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arXiv:astro-ph/9802279

The equation of state of a degenerate Fermi gas

Vladan Čelebonović

Published Feb 21, 1998• 0 citations
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Abstract

An analytical expression for Fermi-Dirac integrals of arbitrary order is presented,and its applicability in obtaining the EOS of a degenerate,non-relativistic,Fermi gas is discussed.
DOI
10.48550/arxiv.astro-ph/9802279

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For an ideal statistical gas, where PV=sEPV=sEPV=sE, all thermodynamic functions can be derived from G(V,T)G(V,T)G(V,T), i.e., A(V,T)A(V,T)A(V,T) is given by a suitable integration over G(V,T)G(V,T)G(V,T). Since $G={N}_{\ensuremath{\mu}}$, the normalization constant, $\ensuremath{\mu}(V,T)$, of the distribution function is sufficient to provide a complete thermodynamic description of such a system. With the aid of the $\ensuremath{\aleph}$-theorem it is shown that there is a sharp physical distinction between the degenerate and non-degenerate Bose-Einstein gases; to any given density there corresponds a transition temperature between them. The method developed is applied to the general (relativistic and non-relativistic) non-degenerate quantum and degenerate Fermi-Dirac gases.