Ideal gas: Energy

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

$E=-T^{2}\left.{\frac {\partial (A/T)}{\partial T}}\right\vert _{V,N}=kT^{2}\left.{\frac {\partial \ln Q}{\partial T}}\right\vert _{V,N}=NkT^{2}{\frac {d\ln T^{3/2}}{dT}}={\frac {3}{2}}NkT$

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)