I just realised the fallacy in my assertion that the mass fraction is a proxy for enthalpy. This is only true along an isobar within vapour dome. Since the partial derivative in question is w.r.t pressure, an evaluation along the vapour dome boundary is meaningless. Very stupid of me not to have realised this earlier.

I have to define the partial derivative at constant enthalpy, not mass fraction. When I evaluate it with a backward finite difference between the density at a point on the saturated liquid line and a point vertically below it within the vapour dome, It all works out as one would expect.

I just realised the fallacy in my assertion that the mass fraction is a proxy for enthalpy. This is only true along an isobar within vapour dome. Since the partial derivative in question is w.r.t pressure at constant enthalpy, an evaluation along the vapour dome boundary is meaningless. Very stupid of me not to have realised this earlier.

I have to define the partial derivative at constant enthalpy, not mass fraction. When I evaluate it with a backward finite difference between the density at a point on the saturated liquid line and a point vertically below it within the vapour dome on a Pressure-Enthalpy plot, It all works out as one would expect.

I just realised the fallacy in my assertion that the mass fraction is a proxy for enthalpy. I have to define the partial derivative at constant enthalpy, not mass fraction. When I evaluate it with a backward finite difference between the density at a point on the saturated liquid line and a point vertically below it within the vapour dome, It all works out as one would expect.

I just realised the fallacy in my assertion that the mass fraction is a proxy for enthalpy. This is only true along an isobar within vapour dome. Since the partial derivative in question is w.r.t pressure, an evaluation along the vapour dome boundary is meaningless. Very stupid of me not to have realised this earlier.

I have to define the partial derivative at constant enthalpy, not mass fraction. When I evaluate it with a backward finite difference between the density at a point on the saturated liquid line and a point vertically below it within the vapour dome, It all works out as one would expect.