Thermodynamic Coefficients of Ideal Fermi-gas

TL;DR

This paper provides analytical formulas for derivatives of the Helmholtz free energy of ideal Fermi-gas, enabling accurate computation of thermodynamic properties and corrections in various regimes.

Contribution

It introduces new analytical expressions for derivatives of the Helmholtz free energy of ideal Fermi-gas and provides a Python module for practical computations.

Findings

Correct asymptotic behaviors for Boltzmann and low-temperature Fermi-gas

Accurate numerical computations of thermodynamic properties

Derivation of thermodynamic function corrections

Abstract

We present analytical formulae for the first and second derivatives of the Helmholtz free energy of non-relativistic ideal Fermi-gas. Important thermodynamic quantities such as heat capacity, sound velocity, heat capacity ratio and others can be easily expressed through the derivatives. We demonstrate correct ideal Boltzmann gas and low--temperature Fermi-gas asymptotes and derive corrections to thermodynamic functions for these limiting cases. Numerical computations of thermodynamic properties of ideal Fermi-gas can be accurately performed using the developed freely available Python module ifg.