The logical foundations of Gibbs' paradox in classical thermodynamics

TL;DR

This paper examines the classical thermodynamics reasoning behind Gibbs' paradox, identifying the preconditions that lead to the paradox and clarifying its relation to assumptions about gas parameters.

Contribution

It clarifies the features of the derivation of entropy of mixing that cause Gibbs' paradox and shows it is not related to the discreteness of gas parameters.

Findings

Identified the preconditions leading to Gibbs' paradox

Showed the paradox is not linked to discrete differences in gas parameters

Clarified the thermodynamic basis of the paradox

Abstract

The analysis of the arguments within the limits of the classical thermodynamics that lead to the Gibbs paradox was made. Features of preconditions used in the derivation of the entropy of mixing of ideal gases that caused the appearance of paradox were established. It was shown that the Gibbs paradox has not connection with the assumption of discrete differences between the parameters of different gases.