On the sign of the chemical potential in the statistical mechanics of ideal boson and fermion gases

Abstract

The chemical potential is one of those concepts in thermodynamics that physics students still find difficult to grasp. An indication of this is the steady stream of papers dealing with different aspects of the phenomenon that appear at regular intervals, particularly in those journals dedicated to the teaching of physics. At undergraduate level, the chemical potential is encountered primarily in (i) the area of statistical thermodynamics where it plays an important role in Bose–Einstein condensation and in the quantum theory of electrical conduction in metals, and (ii) the study of phase equilibria involving the transfer of particles. In the present communication we address an issue that can still present difficulties, namely the sign of the value of the potential as it appears in the statistical thermodynamics of boson and Fermi gases. Our aim is to show the physical reasoning underlying this sign as it varies with changing conditions.