Strange derivation: Statistical thermodynamics

[ApeXaviour]

This isn't a homework question. I'm studying this from a book (Thermal Physics by Kittel & Kroemer) currently. Up til now I've had no problem following it. There's one derivation that's got me a little stumped however. I had thought my calculus was proficient enough, but I'm just not seeing something here and it's very frustrating. Y'know how it is when you just can't let yourself continue until you get past this tiny hurdle

Anyway here it is scanned from the book:
http://www.maths.tcd.ie/~cockburd/thermo.gif

The equation circled is the bit I'm having trouble with, I see where he's going with putting it in that form but I can't see how he got that equation from the one immedietly prior..

by the way:
F is helmholtz free energy,
Z is the partition function,
U is the average energy of the ensemble,
tau is the fundamental temperature and
sigma is the entropy

Thanks
Declan

 

[gdumont]

Quick reply
Take this expression
$$U=-\tau^2 \frac{\partial(F/ \tau)}{\partial \tau}$$
use the product rule for derivatives. And you'll get back to the prior equation

 

[dextercioby]

You could use Greiner's text on Thermodynamics & Statistical Physics. It's much more clear and the calculations are detailed.

Daniel.