ClausiusClapeyronreláció

Clausius–Clapeyron relation, named after Rudolf Clausius and Benoît Paul Émile Clapeyron, is a fundamental equation in thermodynamics that describes how the vapor pressure of a liquid changes with temperature during phase transitions. It provides a link between thermodynamic properties such as enthalpy of vaporization and the pressure–temperature behavior of a substance.

The most common form, the Clapeyron equation, is written as dP/dT = ΔHvap / (T ΔV), where P is pressure, T is temperature, ΔHvap is the molar enthalpy of vaporization, and ΔV is the change in molar volume during vaporization. For many liquids, the vapor behaves approximately as an ideal gas, so ΔV ≈ Vg ≈ RT/P. Under this approximation, the equation can be integrated to yield the commonly used form ln P = -ΔHvap/(R T) + C, or P = P0 exp(-ΔHvap/(R T)). This integrated form relates vapor pressure to temperature and is widely used to estimate boiling points and vapor pressures when data are limited.

Applications of the Clausius–Clapeyron relation span chemistry, meteorology, and engineering. It helps predict how vapor pressure changes with temperature, design distillation and drying processes, and interpret phase diagrams. The relation assumes a single-component, pure substance with relatively constant ΔHvap over the temperature range and, in the ideal-gas form, neglects non-ideal gas and volume effects.

Limitations include variations in ΔHvap with temperature, significant deviations from ideal gas behavior for high pressures, and the need for phase equilibrium conditions. Despite these caveats, the Clausius–Clapeyron relation remains a core tool for understanding phase transitions.