Answer to Question #295567 in Molecular Physics | Thermodynamics for Amit

Question

Explain the difference between claperyon equation and Clausius claperyon equation

Answer 1

The equation $\ln \left( \dfrac{P_1}{P_2} \right) = \dfrac{\Delta H_{vap}}{R} \left( \dfrac{1}{T_2}- \dfrac{1}{T_1} \right)$ is known as the Clausius-Clapeyron equation and allows us to estimate the vapor pressure at another temperature, if the vapor pressure is known at some temperature, and if the enthalpy of vaporization is known. The equation can be also applied to the sublimation process.

On the other hand, for the solid to liquid transition, we need to use the Clapeyron equation

$\dfrac{dP}{dT} = \dfrac{\Delta \bar{H}}{T \Delta \bar{V}}$

where $\Delta \bar{H}$ and $\Delta \bar{V}$ is the molar change in enthalpy (the enthalpy of fusion in this case) and volume respectively between the two phases in the transition.

The difference relies on the molar volume: typically for the gas phase this value is bigger than for the liquid and solid phases and this is the reason why the transition solid-liquid is only studied with the Clapeyron equation.