Microscopic derivation of the collision properties of molecules in two systems at thermal equilibrium.

This article focuses on deriving and analyzing the mean relative speed, relative speed distribution function, mean collision rate, and collision possible distribution function of molecules from two different systems at thermal equilibrium, using a microscopic kinetic theory approach with a hard sphere collision model. It critiques common textbook derivations as lacking physical insight and provides detailed, self-contained derivations based on Maxwell speed distributions for each system, including cases with differing masses and temperatures. The study confirms that the relative velocity distribution remains Maxwellian and introduces the collision possible distribution function, which accounts for the relative speed dependence of collision probabilities relevant to chemical reaction rates. The results offer a comprehensive physical framework useful for understanding molecular collision dynamics and related kinetic phenomena.