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Gibbs Free Energy is Minimized at constant Pressure and Temperature

The Gibbs free energy is partitioned into a potential for each chemical species \bgroup\color{blue}$ i$\egroup, \bgroup\color{blue}$ \mu_i$\egroup and the number of moles of \bgroup\color{blue}$ i$\egroup, \bgroup\color{blue}$ N_i$\egroup. Then, the Gibbs free energy, \bgroup\color{blue}$ G = \ensuremath{\sum_{i=1}^{C}} \mu_i N_i$\egroup must be a minimum. Knowing that it is a minimum means its derivative is zero--and this gives us a bunch of useful equations that apply to states of equilibrium. The fact that it is a minimum also means that its second derivative is positive definite--this implies restrictions on the properties of stable materials (such as the bulk modulus and the heat capacity must be positive).

W. Craig Carter 2002-09-05