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The internal energy of a rubber band is given by

dU = TdS + FdL (2)

where F is the force on the rubber band and L is the length. The unstretched length (F = 0) is L0.

(a) Express F as a function of isothermal derivatives of U and S with respect to L.

(b) Find a function for which F is given by a single isothermal derivative with respect to L.

(c) The force in a rubber band at a given length and temperature can be divided into contributions from internal energy and from entropy. Derive expressions for FU and FS.

(d) The variables that are easy to measure in this problem are T, F, and L. Devise a way to find FU and FS through measuring (controlling) only these variables.

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