F 8. V Consider the isothermal CSTR reactor, as shown in Fig. 2, Information: The chemical reaction is AB. F The rate of reaction in reactor is second-order:r, = kc CA where k=0.5 [mol/m3 min)! The liquid volume is 1.05 m. The mass flow rate of inlet stream and outlet stream Fig. 2 isothermal CSTR reactor. are equal, F = 0.085 m3/min. The inlet concentration of A (Cao) is 0.925 mol/m. 4.1 Derive a dynamic model of this system (dC,/dt ). What is C, at the initial steady state? (5 points) 4.2 Please prove that transfer function, which describes the relationship of inlet concentration of A (C20) and outlet concentration of A(C), is expressed in the below equation 0.2 G(s) = 2.55 +1 and prove that the value of K and rare 0.2 and 2.5 min. (10 points) 4.3 If the inlet concentration of A (CAO) is suddenly changed from 0.925 moUm to 1.85 mol/m, find the response of Ct). How long the concentration of A in the reactor will reach to a new steady- state value? What is the value of CA at a new steady-state? (7 points)