An Exact Solution of Boltzmann's Equation for a Rigid Sphere Gas

Abstract

The second approximation to Boltzmann's equation, in Chapman and Cowling's form, is solved exactly for a rigid sphere gas by using appropriate transformations to reduce the integral equation to a differential equation, which is solved numerically. The values of the transport coefficients, calculated directly from this solution for the velocity distribution function, are in good agreement with those obtained from the usual approximation techniques. A solution for part of the third approximation, with a term of zero order in V, the velocity of a molecule relative to the stream velocity, is also obtained analytically.