# Chemical Potential

1. Apr 9, 2009

### TheDestroyer

Hello Guys,

I'm searching for the best physical definition for the "Chemical Potential" as an energy, what I know is that it's a constant set through Lagrange multiplicands which is set to sustain the number of particles. Actually I'm still not convinced with that, it's an energy, and should have some physical meaning.

What I also happen to know is:

2- In Bosé-Einstein condensation chemical potential for bosons falls to zero when T tends to zero, also mathematically.
3- For photons, phonons, magnons and so have zero chemical potential, because the number of quasi-particles isn't conserved, and so also mathematically!!!

Thanks :)

2. Apr 11, 2009

### TheDestroyer

?????

Hey guys, is the question that complicated?

3. Apr 12, 2009

### alxm

I don't have it in front of me right now, but as I recall, "Density-functional theory of atoms and molecules" by Parr and Yang has a whole chapter devoted to the rigorous derivation and investigation of the chemical potential. Or you could go look at the papers by Mulliken, who I think was the one who did the original pioneering work.

4. Apr 12, 2009

### genneth

The chemical potential is the amount of energy it costs to introduce another particle into the system.

5. Apr 12, 2009

### Mapes

Equivalently, it's the conjugate thermodynamic variable to mass; i.e., $\mu$ is to mass what -P is to V, T is to S, etc.

6. Apr 12, 2009

### sokrates

In the context I use it all the time,

it's the Fermi-Level of a large, equilibrium fermion gas.

That explains, to me at least, why at temperature T, why there's still lots of energy in a Fermi gas, whereas no energy in Einstein-Bose condensate.

7. Apr 12, 2009

### bpsbps

If you want to think about chemical potential in terms of being a conjugate thermodynamic variable, then it doesn't act as an energy, but as a force or pressure.

U = T*S - P*V + mu*N + other terms

T P and mu are conjugates that act of S V and N.

From a practical perspective..... I imagine the system being in contact with a reservoir of particles and mu being the energy for a particle to pass from the reservoir into the system.