# Homework Help: Thermodynamics of a Rubber Band

1. Feb 7, 2014

### derrickb

1. The problem statement, all variables and given/known data
For the rubber band model, calculate the fractional change in (L-L0) that results from an increase δT in temperature, at constant tension. Express the result in terms of the length and temperature.

2. Relevant equations
U=cL0T
τ=bT((L-L0)/(L1-L0)); τ=tension, L1=elastic limit
d/dL(1/T)=d/dU(-τ/T)

3. The attempt at a solution
I'm sort of at a loss on this one. I've tried subbing in all sorts of equations, but can't seem to make any real progress.

2. Feb 11, 2014

### rude man

EDIT:

By using Maxwell's 4th equation you can show that T dS = Cτ dT if τ is constant.

You can also rewrite the 1st law as dU = T dS + τ dL.

Just thinking - if we can assume an "ideal rubber band" analogously to an ideal gas, such that U is a function of T only, then dU = CL dT similar to dU = CV dT for an ideal gas.

Last edited: Feb 11, 2014
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