Entropic Damping of the Motion of a Piston Available to Purchase

The concept of an “entropic force” can be introduced by considering a familiar setup, namely a horizontal cylinder enclosing an ideal monatomic gas by a piston of cross-sectional area A and mass m that can slide without friction. The surrounding atmospheric pressure P_atm keeps the piston from flying out of the cylinder. The cylinder and piston have negligible heat capacity (compared to the gas), but the gas is not thermally insulated from the surroundings at room temperature T_R. Ignore any viscosity or turbulence of the enclosed gas or surrounding air. Two specific and illustrative situations are analyzed here. In the first, the piston is massless, m = 0. The piston is temporarily held in place by a pin while the gas is quickly adjusted to initial pressure P_i = P_atm and temperature slightly larger than that of the room, say T_i = 1.1T_R, using a heater and regulator. The piston is then released from rest, v_i = 0. In the second case, the piston has inertia, m > 0, and the gas is initially in both mechanical and thermal equilibrium with the surroundings so that P_i = P_atm and T_i = T_R. The piston is now given a quick inward push, v_i < 0. In both situations, the aim is the same: Describe the subsequent evolution of the system.