Small Systems Not in Solution

Let us consider an ensemble of N small systems that are open to C components, where N is large enough for the ensemble to be treated by 

The term dN in (5.2) is called the subdivision energy, and is the subdivision potential, that is, the energy term necessary to divide small systems by increasing their number when temperature, pressure, and the total number of molecules Me kept constant. When the average number of molecules per small system Nj increases, the thermodynamic variables approach those of macroscopic systems, and vanishes. 

On the other hand, when a closed ensemble of open systems is in equilibrium at constant T and P, the Gibbs free energy of the ensemble should be minimal (dG, = 0)  

The extensive thermodynamic variables are a first-order homogeneous function of Nj and N, a relation known as Euler s theorem  

Integrating (5.2) with respect to N] and N under constant T and P leads to 

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