Summary of thermodynamic potentials#
Potential |
Symbol |
Natural Variables |
Equation |
Total derivative |
Behavior at Equilibrium |
|---|---|---|---|---|---|
Energy |
\(\underline{U}\) |
\(N, \underline{V}, \underline{S}\) |
\(\underline{U} = T\underline{S} - P\underline{V} + \sum_i^n \mu_i N_i\) |
\(d\underline{U} = Td\underline{S} - P d\underline{V} + \sum_i^n \mu_i dN_i\) |
Minimized |
Entropy |
\(\underline{S}\) |
\(N, \underline{V}, \underline{U}\) |
\(\underline{S} = \frac{1}{T}\underline{U} + \frac{P}{T}\underline{V} - \sum_i^n \frac{\mu_i}{T} N_i\) |
\(d\underline{S} = \frac{1}{T}d\underline{U} + \frac{P}{T}d\underline{V} - \sum_i^n \frac{\mu_i}{T} dN_i\) |
Maximized |
Enthalpy |
\(\underline{H}\) |
\(N, P, \underline{S}\) |
\(\underline{H} = \underline{U} + P\underline{V}\) |
\(d\underline{H} = Td\underline{S} + \underline{V}dP + \sum_i^n \mu_i dN_i\) |
Minimized |
Helmholtz FE |
\(\underline{F}\) |
\(N, \underline{V}, T\) |
\(\underline{F} = \underline{U} - T\underline{S}\) |
\(d\underline{F} = -\underline{S}dT - Pd\underline{V} + \sum_i^n \mu_i dN_i\) |
Minimized |
Gibbs FE |
\(\underline{G}\) |
\(N, P, T\) |
\(\underline{G} = \underline{U} - T\underline{S} + P\underline{V}\) |
\(d\underline{G} = -\underline{S}dT + \underline{V}dP + \sum_i^n \mu_i dN_i\) |
Minimized |