Unified Treatment of Ideal Fermi, Bose, and Classical Gases
We give a unified treatment of ideal Fermi, Bose, and classical gases for temperatures sufficiently large that energy levels can be treated as a quasi-continuous. Sums can be converted to integrals over a density of quantum states to evaluate thermodynamic functions. Pressure is equal to two-thirds of the energy density for all three gases. Relevant integrals can be represented by series expansions if the absolute activity is less than unity, which is always the case for bosons. For fermions, larger values of the absolute activity can be handled by an asymptotic expansion. Virial expansions for the pressure of these ideal gases are power series in the ratio of the actual concentration to the quantum concentration. For absolute activity less than unity, the deviation from ideal gas behavior is practically linear in that ratio, less pressure for bosons, and more for fermions. Formulae for the heat capacity of these gases at constant volume are calculated in terms of several integrals.