The Mathematics of Activity Coefficients

See Section 7.10, where activity and activity coefficients are defined. If we take the logarithm of both sides of Eq. 7.27 we find 

Now we differentiate this with respect to P at constant T and constant x and find 

Substituting the known values of these derivatives we obtain d In jY 

Similarly, if we differentiate Eq. C.36 with respect to T at constant P and x, we find 

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