1. The problem statement, all variables and given/known data In an earlier part of the question, I derived the temperature dependence of the latent heat of vapourisation of a liquid as dL/dT=L/T+ΔCp-L/Vvap(∂Vvap/∂T)p I am asked to find the condition that upon expanding the gas adiabatically, we get condensation to occur, by considering dp/dT and (∂p/∂T)S. 3. The attempt at a solution So I think I should consider the p-T plane here, and there will be a phase boundary between liquid and vapour, and we're currently below the boundary in the vapour region, and we want to get above the boundary somehow. We are on an adiabat so the gradient of our path has to be (∂p/∂T)S. The gradient of the phase boundary itself will be dp/dT. So I was maybe thinking (∂p/∂T)S>dp/dT so we cross the line - however this seems a bit restrictive - surely it could be less than it at some stage, then be greater than it and condensation would still occur. Even so, I don't see how to use that to get anywhere. Any clues? Thanks!