We derived a method to evaluate the liquid-vapor equilibrium pressure, with high accuracy over a large range of temperature, using the quasi-Gaussian entropy theory. The final expression that we obtain for the equilibrium pressure as a function of the temperature can be considered as a very accurate approximate solution of the Clausius-Clapeyron equation. The method was applied to water, methanol and mercury, and was compared to two usual approximations of the Clausius-Clapeyron equation.