The Effect of Vorticity on the Specific Heat Ratio of a Non-Relativistic Fermi-Dirac Gas

P. van Wyk, H. Tajima, R. Hanai +1 more

José M.B Noronha, David J Toms

Alexey Kozharin, Pavel R. Levashov

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 are explicitly 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.

Sergei I. Blinnikov

Francisco J. Sevilla, Omar Piña

Fan Zhao-Lan, Men Fu-Dian, Dou Rui-Bo +1 more

Using the methods of numerical simulation and quantum statistics, based on the thermodynamic quantities of Fermi gas trapped in a general external potential, we studied the thermodynamic properties of a relativistic Fermi gas trapped in hard-sphere potential, gave the analytical expressions of the energy and heat capacity of the relativistic Fermi system, and analyzed the influence of the relativistic effect on the energy and heat capacity. The results showed the energy and heat capacity of the relativistic Fermi system is larger than those of the nonrelativistic case. The larger the relativistic eigenvalue, the lower the change temperature of heat capacity. As the temperature rises, the larger the relativistic eigenvalue, the greater the energy.