Prediction via the Principle of Corresponding States

Reid and T. K. Sherwood, The Properties of Gases and Liquids. Their Estimation and Correlation, McGraw-Hill, New York, 1966, 2nd Edn. 

The curves for Pr 1 terminate at a curve representing orthobaric densities. The latter curve can itself be predicted using the Principle of Corresponding States equations for this purpose have been proposed by Guggenheim.  

So far in this review we have referred to the Principle of Corresponding States solely as an outcome of the van der Waals equation of state. However, Pitzer showed in 1939 that the Principle is a consequence of the forces acting between molecules, if certain assumptions on the nature of these forces hold good. One assumption is that the potential energy, , of a fluid is expressible as the product of an energy parameter, s, and a function of distance r (in dimensionless form) between molecular centres, i.e. u(r) = e Many expressions for u(r) in terms of the two parameters e and a 

A fluid that conforms to the Principle of Corresponding States has Ps.r = 0.1 at 7 = 0.7, i.e. cu = 0 for such a fluid. Non-conforming fluids have w 0, and their second virial coefficients can conveniently be derived from Pitzer and Curl s equation  

The Berthelot curve is found to correspond approximately to a Pitzer and Curl curve with w = 0.21 this fact shows why the Berthelot equation has had comparatively wide applicability, since many polyatomic gases have w values around 0.2. 

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