Clausis Clapeyron Equation:

The Clausius Clapeyron relation, named after Rudolf Clausius and Benoit Paul Emile Clapeyron, who defined it sometime after 1834, is a way of characterizing a discontinuous phase transition between two phases of matter. On a pressure temperature (P -T) diagram, the line separating the two phases is known as the coexistence curve. The Clausius Clapeyron relation gives the slope of this curve. Mathematically,

dP/dT = L / T Δ V

where dP/dT is the slope of the coexistence curve, L is the latent heat, T is the temperature,

V is the volume change of the phase transition.

Applications

Chemistry and Chemical Engineering

The Clausius Clapeyron equation for the liquid vapor boundary may be used in either of two equivalent forms.

where

T1 and P1 are a corresponding temperature (in kelvins or other absolute temperature units) and vapor pressure

T2 and P2 are the corresponding temperature and pressure at another point

Δ Hvap is the molar enthalpy of vaporization

R is the gas constant (8.314 J mol -1K-1)

This can be used to predict the temperature at a certain pressure, given the temperature at another pressure, or vice versa. Alternatively, if the corresponding temperature and pressure is known at two points, the enthalpy of vaporization can be determined.

The equivalent formulation, in which the values associated with one P,T point are combined into a constant (the constant of integration as above), is

For instance, if the p,T values are known for a series of data points along the phase boundary, then the enthalpy of vaporization may be determined from a plot of lnP against 1 / T.

Notes:

As in the derivation above, the enthalpy of vaporization is assumed to be constant over the pressure/temperature range considered

Equivalent expressions for the solid vapor boundary are found by replacing the molar enthalpy of vaporization by the molar enthalpy of sublimation, Δ Hsub