Evolution of ideal gas mixtures confined in an insulated container by two identical pistons

We study the quasistatic adiabatic expansion of monatomic-diatomic ideal gas mixtures bounded by identical pistons and obtain closed form expressions for the temperature of the gas as a function of the time. We find that the temperature decreases as an inverse power of the time for large times, with the exponent as a function of the monatomic to diatomic gas ratio. The piston speeds increase from zero to a maximum value determined by the heat capacity of the gas and the masses of the pistons. Plots of the temperature and piston speed versus the logarithm of the time show points of inflection, which are interpreted as signaling the onset of steady state behavior. These points shift to later times as the monatomic to diatomic gas ratio is varied from purely monatomic to purely diatomic.