Thermodynamics of quantum gases for the entire range of temperature

TL;DR

This paper analytically investigates the thermodynamics of free Bose and Fermi gases across all temperature ranges, including trapped cases, providing approximate chemical potentials that bridge classical and quantum regimes.

Contribution

It introduces closed-form approximate chemical potentials for quantum gases valid over the entire temperature spectrum, enhancing understanding of intermediate thermodynamic behavior.

Findings

Derived approximate chemical potentials valid at all temperatures.

Extended thermodynamic analysis to harmonically trapped gases.

Bridged classical and quantum thermodynamic regimes.

Abstract

We have analytically explored thermodynamics of free Bose and Fermi gases for the entire range of temperature, and have extended the same for harmonically trapped cases. We have obtained approximate chemical potentials of the quantum gases in closed forms of temperature so that the thermodynamic properties of the quantum gases become plausible specially in the intermediate regime between the classical and quantum limits.