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Journal of Langfang Teachers College

The Universal Description of Arbitrary Dimensional Ideal Fermi Gas UNDER the Conditions of the Weak Degeneration of High Temperature and Glacial Non-Degeneration

Zhao Yan-ji

Published Jan 1, 2009• 0 citations
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Abstract

We offer the universal descriptions of chemistry potential,internal energy,degenerate pressure of arbitrary dimensional ideal Fermi gas which have energy spectrum of e=aps,compared with the thermodynamic quantities of the glacial arbitrary dimensional idea gases,we draw a conclusion that when temperature approaches infinite,thermodynamic quantities of the weak degenerate Fermi gases under high temperature trend to that of glacial non-degenerate ideal gases.

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We offer the universal descriptions of chemistry potential,internal energy,degenerate pressure of arbitrary dimensional ideal Fermi gas which have energy spectrum of e=aps,compared with the thermodynamic quantities of the glacial arbitrary dimensional idea gases,we draw a conclusion that when temperature approaches infinite,thermodynamic quantities of the weak degenerate Fermi gases under high temperature trend to that of glacial non-degenerate ideal gases.
we derive the quantum state density, the relation of internal energy and the pressure of arbitrary dimensional ideal gases that have energy spectrum of e = ap5 , and then offer the universal descriptions of chemistry potential, internal energy ,degenerate pressure and relative fluctuation of arbitrary dimensional ideal Fermi gases, through analysis and comparison, we draw a conclusion that when temperature approaches zero, thermodynamic quantities of high degenerate Fermi gases under low temperature trend to that of the complete degenerate Fermi gases.
Thermodynamics of ideal Fermi gas trapped in an external generic power law potential U=∑i=1dci∣xiai∣niU=\sum_{i=1} ^d c_i |\frac{x_i}{a_i}|^{n_i}U=∑i=1d​ci​∣ai​xi​​∣ni​ are investigated systematically from the grand thermodynamic potential in ddd dimensional space. These properties are explored deeply in the degenerate limit (μ>>KBTμ>> K_BTμ>>KB​T), where the thermodynamic properties are greatly dominated by Pauli exclusion principle. Pressure and energy along with the isothermal compressibilty is non zero at T=0KT=0KT=0K, denoting trapped Fermi system is quite live even at absolute zero temperature. The nonzero value of compressibilty denotes zero point pressure is not just a constant but depends on volume.
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.