Two ways of interpolating F(V) to F(P)

[singularitti]

For any function F(V), want to change the variable from V to P, you can either:

1. Interpolate F(V) to a finer grid, use an EOS to find the inversed volumes of pressures, evaluate F on these volumes;
2. Use an EOS to calculate the pressures corresponding to the input volumes, interpolate F(P), and find the properties on output volumes.
   I used to think of the first way, but the second way was what we used in qha (except the fact that we used P from finite difference of E). The first way require we know the inverse function V(P), which, for most EOSs, are not known. So we are going to use the 2nd way.