While the Clapeyron equation (eq. ( )) is rigorously correct, we next make a series of assumptions that will ultimately lead to the Clausius/Clapeyron equation commonly introduced in the undergraduate curriculum. This is motivated by fig. , wherein a plot of ln P sat versus 1/T appears linear from the triple point to the critical point , considering the case of water as an example . We note that all of the figures included in this manuscript were prepared with MATLAB code available in the supporting information accompanying the electronic version of this manuscript. While in this manuscript we only consider the case of water and hexane as examples, additional systems are provided as an example in the supporting information. On the right hand side, first we consider ∆Z vap . At low temperatures well removed from the critical point, it can be assumed the vapor phase is an ideal gas. For this case we take: