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Question: The series of four chemical reactors are shown in Figure. Each reactor is constant volume and constant temperature, and the flow rate is constant. The reaction is A → B with the rate expression ta = -kC&. The con centration of component A in the last reactor is to be controlled, and the feed concentration of the inlet to the first reactor is a potential manipulated variable.

(a) Derive the model (algebraic and differential equations) relating Cao to CA4-

(b) Combine these equations into one input-output model that has only C_A0 and C_A4, with other relevant variables eliminated.

(i) The order of the system
(ii) The stability of the system

(iii) The damping of the system

(iv) The gain of the system

(v) The shape of the response of C_A4 to a step in C_A0

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