According to fundamental thermodynamic definitions and exact Maxwell relations, which of the followi — Thermodynamics and Thermochemistry Chemistry Question
Question
According to fundamental thermodynamic definitions and exact Maxwell relations, which of the following partial derivative equations correctly describe the behavior of the Gibbs Free Energy ($G$)?
💡 Solution & Explanation
The fundamental equation for Gibbs Free Energy is $dG = VdP - SdT$. (A) Holding pressure constant ($dP = 0$), we get $(\frac{\partial G}{\partial T})_P = -S$. (B) Holding temperature constant ($dT = 0$), we get $(\frac{\partial G}{\partial P})_T = V$. (C) This is the classic Gibbs-Helmholtz equation, derived by substituting $-S$ with $(\frac{\partial \Delta G}{\partial T})_P$ in the defining equation $\Delta G = \Delta H - T\Delta S$. Option D is incorrect; $-P$ is strictly the partial derivative of the Helmholtz Free Energy ($A$) with respect to volume at constant temperature.