# Thermodynamics of a rubber band

1. Dec 23, 2011

### XCBRA

1. The problem statement, all variables and given/known data
For a stretched rubber band, it is observed experimentally that the tension f is proportional tot he temperature T if the length L is held constant. Prove that:

(a) the internal Energy U is a function of temperature;

(b) adiabatic stretching of the band results in an increase in temperature;

(c) the band will contract if warmed while kept under constant tension.

2. Relevant equations

3. The attempt at a solution

du = T ds - f dl.

Then I am stuck as to how to continue from here.

I have tried tp then take the total differential of U:

$$du = \frac{\partial U}{\partial S}_Lds +\frac{\partial U}{\partial L}_SdL$$

but that doesn't seem to help. I think I need to use a maxwell relation but I unable to figure out a suitable relationship to do the firs part. Any help will be greatly appreciated.

2. Dec 24, 2011

(a)