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

Abstract

The mean relative speed and relative speed distribution function of molecules play important roles in kinetics and related topics. College textbooks frequently present a simplified derivation of these quantities that, while yielding the correct result, are not well justified. This paper presents a detailed physical picture of collision-related processes based on the microscopic kinetic theory. Formulas for the mean relative speed and mean collision rate along with the relative speed distribution function and the distribution function of relative speed of the paired particles in collisions (collision possible distribution function) are derived for molecules from two different systems that are each at thermal equilibrium.