Truly Solving the Gibbs Paradox by Local Free Space and Collision Potential

Abstract

This paper argues that the Gibbs paradox can be resolved without using the concept of identical particles in quantum mechanics. The molecules in different regions of the gas can be distinguished, so there is no need to introduce the N! factor. For each molecule, the volume of its free movement space is local at every instant. Moreover, collisions are the primary way of interaction between gas molecules and the fundamental driving force for reaching equilibrium. The potential energy during collisions cannot be ignored. Based on the local free space assumption and collision potential energy, this paper uses the canonical ensemble method to rederive the entropy increment formula for gas mixing. It includes parameters such as molecular mass, effective radius, and collision characteristic time, which vary with the type of gas molecules. This solves the problem that the entropy increment of gas mixing is independent of gas properties, that is, it truly resolves the Gibbs paradox instead of providing a new conceptual explanation.