Thermodynamics of a single component systems

In his Ph.D. thesis of 1873, van der Waals proposed the first EoS. The relation is frequently written in terms of reduced variables, indicating expected observance of the corresponding states principle  

16 also introduced the free volume concept — note that as T — 0, V — b. Van der Waals considered that molecules move in cells made by the surrounding molecules with a uniform potential. The volume within which the center of a molecule can freely move, is what defines the free volume. Thus, one may distinguish  

Detailed methods of computation of the van der Waals excluded volume (for any chemical structure) have been developed [Bondi, 1964 van Krevelen, 1976]. Thermodynamically, the free volume is expressed in terms of the entropy of vaporization  

Over the years, many versions of the EoS theories have been proposed. Several comprehensive reviews of the EoS s used in the polymer thermodynamics have been published. For example, Curro [1974] discussed applications of EoS within a full range of materials and variables, viz. to crystals, glasses, molten polymers and monoatomic liquids. The review discusses fundamentals of the theories as well as it provides a list of available experimental data. The comparison between different EoS was made on two levels, first by comparing the derived expressions for physical quantities (e.g., the characteristic reducing parameters, cohesive energy density, or internal pressure), then comparing how well the EoS describes the observed PVT dependencies for polymers. 

The second review focused on the molten state [Zoller, 1989]. The author examined four EoS theories, viz. [Spencer-Gilmore, 1949] (S-G), 

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