Gibbs free energy
G = U − TS + PV, whose decrease decides whether a process runs spontaneously at constant temperature and pressure.
Definition
The Gibbs free energy G = U − TS + PV = H − TS combines the enthalpy and entropy bookkeeping into the single potential appropriate to processes at constant temperature and pressure — the conditions of almost all laboratory chemistry and biology. A process is spontaneous if and only if it lowers G: ΔG = ΔH − TΔS < 0. Equilibrium is the state of minimum G.
The criterion is a contest between energy and entropy refereed by temperature. A reaction proceeds if it releases energy (ΔH < 0) or increases disorder (ΔS > 0); when the two conflict, temperature decides, with the crossover at T = ΔH/ΔS. Ice melts above 0 °C because there the entropy gain finally outweighs the energy cost of breaking the crystal.
G is the Legendre transform of the internal energy in both volume and entropy, with natural variables temperature and pressure: dG = −S dT + V dP. Its derivative with respect to particle number is the chemical potential, making G the foundation of chemical thermodynamics and phase equilibrium.
History
Introduced by J. Willard Gibbs in his monumental 1875–1878 memoir On the Equilibrium of Heterogeneous Substances, which founded chemical thermodynamics and introduced the chemical potential and the phase rule.