For a comprehensive EOS like van der Waals equation, \left(\frac{\partial P}{\partial T}\right)_V is a constant. That's the benefit as choosing vdw eqn as vdw constants seem to be 'fixed' constants not changing with the change of P, V and T.
However if we treat other gases described by Virial...
I'm little confused about what transformation should I do to correctly calculate the entropy change if an analytical EOS (e.g. van der Waals equation, cubic equation, Virial equation, etc.) is available? Do you mean Maxwell's relationship fail while facing a real gas?
Since EOS is expressed in terms of P, V and T (but not U, G, H, A or S), therefore changing it to the differential of S or other non-mesurable variables is not possible for calculation. Besides, what I'm doing is exactly taking the advange of Maxwell relationships to transform dS into mesurable...
To I like Serena,
The equation is derived with the only assumption: reversible process.
As equation of state connects P, V and T like f(P,V,T)=0, the thermodynamical property such as entropy can be expressed (derived) in terms of any two of them.
Now choose T and V, hence S=S(T,V).
The...
For a real gas (non-ideal gas) in a reversible process, the way to calculate \Delta{S} should also be independent to path simply because entropy is a state function.
However, I got strange solution while taking different path.
Here is the condition:
1. Equation of state (EOS) for the real gas...