In this article, we consider the specific heat of an ideal gas composed of monatomic molecules in the view point of the new quantum theory. Thereby we can clarify a new meaning of specific heat of an ideal gas.
It is shown that in two dimensions the specific heat CV(T,N) for an ideal gas of Fermi particles is identical with that for an ideal Bose gas for all T and N. This is true despite the great difference in the distribution functions of the two systems at low temperatures. To shed further light on this identity, the quantum statistics of ideal gases are investigated treating the number of dimensions as a continuous variable: n=2 is seen to be a special case. In the extreme relativistic region, the analogous special case is n=1.
The condensation temperature and the specific-heat anomaly of an ideal relativistic Bose gas are discussed. For a high concentration of bosons with small rest mass there is a marked departure from the normal nonrelativistic theory. The heat capacity Cv remains continuous at the condensation temperature unless the rest mass vanishes.