General Relations between Thermodynamics and Quasicomponent Distribution Functions

General Relations between Thermodynamics and Quasicomponent Distribution Functions 

Let E be any extensive thermodynamic quantity expressed as a function of the variables T, P, and N (where N is the total number of molecules in the system). Viewing the same system as a mixture of quasicomponents, we can express as a function of the new set of variables T, P, and N. For concreteness, consider the QCDF based on the concept of CN. The two possible functions mentioned above are then 

For the sake of simplicity, we henceforth use N(K) in place of Nc E), so that the treatment will be valid for any discrete QCDF. Since E is an extensive quantity, it has the property 

40) and (5.13.41) we have stressed the fact that the partial molar quantities depend on the whole vector N. 

The generalization of (5.13.40) and (5.13.41) to the case of a continuous QCDF requires the application of the technique of functional differentiation. We introduce the generalized Euler theorem by way of analogy with (5.13.40). 

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