# Chemical potential

1. Sep 5, 2011

### Dr. 104

1. The problem statement, all variables and given/known data
Find the chemical potential for an ideal gas as a function of temperature and pressure. Use the "Gibbs-Duhen relation".

2. Relevant equations
$$\mu=\frac{\partial U}{\partial N}$$
$$dU=TdS-pdV+\sum\limits_{i}\mu_{i}dN_{i}$$
$$U=Q+W$$
Gibbs-Duhen relation: $$0=SdT-Vdp+\sum\limits_{i}N_{i}d\mu_{i}$$
Ideal gas law: $$pV=Nk_{b}T$$

3. The attempt at a solution
Well first I just tried putting the second equation (above) into the first one, but that just resulted in $\mu$ again, so that was a dead end.
I also tried plugging in everything I could from the ideal gas equation into the second equation (above) and the Gibbs-Duhen equation, because the problem asks for an ideal gas, hoping something would pop out after that, but I had no luck.

Thermodynamics has always been my weakest subject in physics.
I have several problems like this to do, so I'm not actually looking for a solution for this particular problem, I'm looking for general information on how to solve this type of problem that will help me on all of them.
I have no trouble like this with other areas of physics, but there's something about thermodynamics that my mind just doesn't get.. Maybe I just haven't learned it properly but I don't feel like there's any consistent set of fundamental equations, or underlying theory that I can cling to when I'm lost.