Variable-latent-heat saturation curve ($\ln (p/p_{\ast })={\int }_{T_{\ast }}^{T}L(\theta )/(R{\theta }^2)d\theta$)

For a dilute ideal gas vapor whose specific volume greatly exceeds that of its condensate, the Clausius-Clapeyron relation integrates to the displayed formula. If $L(T)=L_{\ast }(T_c-T)/(T_c-T_{\ast })$, the result is $\ln (p/p_{\ast })=L_{\ast }[T_c(1/T_{\ast }-1/T)-\ln (T/T_{\ast })]/[R(T_c-T_{\ast })]$. Near the liquid-gas critical point, both the ideal gas approximation and the neglect of condensed-phase volume fail; zero latent heat alone does not determine the limiting coexistence slope.