Can the effect of an external gravitational field be incorporated in the classical kinetic theory of gases?

Abstract

This study proposed an extension of the classical kinetic theory of gases (CKTG) that incorporates the gravitational effect on the motions of molecular particles. First, we rederived the CKTG in terms of the kinetics of constituent particles to account for the effect of accelerating particles by external gravitational fields. Consequently, we obtained an extended expression for the virial pressure in molecular dynamics under external potential fields. As indicated by our theoretical model, a pressure difference in the gravitational direction was observed in our particle collision simulations. Further analysis proved that if the external potential energy of each particle was sufficiently small (but not negligible compared to its kinetic energy), a pressure difference emerged between the walls while still maintaining the properties of equilibrium statistical mechanics, following the Maxwell--Boltzmann distribution. Notably, our model was formulated based on only fundamental knowledge of physics and is therefore suitable for educational purposes. Thus, this study obtained fundamental insights into the kinetic theory of gases under gravitational fields that are expected to be useful for both education and practical applications.