Thermodynamic Potentials in Open Systems

We saw in Chapter 5 that the function U = U(S, V) expressed as a total differential is  

In this equation we implicitly consider the system to be capable of changes in U, S, and V, and hence can be heated, cooled, or squeezed, but it always has the same 

Let the original values of the internal energy, etc., of the system be U, S, V and n. If the system is enlarged to k times its original size, the final values of these parameters (which are all extensive, or homogeneous degree one in the masses of the components) will be fcU, kS, fcV, and kn. Thus 

Analogous integration of equations (14.3) to (14.5), recalling that dT and dP are zero, gives 

A number of interesting relationships are inherent in the equations written thus far in fact, they contain or imply just about everything there is to be said about (model) heterogeneous equilibria. 

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