How is the Tension in a Rubber Band Related to Thermodynamics?

[jason177]

Homework Statement

Polymers, like rubber, are made of very long molecules, usually tangled up in a configuration that has lots of entropy. As a very crude model of a rubber band, consider a chain of N links, each of length l. Imagine that each link has only two possible states, pointing either left or right. The total length L of the rubber band is the net displacement from the beginning of the first ling to the end of the last link.

Using the thermodynamic identity,express the tension force F in terms of a partial derivative of the entropy. From this expression compute the tension in terms of L,T,N, and l.

Homework Equations

I'm pretty sure the thermodynamic identity for this system is

dU=TdS+fdl

so then solving for f gets

f=dU/dl - TdS/dl

The Attempt at a Solution

so I found an equation for dS/dl but I have no idea how to get dU/dl in terms of L,T,N, and l.

 

[jason177]

Never mind, I got it