A closed stirred-tank reactor with two compartments is shown in Fig. E2.6. The basic idea is to feed the reactants continuously into the first compartment, where they will be preheated by energy liberated in the exothermic reaction, which is anticipated to occur primarily in the second compartment. The wall separating the two compartments is quite thin, thus allowing heat transfer; the outside of the reactor is well insulated; and a cooling coil is built into the second compartment to remove excess energy liberated in the reaction. Tests are to be conducted initially with a single-component feed (i.e., no reaction) to evaluate the reactor's thermal characteristics. (a) Develop a dynamic model for this process under the conditions of no reaction. Assume that q0, T;, and Tc all may vary. (b) Make a degrees of freedom analysis for your modelidentifying all parameters, outputs, and inputs that must be known functions of time in order to obtain a solution. (c) In order to estimate the heat transfer coefficients, thereactor will be tested with T; much hotter than the exit temperature. Explain how your model would have to be modified to account for the presence of the exothermic reaction. (For purposes of this answer, assume the reaction is A~ Band be as specific as possible.) Notes: Overall heat transfer coefficient and surface area between compartments. Uc, Ac: Overall heat transfer coefficient and surface area of cooling tube. V1: Volume of Compartment 1. Vz: Volume of Compartment 2.

Problem 2.6A closed stirred-tank reactor with two compartments is shown in Fig. E2.6. The basic idea isto feed the reactants continuously into the first compartment, where they will be preheatedby energy liberated in the exothermic reaction, which is anticipated to occur primarily in thesecond compartment. The wall separating the two compartments is quite thin, thus allowingheat transfer; the outside of the reactor is well insulated; and a cooling coil is built into thesecond compartment to remove excess energy liberated in the reaction.Tests are to be conducted initially with a single-component feed (i.e., no reaction) toevaluate the reactor's thermal characteristics.(a) Develop a dynamic model for this process under the conditions of no reaction. Assumethat q0 Ti and T cl may vary.(b) Make a degrees of freedom analysis for your model identifying all parameters, outputs,and inputs that must be known functions of time in order to obtain a solution.(c) In order to estimate the heat transfer coefficients, the reactor will be tested with T much ihotter than the exit temperature. Explain how your model would have to be modified toaccount for the presence of the exothermic reaction. (For purposes of this answer, assumethe reaction is A - Band be as specific as possible.)Notes:UtAtOverall heat transfer coefficient and surface area between compartments.U , A : Overall heat transfer coefficient and surface area of cooling tube. c cV : Volume of Compartment 1. 1V2 Volume of Compartment 2. Step-by-step solution Step 1 of 4 ^Refer to Figure E2.6 in the text book for the closed stirred-tank reactor with two compartments.The following are the assumptions made to establish the dynamic model: 1. All subparts off the tank are perfectly matched. 2. The specific hear and density of the liquid is constant. 3. The total heat remains conserved throughout the process.\nConsider the following parameters: Uts the overall heat transfer coefficient of compartments At the surface area between compartments Ucs the overall heat transfer coefficient of cooling tube Acs the surface area of cooling tube V1s the volume of compartment 1 V2s the volume of compartment 2