$\begin{array}{l}\displaystyle G(p,T)= H-TS =U+pV-TS\end{array}$

where:

$\begin{array}{l}p\end{array}$	pressure	$\begin{array}{l}U\end{array}$	internal energy
$\begin{array}{l}V\end{array}$	volume	$\begin{array}{l}S\end{array}$	entropy
$\begin{array}{l}T\end{array}$	temperature	$\begin{array}{l}H\end{array}$	enthalpy

The expression for the infinitesimal reversible change in the Gibbs free energy $\begin{array}{l}G\end{array}$ as a function of its "natural variables" p and T, for an open system, subjected to the operation of external forces (for instance, electrical or magnetic) X_i, which cause the external parameters of the system a_i to change by an amount da_i, can be derived as follows from the first law for reversible processes:

(1)	$\begin{array}{l}\displaystyle {\displaystyle \mathrm {d} G=V\,\mathrm {d} p-S\,\mathrm {d} T+\sum _{i=1}^{k}\mu _{i}\,\mathrm {d} N_{i}-\sum _{i=1}^{n}X_{i}\,\mathrm {d} a_{i}+\cdots }\end{array}$

where

μ_i	chemical potential of the i-th mixture component
N_i	number of particles (or number of moles) composing the i-th mixture component

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See also