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I have a question on the quantity -(dV/dP)T,N where V = volume, P = pressure, T = temp, N = number of moles and T, N are held constant. I see in text books that this quantity is always positive at equilibrium. It makes intuitive sense, as if it were negative, it would be unphysical. I've been playing around with different maxwell relations, partial derivate relations, but can't seem to get to it. I know that Cv/T = (dS/dT)V,N where S = entropy is a positive quantity from the 2nd law. I should be able to relate this to my problem above. I have similar issues with -(dV/dP)S,N, (dN/du)S,N where u = chemical potential, (dN/du)T,V, which are all supposed to be positive. Thanks.

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