Clausius-Clapeyron Equation

Tags: Temperature Pressure Enthalpy Vapor

Clausius-Clapeyron equation is the vapor pressure of given liquids or solids.  This allows us to estimate the pressure temperature, if the vapor pressure is known at some temperature and if the enthalpy of vaporization is known.  This equation describes the behavior of the equilibrium vapor pressure of a substance as a function of temperature.  It's particularly important in the study of phase transitions, such as the transition between liquid and vapor (boiling) or solid and vapor (sublimation).

This equation provides insight into how the vapor pressure of a substance changes as its temperature changes, based on the enthalpy of vaporization and the properties of the substance.  It's often used to estimate vapor pressures at temperatures other than the boiling point and to understand the conditions under which phase transitions occur.  It's important to note that the equation assumes ideal behavior, which might not be the case for all substances under all conditions.

 

Clausius-Clapeyron Equation
\(\large{ In \; \left(  \frac {p_2}{p_1} \right)  =  \frac {\Delta H}{R}  \; \left(  \frac {1}{T_1}  -  \frac {1}{T_2}   \right)        }\)
Symbol	English	Metric
\(\large{ \Delta H }\) = enthalpy of vaporization of the liquid	\(\large{\frac{Btu}{lbm}}\)	\(\large{\frac{kJ}{kg}}\)
\(\large{ p_1 }\) = vapor pressure at the temperature	\(\large{\frac{lbf}{in^2}}\)	\(\large{\frac{kg}{m-s^2}}\)
\(\large{ p_2 }\) = vapor pressure at the temperature	\(\large{\frac{lbf}{in^2}}\)	\(\large{\frac{kg}{m-s^2}}\)
\(\large{ R }\) = real gas constant	\(\large{\frac{lbf-ft}{lbmol-R}}\)	\(\large{\frac{J}{kmol-K}}\)
\(\large{ T_1 }\) = temperature at which the vapor pressure is known	\(R\)	\(K\)
\(\large{ T_2 }\) = temperature at which the vapor pressure is to be found	\(R\)	\(K\)