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\sect{Elasticity of a rubber band}
The elasticity of a rubber band can be described by a one
dimensional model of a polymer, involving ${N}$ molecules of length
a each, linked together end-to-end. The angle between successive
links can be taken as ${0}$ \˚ or ${180}$ \˚ and the
joints can turn freely. The distance between the end points is
${x}$, and the temperature is ${T}$. Find the force (tension) ${f}$
which is necessary to maintain the distance ${x}$. Does the polymer
try to expand or to contract? You can use the canonical formalism in
order to solve the problem. Explain why the effect is of "entropic"
nature.