Clausius–Clapeyron relation

The Clausius–Clapeyron relation connects the slope of a phase boundary in pressure–temperature space to the entropy and volume changes between phases.

Clapeyron equation: The exact relation between a phase boundary’s pressure–temperature slope and the entropy and volume changes across it. It gives the general slope relation from which the Clausius–Clapeyron form follows.
Antoine equation: An empirical equation that approximates a substance’s vapor pressure as a function of temperature. It offers a fitted vapor-pressure curve where the Clausius–Clapeyron approximation is insufficient.
Phase equilibrium: A state in which distinct phases coexist without net transfer of matter between them. The relation applies along conditions where two phases remain in equilibrium.
Clausius–Clapeyron equation: An integrated approximation relating saturation pressure to temperature for vaporization or sublimation. It is often called the same name, but assumes negligible condensed-phase volume and ideal vapor behavior.
Chemical potential: A thermodynamic potential that measures how a system’s free energy changes when particles are added. Equality of chemical potentials in coexisting phases underlies the phase-boundary slope.
Boiling point: The temperature at which a liquid’s vapor pressure equals the surrounding pressure. The relation estimates how boiling temperature shifts when external pressure changes.
Entropy: A thermodynamic state function measuring energy dispersal and the number of accessible microscopic arrangements. The entropy difference between phases sets the thermal part of the boundary slope.
Phase diagram: A chart showing which phases are stable under specified thermodynamic conditions. A phase diagram displays the curves whose local slopes the relation constrains.
Latent heat: Energy absorbed or released during a phase transition without a temperature change. For a first-order transition, latent heat supplies the entropy change in the relation.
Sublimation: A phase transition in which a solid becomes a gas without passing through a liquid state. The relation describes the pressure–temperature slope along a solid–vapor boundary.

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