One of the many statements of the second law of thermodynamics is: Heat cannot flow from a colder body to a warmer one without external aid. Assume two systems. 1 and 2. at T1 and T3 (T2 > T1). Show that if a quantity of heat q did flow spontaneously from 1 to 2. the process would result in a decrease in the entropy of the universe. (You may assume that the heat flows very slowly so that the process can be regarded as reversible. Assume also that the loss of heat by system 1 and the gain of heat by system 2 do not affect T: and T2. Explain why you need to introduce a free energy.