The change of Gibbs free energy (for a single phase or constitute system) is

$$dG = -SdT + VdP +{\mu}dn$$

By using the fact that $T$ and $P$ are intensive properties and $n$(mole) is an extensive property,

$G = n\mu$ is derived in my lecture note.

But I am not sure about that, because, with the definition of $dG$, $G$ is the function of $(T,P,n)$.

Where are the dependency of $T$ and $P$?

This interpretation is only valid for constant temperature and pressure situations?

like, $G = G_{0}(T,P) + n\mu$?


1 Answer 1


$G$ depends on $T$ and $P$ through the chemical potential:

$$G(T,P,n) = \mu(T,P,n) \cdot n$$

Recall that $\mu = \left(\frac{\partial G}{\partial n}\right)_{T,P}$. If $G$ is a function of some set of variables, then its derivatives (and in particular, $\mu$) are functions of the same set of variables. Note also in this case that $\left(\frac{\partial \mu}{\partial n}\right)_{T,P} = 0$, in accordance with the assumptions used to derive $G = \mu n$ (though these assumptions do not universally hold for all thermodynamical systems).


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.