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What is the physical or mathematical meaning of the Gibbs-Duhem equation?

The Gibbs-Duhem equation states $$0~=~SdT-VdP+\sum(N_i d\mu_i),$$ where $\mu$ is the chemical potential. Does it have any mathematical (about intensive parameters) or physical meaning?
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Thermodynamics and the state postulate: should it be a Fourth Law?

The state postulate is as follows: The state of a simple compressible system is completely specified by two independent, intensive properties. My first question is whether there is any justification ...
SalahTheGoat's user avatar
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Definition of the pressure in statistical mechanics

I just had a glimpse of Feynman's statistical mechanics. On page 8, I saw a 'third' definition of pressure: $$ P = - \frac{\partial U }{\partial V} (V, S) . $$ I am curious why it is $S$ but not $T$. ...
poisson's user avatar
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