# Thermodynamics without partition function

1. Feb 23, 2014

### cryptist

Is there a way to derive entropy or free energy without using partition function?

2. Feb 23, 2014

### Staff: Mentor

Yes.

If you want a more complete answer, you'll have to post a more detailed question.

3. Feb 24, 2014

### Jorriss

Thermodynamics came before statistical mechanics.

4. Feb 24, 2014

### cryptist

As you all know, N=∑ni, U=∑εi, F=Nμ-kT∑Z and S=(U-F)/T

Here, I do not want to use partition function Z. How do I write F and S then?

Last edited: Feb 24, 2014
5. Feb 24, 2014

### Staff: Mentor

The Helmoholtz free energy is defined as
$$F \equiv U - TS$$
Entropy you can get from the heat capacity:
$$C_V \equiv T \left( \frac{\partial S}{\partial T} \right)_V$$

6. Feb 24, 2014

### cryptist

Let me specify the problem. I am using grand canonical ensemble and I am in Fermi-Dirac statistics.

Considering these, entropy is written as S=k[lnZ+β(E-μN)]. How do I write S, without using Z?

Last edited: Feb 24, 2014
7. Feb 25, 2014

### cryptist

Heat capacity is a derived quantity. It is really complicated to extract S from Cv.

8. Feb 25, 2014

### cryptist

Ok. Then, how do I derive S without using partition function (a statistical mechanics tool)? Btw, by deriving S, I mean I'll calculate the entropy of a system over momentum states, I am not talking about S=klnΩ which apparently does not include partition function.

9. Feb 25, 2014