It would be very difficult to obtain this reply from usual chemical thermodynamics literature. I believe
As said the usual physical chemistry literature is very outdated
Some physicists textbook are also, but this is more strange. Geodeome, what is the textbook?
There is an emphasis on chemical literature on the equations of state. The equation of state is not fundamental. Please forgot many of theoretical chemical literature
There are three levels of information in macroscopic thermal canonical science.
- The first level: fundamental level. The fundamental equation for potentials, especially for entropy S, is the basic equation. All thermodynamic information is contained therein
. In fact, the ratios for any process (equilibrium is also a process because velocity zero is also a velocity) are guided by first order differentials of entropy in the macroscopic limit.
- Second level: Formed by thermal and caloric equations of state. The fact of that are not fundamental is easily see since there is no procedure for obtaining the fundamental equation from them (this indicated less information about the system). You have just the thermal equation of state.
- Third level is composed by many coefficients: compresion, etc. and expressions for Cv and Cp. The information is still lower.
You need the first level or the second more additional expressions.
In the first level one can see that the thermodynamic potential U is
U = U(ideal) + INT
(part (p/T) / part T ) ) dVINT
signifies integration between infinite and V. The partial is for constant V.
If you prefer to use the expresion for Cv (it arises directly from above U. The inverse is not possible).
Cv = Cv(ideal) + INT
( T (part2
p / part T2
) ) dV.
After use the relation between Cv and Cp.
Structure of equation for Cv shows that for any
gas with p = f(T) with f a linear expresion Cv = Cv(ideal).
ThereforeCv for a Van der Waals gas does not depend of temperature
This is not so strange. Cv is the change in kinetic energy per unit change in temperature. since that "VDW molecules" interact only with energy that depend on density (N/V), the value of Cv is unaffected by intermolecular forces in the VDW model.