Partial derivatives to measurables for pure fluid

Of great practical importance is the fact that the thermodynamic properties of pure substance can all be constructed from two sources: volumetric equation of state $V(T, P)$, and the heat capacity $C_P(T)$ of the substance in the ideal gas limit. Correspondingly, the partial derivatives can all be expressed in terms of isobaric thermal expansion coefficient $\alpha$, isothermal compressibility $\kappa_T$, $C_P$, and the elementary quantities. $$ C_P \equiv T \left.\frac{\partial S}{\partial T}\right|_P,\quad \kappa_T \equiv - \frac{1}{V} \left.\frac{\partial V}{\partial P}\right|_T,\quad \alpha \equiv \frac{1}{V} \left.\frac{\partial V}{\partial T}\right|_P.\quad $$ The follow code shows how this can be done, and gives explicit results for all partial derivatives. The Maxwell relations have been appliced recursively.

The heat capacity in the ideal gas state is determined by the intramolecular modes, and only depends on temperature. The temperature-dependence for standard chemicals has been fitted, and the expressions and coefficients can be found from the standard text. The volumetric properties of normal fluids at typical tempeature and pressure can most conveniently estimated using the Lee-Kesler correlation, which needs as inputs the critical temperature, critical pressure, and acentric factor for the substance of interests.