2. A jacketed vessel is used to cool the process stream as shown in the figure below. Some information is given for this process; (i) the volume of liquid in the tank, V, and the volume of refrigerant in the jacket, VJ, are constant. The volumetric flow rate gF is constant. But g h changes with time. (ii) the heat transfer coefficients from the jacketed vessel can be neglected. (iii) tank contents and jacket contents are well mixed and have significant heat capacitances. (iv) the thermal capacitances of the tank wall and the jacket wall are negligible. (v) the overall heat transfer coefficient used for heat transfer between the tank liquid and the coolant varies with the coolant flow rate: U=K.qJ0.8 Here, U(Btu/hr.ft2.0F), gl (ft3/hr), K (constant) Derive the dynamic model for this system. Analyze degrees of freedom. Do not forget to write down additional assumptions