Thermodynamics Potentials Relations

Prof. Rebecca Brannon's scheme is an excellent resource for looking up or evaluating complex thermostatic derivatives such as $(partial U/partial T)_{G,N}$, which turns out to be $alpha_P T(VB_S-S)-P(VB_V-S)/K_T$, where $alpha_P$ is the thermal expansion coefficient at constant pressure, $B_X$ is the change in pressure with respect to temperature at constant $X$ (here, entropy or volume), and $K_T$ is the isothermal bulk modulus. (All parameters are taken at constant $N$.)

Table 5-1 here gives the equivalent $(partial U/partial T)_G=mc_P-alpha TS-Palpha V-PS/K_T$ and is easier to use but gives less explanation and insight.