Dynamics of a diathermal versus an adiabatic piston in an ideal gas: Langevin's and phase-space approaches

We present a comparison between the random motion of an adiabatic and a diathermal piston sliding in a perfect gas. In particular, their dynamical behaviour, if investigated by means of Langevin’s approach, shows the amplitude of the adiabatic-piston random displacements around the equilibrium position to be much larger (by a factor (M/m)^(1/2), where M and m are the piston mass and the mass of the single gas molecule) than that of the diathermal piston. The origin of this intriguing difference, which is accounted for in the frame of Langevin’s approach, is also explored in terms of a space-phase analysis.