# Entropy, chemical potential, temperature

1. Feb 5, 2014

### aaaa202

For a thermodynamic system there exists a function called entropy S(U,N,V) etc.
We then define for instance temperature as:
1/T = ∂S/∂U
μ = ∂S/∂N
etc.
When taking these partial it is understood that we only take the derivative of S wrt the explicit dependece on U,N etc. right? Because couldn't U carry an N dependence? I mean it does not for me make physical sense that the energy of the system should not be related to the number of particles in it. Actually it seems also a bit weird that there should be an explicit U dependence. Does this come from the fact that we are given the mean value of the internal energy of the system?

2. Feb 5, 2014

### DrDu

Yes, that is the definition of a partial derivative as opposed, e.g. to a total derivative.

3. Feb 7, 2014

### Useful nucleus

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In the entropy representation U,V,N are independent variables. On the other hand in the energy representation S,V,N are independent variables. One should not mix the two representations in the same time.