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Physics 404
Problem Set #2
(70 points total)
Due Sept 30, 2008
1.
(worth 20 points)
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 j. 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 link to the end of
the last link.
(a) Find an expression for the entropy of this system in terms of N and Nr the
number of links pointing to the right.
(b) Write down a formula for L in terms of N and Nr.
(c) For a one-dimensional system such as this, the length L is analogous to the
volume V of a three-dimensional system. Similarly, the pressure P is replaced
by the tension force F. Taking F to be positive when the rubber band is pulling
inward, write down and explain the appropriate thermodynamic identity for
the system.
(d) Using the thermodynamic identity, you can now express the tension force F in

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