Clausius-Clapeyron relation
The slope of a phase boundary in a P - T phase diagram is not arbitrary. The Clausius-Clapeyron equation connects it directly to the latent heat and the change in volume at the transition. The change in volume between the liquid and the gas, Vgas - Vliquid can be approximated by noting that the liquid is much denser than the gas if you are not too close to the critical point. We can also approximate the latent heat by a constant under the same assumption. Find an analytic approximation for the function P(T) along the liquid-gas phase boundary. Sketch your answer and compare it to a phase diagram of water that you can find on the Web.