Gibbs free energy where T, V, and P change simultaneously

So $\Delta G = \Delta H - T\Delta S - S\Delta T$.


Is there a way to express $\Delta G$ for a process where T, V, and P change simultaneously only in terms of the initial and final T, V, P? Assume this process is for an ideal gas.


Since $G$ is a state function I can calculate it separately for an isothermal process and an isochoric process, but in that case $\Delta G$ for the isochoric process has dependence on the entropy of one of the states.




Your original equation is incorrect. It should read $\Delta G=\Delta H -\Delta (TS)$, and $\Delta (TS)\neq T\Delta S+S\Delta T$ unless the changes are infinitesimal. 


That said, for an ideal gas, irrespective of path, $$\Delta S=S\_f-S\_i=C\_p\ln{(T\_f/T\_i)}-R\ln{(P\_f/P\_i)}=C\_v\ln{(T\_f/T\_i)}+R\ln{(V\_f/V\_i)}$$and$$\Delta H=C\_p(T\_f-T\_i)$$So, $$\Delta G=G\_f-G\_i=C\_p\Delta T-\frac{(T\_f+T\_i)}{2}\Delta S-\frac{(S\_f+S\_i)}{2}\Delta T$$Clearly the 3rd term on the rhs depends on either $S\_i$, $S\_f$, or both, so $\Delta G$ depends on these. It then all comes down to how you assign your reference state values for G, H, and S, such that $G\_{ref}=H\_{ref}-T\_{ref}S\_{ref}$.


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