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

TL;DR

This paper compares the stochastic dynamics of adiabatic and diathermal pistons in an ideal gas using Langevin and phase-space methods, revealing significant differences in their fluctuation amplitudes.

Contribution

It provides a detailed analysis of the dynamical differences between adiabatic and diathermal pistons using Langevin and phase-space approaches, highlighting the impact of thermal properties.

Findings

Adiabatic piston exhibits larger random displacements than diathermal piston.

The amplitude difference scales with (M/m)^(1/2), where M is piston mass and m is gas molecule mass.

Langevin and phase-space analyses explain the origin of these differences.

Abstract

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.