Chemical damping of the motion of a piston: irreversibilities arising from nonequilibrium conditions on the chemical potential

Abstract We revisit the thermodynamic analysis of an isothermal ideal gas mixture enclosed within a cylinder and separated from the surrounding atmosphere by a movable and frictionless piston. When equilibrium conditions based on the chemical potentials of one or more species in the mixture are not satisfied at all times, which occurs for example for a chemical reaction with finite and non-zero reaction rates in the forward and reverse directions and for mass transfer of one species across a permeable membrane occurring at a finite and non-zero rate, an irreversibility is necessarily introduced into the system with a resulting increase in the entropy of the Universe. Consequently, when the piston is set in motion, it cannot oscillate indefinitely. The piston must again come to rest despite there not being any mechanical dissipative mechanisms, i.e. friction or viscous dissipation, nor a thermal dissipative mechanism, i.e. irreversible heat transfer, operating within the system. Only when the system is reversible, such that the entropy of the Universe remains constant at all times, will the piston oscillate indefinitely. ‘Chemical damping,’ or an irreversibility arising from nonequilibrium conditions on the chemical potential, provides another dissipative mechanism that has not yet been analyzed before.