How Do You Derive Temperature from Entropy?

[jorgen]

Hi all,

I have determined the entropy previously which gives the following results

S = k*(N Log N - n Log n -(N-n)*Log(N-n)

I have furthermore deduced the relation between state n and the energy as

$$n = \frac{E+N*\epsilon}{2*\epsilon}$$

I know that the temperature is

$$\frac{\partial S}{\partial E}=\frac{1}{T}$$

I am not quite sure how to proceed - I could replace small n with an expression containing the energy but what about capital N - should I isolate that from the relation and insert that into the entropy expression and then differentiate with respect to the energy - any hints or commands appreciated thanks in advance.

Best
J

 

[gabbagabbahey]

Replacing 'n' in your expression for the entropy seems like a good start to me. The next question is "which variables are held fixed when you compute the partial derivative of S with respect to E"? ...Surely if 'N' is fixed during this differentiation, the problem is simplified.