On the Sackur-Tetrode equation in an expanding universe

TL;DR

This paper demonstrates that the Sackur-Tetrode equation for entropy remains valid in an expanding universe filled with a monoatomic ideal gas, under certain conditions, extending its applicability beyond static systems.

Contribution

It shows that key thermodynamic equations, including the Sackur-Tetrode equation, hold true in an expanding universe scenario for an ideal gas.

Findings

The energy density, entropy density, and chemical potential equations are unchanged in an expanding universe.

The Sackur-Tetrode equation remains valid in an expanding universe with proper entropy normalization.

Thermodynamic properties of an ideal gas are consistent with those in a static volume, even in an expanding cosmological setting.

Abstract

In this work we investigate the thermodynamic properties satisfied by an expanding universe filled with a monoatomic ideal gas. We show that the equations for the energy density, entropy density and chemical potential remain the same of an ideal gas confined to a constant volume V . In particular the Sackur-Tetrode equation for the entropy of the ideal gas is also valid in the case of an expanding universe, provided that the constant value that represents the current entropy of the universe is appropriately chosen.