Ideal gas: Energy

The energy of the ideal gas is given by (Hill Eq. 4-16)

$E=-T^2{\frac{\partial (A/T)}{\partial T}|}_{V,N}=k{T}^2{\frac{\partial \ln Q}{\partial T}|}_{V,N}=Nk{T}^2\frac{d\ln T^{3/2}}{dT}=\frac{3}{2}NkT$

This energy is all kinetic energy, $1/2.kT$ per degree of freedom. This is because there are no intermolecular forces, thus no potential energy.

References

1. Terrell L. Hill "An Introduction to Statistical Thermodynamics" 2nd Ed. Dover (1962)