Consider a 'random-coil' polymer maintained as a fixed temperature T . Assume that one end of the polymer is fixed at x = 0. Imagine pulling the other end with a constant external force f away from the end fixed at x = 0. Let x be the end-to-end distance between the two ends and k the effective (entropic) spring constant of the polymer. (a) (3 pts) Explain the physical origin of polymer's elasticity. (b) (7 pts) Obtain the free energy of the resulting system as a function of x and find the equilibrium value of x. (You do not need to derive an expression for k.)