the proof here is nice to help understanding but its not a real proof.
Can someone who applications in a binary system with x1 and x2 being the two compositions?
Performed a reasonably extensive rewrite of this page, including trying to make variables of consistant case and tracking whether they are intensive or extensive. Added references to Moran and Shapiro and Poling et al. Changed the term "Proof" to what I think is the more appropriate "Derivation" and added a more appropriate form of it. Tried to expand the "Applications" section to include the form of Gibbs-Duhem used in activity coefficient derivation (Margules, van Laar, NTRL, UNIQUAC). Also included basic explanation and link to Gibbs' phase rule, which seemed appropriate.
Thermodude 16:28, 29 June 2007 (UTC)
Re: updates made by ChrisChiasson -- The chemical potential is defined with reference to the Gibbs Free Energy (or whatever you chose to call it). The expression for the internal energy for the system, while understandable from a physical perspective, is actually derived mathematically from the definition I put back in. Thanks to ChrisChiasson for the other work done on the page; it's always good to see people putting time on on these pages. Thermodude 21:15, 2 November 2007 (UTC)
- Interesting, I always thought that the expression for the (differential of) internal energy came from the first law of thermo, not the defintion of gibbs free energy. I can see what you are saying though. It doesn't really matter, because the equations are all consistent. ChrisChiasson 16:32, 3 November 2007 (UTC)
The derivation of the Gibbs-Duhem relation in this article relies on a crucial fact about the Gibbs free energy, and instead of proving it here, there is a link to the article on the Gibbs free energy. In that article, the derivation of the same fact uses the Gibbs-Duhem relation and links to this article....
I'd suggest rewriting the derivation section. The lecture notes listed as a reference for both articles are also not very enlightening on this point. After some searching it appears Euler's homogeneous function theorem is really necessary for a derivation of the Gibbs-Duhem relation. — Preceding unsigned comment added by 18.104.22.168 (talk) 18:33, 5 August 2013 (UTC)
"... for a system in thermodynamical equilibrium (and, by definition, in reversible condition) the infinitesimal change in G must be zero ..."
I think this is extraneous and either wrong or unclear. It's true that a system will tend to the state with minimum G given the freedom to do so (e.g. minimize G by exchanging liquid/vapor at fixed T,p), but it can't be true that any infinitesimal change from an equilibrium state has dG = 0, or else G would be flat everywhere, right? Setting the dG equal to each other is sufficient to derive the Gibbs-Duhem equation.
It shows that in thermodynamics intensive properties are not independent but related, making it a mathematical statement of the state postulate.