The molar Gibbs energy for a monatomic ideal gas is given by $\bar{G} = -T \ln(\frac{T^{5/2}}{P})$, where numerical constants have been omitted so that only the functional dependence on the natural variable of $\bar{G}$, that is $T$ and $P$, is shown. Derive corresponding equations for $\bar{S}$, $\bar{H}$, $\bar{V}$, $\bar{U}$, and $\bar{A}$.
