A note on integrating the Clapeyron equation without neglecting the specific fluid volume

Under certain approximations, the Clapeyron equation can be integrated to yield a simple exponential relation giving the saturation vapor pressure over a condensed phase as a function of temperature. The derivation usually assumes that the vapor behaves as an ideal gas with constant specific heat, and that the fluid also has constant specific heat. In addition, the specific fluid volume is neglected in comparison with the specific vapor volume. In this case, the Clapeyron equation is separable and readily integrable in closed form. It is shown here that this latter assumption is not required. A simple closed-form relation between saturation vapor pressure and temperature is derived which includes the condensed phase-specific volume. Two examples of the use of this result are presented.