Two equal quantities of water, of mass m and at temperatures T1 and T2, (T1 > T2) are mixed together with the pressure kept constant. Assume heat exchange occurs only between the two water containers. (a) Show that the entropy change of the universe is delta S = 2mc_P ln(T_1 + T_2/2 squareroot T_1T_2), where c_P is the specific heat capacity of water at constant pressure. Show that delta S > 0 for any finite temperatures T_1 and T_2.