Thermal damping of the motion of a piston: Any irreversibility implies dissipation

Abstract

We consider the motion of a frictionless piston that separates the surrounding atmosphere from an ideal gas enclosed within a cylinder, with no friction or viscous dissipation arising within the gas or surrounding atmosphere. Although no mechanically based dissipative mechanisms act, the motion of the piston is still damped if heat transfer between the gas and the piston occurs at a finite rate. Hence, as long as some kind of irreversibility develops within the system, such as irreversible heat transfer, the piston will not oscillate back-and-forth indefinitely and must eventually come to rest. We provide detailed thermodynamic and numerical analyses of this thermal damping, various aspects of which should prove useful to both students and instructors when discussing the first and second laws of thermodynamics.