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

Abstract

We discuss the adiabatic two-piston problem for an ideal gas confined between two pistons of equal mass and extend recent work based on the reversible approximation. More realistic equations that account for the roles of the gas temperature and particle mass are applied to extend the analysis of the expansion of the gas from reversible to irreversible behavior to the limit of free expansion. The evolution of quantities, such as temperature, piston speed, adiabatic reversibility coefficients, and entropy, is obtained, and differences between the irreversible and the reversible solutions are investigated.

Symmetry of the adiabatic condition in the piston problem

“…The above equation means that the pressures exerted by each gas on the piston are exactly equal to the gas pressures, which contradicts what is known from the literature that the pressure exerted on the piston by either gas is greater when it is moving towards the gas than when it is moving away from the gas, even assuming that the gas pressure is always well defined [1,3,4]. Besides, inserting (10) into either ( 8) or ( 9), the equation for dS becomes dS = 0.…”

“…As in [1,3,4], it is assumed here that gases instantaneously adjust to the motion of the piston so that P i and T i are well defined and uniform throughout the process.…”

“…Each subsystem having different initial pressures and temperatures, once the piston is released, the subsystems will interact through the oscillatory motion of the piston, which is a damped motion because the pressure exerted on the piston by either gas is greater when it is moving towards the gas than when it is moving away from the gas [1,3,4]. These differences between the pressure that each gas exerts on the piston and its own pressure act as frictional forces on the piston and ultimately bring it to rest [1,5], i.e.…”