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Journal of Anhui Science and Technology University

Study of Thermodynamic Properties of an Ideal Fermi Gas in Finite Gravitational Field

Hui Liu

Published Jan 1, 2009• 0 citations
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Abstract

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.

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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 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 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 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.
Based on the semiclassical(Thomas-Fermi) approximation,the macrocanonical partition function and macrocanonical potential of a relativistic Fermi gas in a general external potential in any dimensional space are studied.The general analytical expressions of the total particle number N,total energy U and heat capacity C have been derived with thermodynamic fundamental equations,where N,U and C are expressed by the modified Bessel function.Moreover,the analytical expressions of the total energy,chemical potential and heat capacity in the high-and low-temperature approximations are given.From these results,how the characteristics of the Fermi gas depend on various factors is discussed.
Abstract Using the semi-classical (Thomas–Fermi) approximation, the thermodynamic properties of ideal Fermi gases in a harmonic potential in an n -dimensional space are studied under the generalized uncertainty principle (GUP). The mean particle number, internal energy, heat capacity and other thermodynamic variables of the Fermi system are calculated analytically. Then, analytical expressions of the mean particle number, internal energy, heat capacity, chemical potential, Fermi energy, ground state energy and amendments of the GUP are obtained at low temperatures. The influence of both the GUP and the harmonic potential on the thermodynamic properties of a copper-electron gas and other systems with higher electron densities are studied numerically at low temperatures. We find: (1) When the GUP is considered, the influence of the harmonic potential is very much larger, and the amendments produced by the GUP increase by eight to nine orders of magnitude compared to when no external potential is applied to the electron gas. (2) The larger the particle density, or the smaller the particle masses, the bigger the influence of the GUP. (3) The effect of the GUP increases with the increase in the spatial dimensions. (4) The amendments of the chemical potential, Fermi energy and ground state energy increase with an increase in temperature, while the heat capacity decreases. T F0 is the Fermi temperature of the ideal Fermi system in a harmonic potential. When the temperature is lower than a certain value (0.22 times T F0 for the copper-electron gas, and this value decreases with increasing electron density), the amendment to the internal energy is positive, however, the amendment decreases with increasing temperature. When the temperature increases to the value, the amendment is zero, and when the temperature is higher than the value, the amendment to the internal energy is negative and the absolute value of the amendment increases with increasing temperature. (5) When electron density is greater than or equal to 10 37 m −3 , the influence of the GUP becomes the dominant factor affecting the thermodynamic properties of the system.