Symmetric Corrections to Scaling

The equations presented thus far describe the behaviour of the thermodynamic properties of fluids asymptotically close to the critical point. The actual temperature range of asymptotic scaling behaviour depends on the magnitude of correction-to-scaling terms. They are incorporated by extending eq 10.1 to 

To obtain a simple extended linear-model equation of state consistent with eq (10.53) in terms of the parametric variables r and 6, defined by eq (10.9), one has proposed to extend eq 10.10 for the order parameter to 

The reduced pressure P satisfies a differential relation of the form 

Upon comparing with eq 10.19 we note that in terms of these modified variables the role of the reduce entropy density s is taken over by that of the reduced energy density u. The extended linear model, defined by eqs 10.9 and 10.54, has been used to represent the thermodynamie properties of a number of fluids in the eritical region in the revised-scaling approximation, including light 

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