6.19 Consider the following cascade connection of isothermal reactors. A first-order reaction A→B occurs in both reactors, with reaction rate constant k. The volumes of liquid in the reactors, V, are constant and equal; the flow rates Fo, F1, F2 and R are constant. Assume constant physical properties and a negligible time delay for the recycle line. Figure E6.19 Fo.Co F₁.C₁ R, C2 C FC₂ a. Write a mathematical model for this process. b. Derive a transfer function model relating the output concentration of A, C2 to the inlet concentration of A, Co. c. Verify that, in the limit of no recycle (R→ 0), the transfer function derived in (b) is equivalent to the transfer function of the two tanks connected in series. - *), the transfer function derived in (b) becomes d. Show that when k = 0 and a very large recycle flow rate is used (i.e., the limit as R the transfer function of a single tank that has the volume equal to 2V and a gain of one. Hint: Recognize that F₁ = R + F2 and F0 = F2.