(4) [10 points] Let us revisit the rubber model that we discussed in lecture. We treated rubber as a polymer, which was a sequence of N monomers with each monomer taking one of the two different states (i.e. directions). Here, each monomer takes four different states ((1,0); (a,0); (0,11); (0,a), and their corresponding energies are fa: fa: 0; 0, where a is the monomer length and f is the externally given tension on the polymer. The polymer is in equilibrium at temperature T (or 6 = 1/kT). (a) Calculate the entropy of the system. (b) Evaluate how the temperature of the polymer changes when the tension f is increased slowly and adiabatically