Consider the thermodynamics of a rubber band. Let the rubber band be the system and consider the system to be closed with no change of composition. If a force (f) stretches a rubber band to a new length (L), it does work on the system. For this system, lets assume that this is the only kind of work possible, i.e., there is no PV work.

a) Start with the first and second laws, and let d w = fdL . Assume reversible processes. Derive an expression for dU. For the conditions specified, U is only a function of S and L.

b) Show that dA = fdL - SdT.

c) What Maxwell relation results from your expression for dA? (Note that this Maxwell relation equates something interesting/useful with something easy to measure.)