# Chemical potential

1. Nov 27, 2013

### iScience

in class, we just learned that the chemical potential was μ=∂G/∂N

i'm looking in my book and it says that μ=-T(∂S/∂N) this looks alot like the partial of heat energy with respect to N. is my interpretation correct?

(assuming my interpretation was correct): so qualitatively, the chemical potential is the heat energy carried by a constituent particle of a system?

2. Nov 28, 2013

### DrDu

When taking the partial derivative, S is a function of what besides N?
Clearly you can write
$dS(V,U,N)=1/T dU+p/T dV + \mu/T dN$, so $\mu=T (\partial S/\partial N)_{V, U}$

3. Nov 28, 2013

### iScience

okay silly question: where does the minus come from? Q=-TdS, but that minus gets cancelled when rearranging to solve for dS like you did so then you end up with positive like you did.

4. Nov 28, 2013

### DrDu

There may be different sign convention. The most common one which I also use is Q=TdS.