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Journal of Shaanxi University of Technology

The thermodynamic properties of weak degenerate ideal Fermi gas in finite gravitational field

Zhao Sheng-pin

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

The study is on the thermodynamic properties of finite gravitational field weak degenerate ideal Fermi gas.Base on the Thomas-Fermi semiclassical approximation,after deriving the density of states of an ideal Fermi gas in finite gravitational field,the analytic formula of the chemical potential,internal energy and pressure under the condition of weak degeneration is obtained in this paper.The specific impact of the gravity field on the thermodynamic properties of weakly degenerate ideal Fermi gas is analyzed.The result showed that finite gravitational field has effect on the thermodynamic property of the system.

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The study is on the thermodynamic properties of finite gravitational field weak degenerate ideal Fermi gas.Base on the Thomas-Fermi semiclassical approximation,after deriving the density of states of an ideal Fermi gas in finite gravitational field,the analytic formula of the chemical potential,internal energy and pressure under the condition of weak degeneration is obtained in this paper.The specific impact of the gravity field on the thermodynamic properties of weakly degenerate ideal Fermi gas is analyzed.The result showed that finite gravitational field has effect on the thermodynamic property of the system.
The properties of an ideal Fermi gas in finite gravitational field are studied,based on the semiclassical(Thomas-Fermi) approximation.The general analytical expressions of the total energy,Fermi energy,chemical potential and heat capacity are derived.Moreover,the analytical expressions of the chemical potential and heat capacity in the high-and low-temperature approximations are given,and then,the example of electron gas is used to calculate exactly.All these results are compared with those of free Fermi gas and Fermi gas in infinite gravitational field.The effects of finite gravitational field on properties of Fermi gas are discussed.
The low-temperature properties of an idea and a weakly interacting Fermi gas in homogenous gravitational field are studied,based on the semiclassical(Thomas-Fermi) approximation and local-density approximation.The general analytical expressions of several thermodynamic quantities have been derived.The free system,idea system in homogenous gravitational field,and interacting system in homogenous gravitational field are compared.The effects of gravitational field and interparticle interactions on properties of Fermi gas are discussed.
The properties of a weakly interactlng Fermi gas in homogenous gravitational field are studied when the temperature is higher than Fermi temperature,based on the local-density approximation(LDA).The general analytical expressions of several important thermodynamic quantities are derived and the rules of distribution of particle-number density and energy density of the system are analyzed.Both of systems in homogenous gravitational field with and without internal interactlons are compared.The effects of gravitational field and inter-particle interactions on properties of Fermi gas are discussed.
Based on the semiclassical approximation,the energy spectrum of single fermion trapped in both gravitational field and strong magnetic field is given. By using Poisson's formula,the thermodynamic potential function of Fermi gas is derived. Furthermore,by using the thermodynamic relationships,the analytical expressions of the stability and magnetic susptibility of the system at low temperature are obtained. The influence mechanism of gravitational field on the thermodynamic properties of the system in the background of strong magnetic field is analysed by numerical simulation.
The properties of an ideal Fermi gas in an external potential in any dimensional space are studied, based on the semiclassical (Thomas-Fermi) approximation. The general analytical expressions of the total particle number N,N,N, density of states $D(\ensuremath{\varepsilon}),$ Fermi energy EF,{E}_{F},EF​, total energy E,E,E, and heat capacity CCC have been derived, where N,N,N, E,E,E, and CCC are expressed by the Fermi integration. Moreover, the analytical expressions of the total energy E,E,E, chemical potential \ensuremath{\mu}, and heat capacity CCC in the high- and low-temperature approximations are given. From these results, how the characteristics of the Fermi gas depend on an external potential and the dimension of space is discussed.
The analytical expressions of internal energy, chemical potential and heat capacity of the little parameter r for a weakly interacting Fermi gas in weak magnetic field are derived by using “pseudopotential" method and ensemble theory. Based on the derived expressions, the thermodynamic properties of a weakly interacting Fermi gas in weak magnetic field at both high and low temperatures are given. The effects of magnetic field and interparticle interactions on the thermodynamic properties are discussed. The difference in the effects of magnetic trap and three-dimensional harmonic trap on the properties of the system and their reasons are analyzed.