The thermodynamic equilibrium of gas in a box divided by a piston

TL;DR

This paper revises the conditions for thermodynamic equilibrium in a gas-piston system, clarifying how energy and entropy principles determine pressure and internal energy consistency.

Contribution

It explicitly resolves the apparent indeterminacy in the equilibrium conditions by applying the entropy maximum principle with a constant internal energy constraint.

Findings

Pressures are equalized through spontaneous piston movement.

The entropy maximum principle determines equilibrium conditions.

The energy minimum principle is also analyzed in this context.

Abstract

The equilibrium conditions of a system consisting of a box with gas divided by a piston are revised. The apparent indetermination of the problem is solved by explicitly imposing the constancy of the internal energy when the Entropy Maximum Principle is applied. The equality of the pressures is naturally concluded from this principle when the piston is allowed to spontaneously move. The application of the Energy Minimum Principle is also revised.