Long-Range Many-Molecule Interactions in an Extended van der Waals Equation of State

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Abstract
Distinction between the effects of pairwise and nonadditive interactions on thermodynamic functions can be made only in an approximate sense and then only for the long‐range part of the interaction. Within such an approximation the entire contributions of all long‐range many‐body interactions to the free energy and pressure are obtained in closed form. These appear as simple extensions of the well known long‐range terms of the van der Waals equations. Using a simple harmonic oscillator model for the molecule it is found that the relative contributions of the entire nonadditive to additive interactions to the free energy and pressure are functions only of a reduced polarizability of the molecule. Taking actual values of polarizabilities and densities of the noble gases it is found that the nonadditive effects contribute at most about 7% to the pressure and 4% to the free energy even at the liquid densities. Using van der Waals' expression for the short‐range part of the pressure, the corrections to the critical constants are also estimated. As a rule inclusion of nonadditive effects improves the agreement between calculated and experimental values of all thermodynamic functions.