(a) An infinitesimal amount of heat is added reversibly to a system. By combining the first and second laws, show that dU = TdS - dW. . (b) When heat is added to an ideal gas, its temperature and volume change from T1 and V1 to T2 and V2. Show that the entropy change of n moles of the gas is given by V V + nR ln T T S = nC ln 1 2 1 2 v 