I. On the applications of the kinetic theory to dense gases

Abstract

The motion of a great number of elastic spheres, when their aggregate volume does not bear an evanescent ratio to the containing space, has received little attention from writers on the kinetic theory. In what respect, beyond the shortening of the mean free path, will it differ from that of the rare medium usually discussed ? I think that the answer to this question is that there exists in all systems, dense or rare, a tendency for the spheres to move together in masses or streams, and so to diminish the mean pressure per unit of area, and the number of collisions per unit of volume and time. And this tendency has an appreciable influence on the form of the motion as soon as the ratio of the aggregate volume of the spheres to the containing space becomes appreciable. If a part of the system, say n spheres, be at any instant contained in a volume V, they have energy, T r of the motion of their common centre of gravity. And they have energy, T r , of relative motion. As the spheres increase in diameter, the ratio T r /T s , will be found to diminish on average. But the number of collisions per unit of volume and time, given T, or T r , + T s , depends on T r , and therefore diminishes by the diminution of T r .