The trickle-bed catalytic reactor shown in the figure utilizes product recycle to obtain satisfactory operating conditions for temperature and conversion. Use of a high recycle rate eliminates the need for mechanical agitation. The concentration of the reactant is measured at a point in the recycle line where the product stream is removed. A liquid phase first-order reaction is assumed. Under normal operating conditions, the following assumption may be made i. The reactor operates isothermally with a reaction rate given by r = kc, where r denotes the rate of disappearance of reactant per unit volume, c is the concentration of reactant, and k is the rate constant ii. All flow rates and liquid volume V are constant No reaction occurs in the piping. The dynamics of the exit and recycles line lines can be approximated as constant time delays. 01 and 62, as indicated in the figure. Let C1 denote the reactant concentration at measurement point (by the effluent stream arrow) iv. Because of the high recycle flow rate, the reactor is completely mixed a) Derive an expression for the transfer function C(s)/C(s) b) Using the following information, calculate c(t) for a step change in c(t) of 2000 kg/m Parameters Values V = 5m3 a = 12 q = 0.05m3/min 01 = 0.9 min k = 0.04 min-1 02 = 1.1 min 111. = 9 09 -82 c2V Recycle line 01 Product line 9 (1 + alq AT