Chemical Potential in Multicomponent Systems

Classical and Geometrical Theory of Chemical and Phase Thermodynamics. By Frank Weinhold Copyright 2009 John Wiley Sons, Inc. 

The differential variations dU of (6.1) are given as usual by the chain rule 

The coefficients (dU/drii)s vn of the dnt in (6.7) are evidently an important new set of intensive properties that control the chemical flows (analogous to the manner in which T controls the entropy flow and P the volume flow). Following Gibbs, we identify each coefficient (dU/dni)s v n as the chemical potential (/ ) of the corresponding species At  

With this notation, the combined first/second law is written as 

With the inclusion of chemical potential terms, (6.9a,b) now incorporate the important variations of internal energy with chemical changes. 

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