Ehrenfest equations
E735843
The Ehrenfest equations are relations in thermodynamics that describe how phase transition properties change with pressure and temperature, particularly for second-order phase transitions.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
equation in thermodynamics
ⓘ
phase transition relation ⓘ thermodynamic relation ⓘ |
| appliesTo |
continuous phase transitions
ⓘ
second-order phase transitions ⓘ |
| assumes |
continuity of Gibbs free energy across the phase boundary
ⓘ
continuity of first derivatives of Gibbs free energy for second-order transitions ⓘ reversible processes at the phase boundary ⓘ |
| basedOn | Gibbs free energy NERFINISHED ⓘ |
| category | thermodynamic equations of state ⓘ |
| characterizes | second-order phase transition via discontinuity of second derivatives of Gibbs free energy ⓘ |
| comparedTo | Clapeyron equation NERFINISHED ⓘ |
| describes |
behavior of phase transitions under changes of pressure and temperature
ⓘ
discontinuities in response functions at a phase transition ⓘ |
| field |
statistical mechanics
ⓘ
thermodynamics ⓘ |
| generalizes | Clapeyron equation to second-order transitions ⓘ |
| hasForm |
dT_c/dp = (V_2 - V_1)/(S_2 - S_1) for a phase transition
ⓘ
dT_c/dp = (κ_{T2} - κ_{T1})/(α_2 - α_1) T_c for a second-order transition ⓘ dT_c/dp = T_c (α_2 - α_1)/(C_{p2} - C_{p1}) for a second-order transition ⓘ |
| hasVariable |
molar entropy
ⓘ
molar volume ⓘ pressure ⓘ temperature ⓘ |
| historicalContext | introduced in early 20th century ⓘ |
| involves |
entropy
ⓘ
heat capacity at constant pressure ⓘ isothermal compressibility ⓘ pressure ⓘ thermal expansion coefficient ⓘ transition temperature ⓘ volume ⓘ |
| namedAfter | Paul Ehrenfest NERFINISHED ⓘ |
| relates |
changes in transition temperature to pressure
ⓘ
critical exponents approximately in mean-field theories ⓘ heat capacity discontinuity at a phase transition ⓘ isothermal compressibility discontinuity at a phase transition ⓘ slope of phase boundary in pressure–temperature space ⓘ thermal expansion coefficient discontinuity at a phase transition ⓘ |
| requires | equilibrium between phases ⓘ |
| usedFor | classifying phase transitions by order ⓘ |
| usedIn |
analysis of lambda transitions
ⓘ
condensed matter physics ⓘ equilibrium thermodynamics ⓘ materials science ⓘ solid-state physics ⓘ study of critical phenomena ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.