Critical index calculation by the van der Waals equation

Let us apply the van der Waals equation 1.2-.34 to calculate the critical indices (Stanley, 1971). It is reasonable to rewrite Equation 1.2-67, introducing new variables 

Multiplying both the sides by (1 + and reducing the similar terms yield 

Consider the behaviour of the temperature dependence of isothermal compressibility (Equation 1.1.2-41) while the configurative point approaches from the side of lower temperatures T - T along the critical isochore (v = 0). 

Now we should substitute p from Equation 18 into Equation 22, integrate, and reduce both the sides by (u, — V/). All this yields 

The latter equation is useful after subtracting Equation 19 from Equation 20  

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