Gibbs free energy

Remarks

From $dU = T \, dS - p \, dV$ one gets $dG = -S \, dT + V \, dp$. So the natural variables of $G$ are $T$ and $p$, and $S = -(\partial G / \partial T)_p$, $V = (\partial G / \partial p)_T$. When the amounts $N_i$ of substances may change, $dG = -S \, dT + V \, dp + \sum_i \mu_i \, dN_i$, where $\mu_i$ is the chemical potential of substance $i$. Example: for a reaction at $T = 300$ K with $\Delta H = -10$ kJ and $\Delta S = -20$ J/K, one finds $\Delta G = -10\,000 + 300 \cdot 20 = -4\,000$ J, so the reaction can run by itself at fixed $T$ and $p$. Non-example: $H - TV$ is not the Gibbs free energy, since $T$ must multiply its conjugate variable $S$.