (1) molecules which interact only through impulsive forces of repulsion, (2) molecules for which the only internal degrees of freedom are rotational degrees, and (3) a combination of both special cases. The third special case leads to a Boltzmann equation appropriate to a fluid composed of rigid nonspherical molecules, and provides a firm basis upon which to develop a formal kinetic theory. As a special example we consider a gas made up of rigid, convex, nonspherical molecules with symmetric‐top mass distributions. Rigorous equations of hydrodynamics are presented for such a fluid. It is shown that the kinetic theory of a dilute multicomponent system of these molecules is formally the same as that for the loaded‐sphere system recently studied by Dahler and Sather. Finally, it is shown how the methods developed by these authors can be applied to the problems of solving the Boltzmann equation and of calculating the transport coefficients for the nonspherical molecular species considered in the present paper.