How is Gibbs free energy for a reaction different from that in a process? Is it because a reaction generally occurs at a constant temperature and pressure, and so dG = dH - TdS, while for a process temperature may or may not be fixed for a process, say expansion of a gas, and so dG = dH - TdS - SdT? Also, how do we define H at non-constant pressure? Is it dH = dU + d(PV)?
Also, why do we say that The G at any point is the max non-mechanical work that can be drawn out? Why does this not include mechanical work too?