On a slow drift of a massive piston in an ideal gas that remains at mechanical equilibrium

TL;DR

This paper rigorously analyzes the slow drift of a massive piston in an ideal gas at mechanical equilibrium, revealing how temperature differences induce a gradual piston movement and heat transfer, supported by mathematical proofs.

Contribution

It provides the first rigorous mathematical proof of the slow piston drift phenomenon under specific distribution conditions, advancing theoretical understanding.

Findings

Proves the existence of slow piston drift due to temperature differences.

Shows heat transfer occurs across the piston in equilibrium conditions.

Establishes mathematical conditions for the phenomenon's occurrence.

Abstract

We consider a heavy piston in an infinite cylinder surrounded by ideal gases on both sides. The piston moves under elastic collisions with gas atoms. We assume here that the gases always exert equal pressures on the piston, hence the piston remains at the so called mechanical equilibrium. However, the temperatures and densities of the gases may differ across the piston. In that case some earlier studies by Gruber, Piasecki and others reveal a very slow motion (drift) of the piston in the direction of the hotter gas. At the same time the hotter gas slowly transfers its energy (heat) across the piston to the cooler gas. While the previous studies of this interesting phenomenon were only heuristic or experimental, we provide first rigorous proofs assuming that the velocity distribution of the ideal gas satisfies a certain ``cutoff'' condition.