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

Abstract

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.

The two-piston problem revisited: Generalization from reversible to irreversible expansion

“…6 in a form that enables us to take into account the ratio of the piston speed to the root mean square (rms) particle speed. In the reversible approximation, which is valid when the piston's speed v is negligible, the pressure exerted on the piston P is given by the gas pressure P (P ¼ P).…”

“…The adequacy of our numerical procedure was checked by comparing the calculations for r 0 ¼ 1 with the ones given by the analytical expressions in Ref. 6. The discrepancies were less than 0.02% for Dt ¼ 0.001 s and a piston mass M ¼ 0.0001 kg.…”

“…It was assumed that the gas instantaneously adjusts to the motion of the two pistons so that the pressure P and temperature T of the gas are well defined and uniform throughout the process; 6 that is, the system undergoes a quasistatic process and is always infinitesimally near equilibrium. 7 Additionally, their analysis 6 assumed that the pressure exerted on the pistons P is equal to the gas pressure P, which, together with the quasistatic assumption, implies that the expansions are reversible. During such a reversible expansion, the system evolves to a steady state and the energy of the gas is completely transferred to the pistons, so the gas temperature becomes zero.…”