Evolution of one-dimensional gases in expanding containers

Abstract

We investigate the time evolution of the number density of an ideal gas bounded by pistons. We find that the short-term behavior is heavily influenced by the initial number density. The long-term behavior depends on the initial velocity distribution and the velocity of the pistons. For piston velocities much greater than the root mean square value of the particle velocities, the ideal gas behaves as if no boundaries exist, the number density displaying a narrow profile centered at the initial center of mass location. For comparable piston and particle velocities, more gas particles situate themselves near the boundaries. An initial asymmetry in the number density is manifested in the long-term behavior.