Clausius–Clapeyron relation
The Clausius -Clapeyron equation was developed in 1834 by Émile Clapeyron and Rudolf Clausius derived later from the theories of thermodynamics. It is a special form of the Clapeyron equation ( derivation there). About the Clausius -Clapeyron equation, the course of the boiling point curve calculated, ie of the phase boundary line of the phase diagram between the liquid and the gaseous phase of the substance.
Thermodynamically correct equation
The thermodynamically correct version of the equation
With
- - Vapor pressure
- - Temperature in K
- - Molar enthalpy of vaporization ( index for evaporation or vapor English = vapor) and
- - Change of the molar volume between gaseous and liquid phase.
Approximation in the case of an ideal gas
As a rule, is called the Clausius- Clapeyron equation, the approximate equation valid
With
- - Universal gas constant.
Derivation: Since the majority of uses, the molar volume of the gas is much greater than that of the liquid:
The difference in volume was expressed by the molar volume of the gas in relation to the correct thermodynamic equation:
Also an ideal gas was adopted for the gas phase, the following condition applies to the equation:
Integrated form
Considering the enthalpy of vaporization of a substance to be constant over a small temperature range (up ), the Clausius- Clapeyron equation over this temperature range can be integrated. Then:
With
- The well-known saturation vapor pressure and the temperature of the initial state,
- The pressure and the temperature of the calculated state.