(a) Find an expression for the entropy of this system in term of N and
(b) Write down a formula for L in terms of N and N1,
(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
(d) Using the thermodynamic Identity, you can flow 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
(e) Show that when
(f) Discuss the dependence of the tension force on temperature. If you increase the temperature of a rubber band, does it tend to expand or contract? Does this behavior make sense?
(g) Suppose that you hold a relaxed rubber band in both hands and suddenly stretch it. Would you expect its temperature to increase or decrease? Explain. Test your prediction with a real rubber band (preferably a fairly heavy one with lots of stretch), using your lips or forehead as a thermometer. (Hint: The entropy you computed in part (a) is not the total entropy of the rubber band. There is additional entropy a8sociated with the vibrational energy of the molecules; this entropy depends on U but is approximately independent of L.)
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