Home / Topics / Heat & Thermodynamics
Clausius–Clapeyron equation
Advanced
Slope of the phase boundary.
dP/dT = L/TΔvThe slope of the coexistence curve dP/dT = L/(TΔv) relates latent heat to boiling-point changes. Higher altitudes lower the boiling point.
Water boils at 90 °C at 3000 m.
For ice, Δv is negative so the slope is negative.
In more detail
The Clausius-Clapeyron equation describes the slope of the boundary between two phases, relating pressure and temperature to latent heat. It explains how boiling point depends on pressure.
Real-world uses
- Pressure cookers raise the boiling point of water by increasing pressure.
- Weather models use it to relate vapour pressure to temperature.
- Engineers use the Clausius–Clapeyron equation to predict how the boiling point of water changes with pressure in a pressure cooker.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
Why does water boil at lower temperature on mountains?
Because atmospheric pressure is lower, so the vapour pressure reaches it at a lower temperature.
Does it apply to melting too?
Yes, the same equation describes the solid-liquid boundary.
Why does water boil at a lower temperature on a mountain?
The lower atmospheric pressure reduces the boiling point, because the vapour pressure needs to reach a smaller value to boil.
Related topics in Heat & Thermodynamics
Free energy · Third law · Maxwell relations · Joule–Thomson effect · Heat death of the universe · Arrow of time