Potential for Open Systems

Historically, one of the main contributions of J. W. Gibbs to the development of thermodynamics was his extension of G = H TS to open systems. This is an important consideration for onstream processes encountered by chemical engineers. We have already introduced the concept of the chemical potential, p., = (Gilni), in two previous applications in this chapter first in the treatment of gas species p(T, F) = p° - - RT In P and then again in the discussion of the Gibbs phase rule. So far the treatments referred to closed systems and it seemed that p is just 

This shows that the change in G depends on the changing amount of moles of each component. Thus, we have dG = —S dT +VdP + ) dn, for an open system. 

This can have far reaching effects in the analysis of an on-stream process but we will just show the implications here and leave further treatment to engineering texts. Recall that 

Comparing the total differentials to the derived equations in terms of p,- drii we find that 

To reinforce the idea, we say again that in every case we have jl, 

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