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Homework Statement
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.
Homework Equations
The Attempt at a Solution
Start with the fundamental equation for a thermoelastic system
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:
[tex] du = \frac{\partial U}{\partial S}_Lds +\frac{\partial U}{\partial L}_SdL [/tex]
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.