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Journal of Science of Teachers' College and University

Entropy of ideal weak degenerate Bose and Femi gas

Liu Jian-jun

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

On the basis of the computation of the grand partition function and the statistic expression of thermodynamic quantities,the internal energy,pressure and entropy of ideal weak-degenerate Bose or Femi gas are given and are consistent with present literature.

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•Aug 1, 2023•0 citations
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The paper is devoted to the theory of an ideal Bose-gas with a finite number N of particles. The exact expressions for the partition functions and occupation numbers of the model in the grand canonical, canonical, and microcanonical ensembles are found. From the calculations, it is followed that, oppositely to the accepted opinion that the chemical potential μ of an ideal Bose-gas is only negative, it can take values in the range −∞ < μ < ∞. The asymptotic expressions (in the case N ≫ 1) for the partition functions and occupation numbers for all above-mentioned thermodynamic ensembles are also evaluated.
Aim Based on the generalized Bose-Einstein distribution function in nonextensive statistical mechanics,thermodynamical quantities of the two-dimensional Bose gas such as internal energy,entropy,free energy,heat capacity,etc.,are calculated. Methods The factorization approach is incorporated,and the ensuing statistics is derived. Results/Conclusion Comparing these results with those of the conventional Bose statistics,it is found that the thermodynamical quantities are of similar forms.In the limit q→1,the thermodynamical quantities of the generalized two-dimensional Bose gas will return to the results of the Bose statistics.
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.
Abstract Chapter 11 presents a statistical mechanical treatment of the quantum ideal gases, i.e., the ideal Boltzmann, fermion, and boson gases. The discussion begins with the microscopic description and the solution of the eigenvalue problem for a quantum ideal gas. It is argued that calculating the partition function is most readily accomplished in the grand canonical ensemble using a second-quantized formulation. When the particles are distinguishable, the equation of state is identical to that of a classical ideal gas. For fermions and bosons, however, the problem of computing thermodynamic properties is significantly more complex and can only be solved exactly in certain limits. Away from these limits approximations are needed and are discussed in detail. The relevant distributions - the Fermi-Dirac and Bose-Einstein distributions are derived. The local density approximation of density functional theory is derived for the ideal electron gas. For the ideal boson gas, the phenomenon of Bose-Einstein condensation is discussed