Gibbs–Duhem equation
E517575
The Gibbs–Duhem equation is a fundamental thermodynamic relation that links changes in chemical potential, temperature, and pressure for multicomponent systems, ensuring consistency among intensive variables.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Gibbs–Duhem equation canonical | 2 |
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
physical law
ⓘ
thermodynamic equation ⓘ |
| appliesTo |
gas mixtures
ⓘ
liquid mixtures ⓘ multicomponent systems ⓘ solid solutions ⓘ |
| assumes |
extensivity of thermodynamic potentials
ⓘ
reversible changes in state variables ⓘ |
| category | equations of state and relations ⓘ |
| constrains | independent intensive variables ⓘ |
| derivedFrom |
Euler’s homogeneous function theorem
NERFINISHED
ⓘ
Gibbs free energy ⓘ |
| ensures | consistency of intensive variables ⓘ |
| expresses | dependence of chemical potentials on temperature and pressure ⓘ |
| field | thermodynamics ⓘ |
| governs | variation of chemical potentials with composition ⓘ |
| holdsFor | closed systems with variable composition ⓘ |
| implies | only two independent intensive variables for a single-component system ⓘ |
| imposes | consistency condition on activity coefficients ⓘ |
| mathematicalForm | S dT − V dP + Σ n_i dμ_i = 0 ⓘ |
| namedAfter |
Josiah Willard Gibbs
NERFINISHED
ⓘ
Pierre Duhem NERFINISHED ⓘ |
| relatedTo |
Gibbs free energy equation
NERFINISHED
ⓘ
Gibbs–Duhem integration NERFINISHED ⓘ Maxwell relations NERFINISHED ⓘ |
| relates |
chemical potential
ⓘ
pressure ⓘ temperature ⓘ |
| role | reduces number of independent chemical potentials ⓘ |
| type | differential relation ⓘ |
| usedIn |
calculation of activity coefficients
ⓘ
chemical engineering thermodynamics ⓘ derivation of Margules and other activity models ⓘ derivation of Raoult’s law consistency relations ⓘ phase equilibrium analysis ⓘ solution thermodynamics ⓘ validation of thermodynamic models ⓘ |
| usedToCheck | thermodynamic consistency of experimental data ⓘ |
| validFor | systems at thermodynamic equilibrium ⓘ |
| variable |
amount of substance n_i
ⓘ
chemical potential μ_i ⓘ entropy S ⓘ pressure P ⓘ temperature T ⓘ volume V ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.