Advanced Topic 396 of 1102 Thermodynamics & Energetics
Clapeyron Equation
Gives the slope of a phase boundary in terms of enthalpy and volume change.
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In-depth explanation of Clapeyron Equation
The Clapeyron equation gives the slope of a phase boundary on a pressure-temperature diagram as dP/dT equals delta H divided by T times delta V, where delta H is the enthalpy of transition and delta V is the volume change. It follows from the requirement that the chemical potentials of the two phases remain equal along the boundary. For vaporization, where the gas occupies a much larger volume, the approximation delta V close to RT/P leads to the Clausius-Clapeyron equation. The slope depends on the sign of delta V, and for water melting delta V is negative because liquid water is denser than ice. This makes the melting curve slope negative, so applying pressure to ice slightly lowers its melting point.
Going deeper: Clapeyron Equation
Key ideas: Slope of the boundary is delta H over T delta V. Positive for most melting curves, negative for water, since ice is less dense. Combine with the ideal gas law for vaporization to get d ln P over dT equals delta H vap over R T squared.
Common mistakes and connections: Using inconsistent units for delta V and delta H gives errors, so keep J and m cubed. The slope for water explains why ice skates may glide, although the main reason is friction heating. It leads to the Clausius-Clapeyron equation for vapor pressure.
Visualization of Clapeyron Equation
The slope dP/dT of each phase boundary equals delta H / (T delta V): steep for solid-liquid lines, gentle for liquid-gas lines. CO2 is shown. The interactive lesson shows this as a live animation or chart.
Worked example and use case
Increasing pressure lowers the melting point of ice by about 0.0074 K per atmosphere.
Frequently asked questions about Clapeyron Equation
What is Clapeyron Equation?
Gives the slope of a phase boundary in terms of enthalpy and volume change.
Is Clapeyron Equation a beginner, intermediate or advanced topic?
Clapeyron Equation is a advanced topic in Thermodynamics & Energetics. It builds on beginner and intermediate topics, so review those first if needed.
What should I learn before Clapeyron Equation?
Study these earlier topics in Thermodynamics & Energetics first: Chemical Potential, Fugacity and Activity, Gibbs Phase Rule.
What comes after Clapeyron Equation?
The next topics in Thermodynamics & Energetics are Thermodynamic vs Kinetic Control and Fuel Calorific Value.
Can I practise Clapeyron Equation with quizzes?
Yes. The interactive lesson includes a self-check question on Clapeyron Equation, and the Thermodynamics & Energetics quiz draws on every topic in this area.
Where Clapeyron Equation fits in Thermodynamics & Energetics
Clapeyron Equation is topic 68 of 91 in Thermodynamics & Energetics.