(3 points) A jacketed vessel is used to cool a process stream, as shown below. No reaction occurs in the vessel. Derive dynamic the dynamic energy balance on the vessel and on the cooling jacket, where the dependent variables of the balances are T and Tc, respectively. The following information is available: a. The volumetric flowrates of liquid into the vessel (F) and the cooling jacket (Fc) are constant. Therefore, the corresponding volume volume of liquid in the vessel, V, and the volume of coolant in the jacket, Vc, remain constant. b. The contents of the vessel and the jacketed vessel can be considered well mixed. c. Density of the liquid, , and density of the coolant, c, is constant. The specific heat of the liquid, Cp, and the coolant, Cpc, are constant. d. U is the overall heat transfer coefficient for transfer between the liquid in the tank and the coolant. The area of the heat exchanger is A