Find expressions as function of temperature in the region < E for the energy, heat capacity, and entropy of a gas of N non

Find expressions as function of temperature in the region τ < τE for the energy, heat capacity, and entropy of a gas of N non interacting bosons of spin zero confined to a volume V. Put the definite integral in dimensionless form; it need not be evaluated. The calculated heat capacity above and below τε is shown in figure. The experimental curve was shown in figure. The difference between the two curves is market: It is ascribed to the effect of interactions between the atoms.