Equivalence of the Chapman-Enskog and the Mean-Free-Path Theory of Gases

The model considered is restricted to monatomic particles interacting with a finite-range central field force. The integral equation for the second Chapman-Enskog approximation to the velocity distribution function is solved by a Liouville-Neumann iteration scheme. It is then shown that the Nth iteration corresponds to a mean-free-path theory where the trajectory of a particle has been followed through N + 1 collisions. The zeroth-order approximation is then compared with the elementary mean-free-path theory to show their equivalence.