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The London Edinburgh and Dublin Philosophical Magazine and Journal of Science

XIV. The condensation of a perfect Bose-Einstein gas.—I

A. R. Fraser

Published Feb 1, 1951• 11 citations
Publisher

Abstract

Abstbact Schubert (1946) and others have drawn attention to the fact that the standard derivations of the formulae for the behaviour of a perfect Bose-Einstein gas are invalid in the region where condensation should occur. In this paper a new and rigorous derivation is given of formulae for the macroscopic behaviour of such a gas.
DOI
10.1080/14786445108560983

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In a recent letter to Nature F. London(3) has called attention to a discontinuity in the derivative dCV/dT of the specific heat with respect to temperature which arises in a perfect Einstein-Bose gas at low temperatures. When discussing the properties of a perfect gas satisfying the Bose statistics, Einstein(1) remarked that at low temperatures something resembling a condensed phase should appear. The temperature at which this condensation should begin is given by the equation where n is the number of particles of mass m per unit volume and the other symbols have their usual significance.
Abstract The theory of quantum-mechanical grand canonical ensembles is used to derive for the case of a perfect Bose-Einstein gas the average number of particles in the different energy levels, the fluctuations in these numbers and the equation of state. The Einstein condensation phenomenon is then discussed, and it is shown that in a p-v diagram (v being the specific volume) the isotherm consists of two analytically different parts in the limit where the number of particles in the system, JV, goes to infinity. It is also shown that for finite N at the critical volume ∂np/∂vn is of the order N1/3(n-2) in accordance with a result obtained by Wergeland & Hove-Storhoug.