$(20$ pt$)$ In the two continuous stirred tank reactors shown in Figure $P4\mathrm{.}9$ the reaction $AB$ takes place under constant temperature, constant volumes $(V$ and $V_R)$ and constant volumetric flowrates and $R).$ Part of the product stream of the first tank is feed for the second reactor and the product stream from the second reactor is mixed with the fresh feed and is fed back to the first reactor. The concentration of the reactant in the feed stream is $C_0$ and it is the main input to the system. Derive the transfer function between the fresh feed concentration and the concentration $C$ of the reactant in the effluent. The reaction is first order with respect to the reactant concentration. Use the notation shown in Figure P$4\mathrm{.}9$ where $C_0,C$ and $C_R$ refer to reactant concentrations.

rigure r$4.$y