5.21 An exothermic reaction, A2B, takes place adiabatically in a stirred-tank system. This liquid phase reaction occurs at constant volume in a 100 -gal reactor. The reaction can be considered to be first order and irreversible with the rate constant given by k=2.41015e20,000T(min1) where T is in R. Using the information below, derive a transfer function relating the exit temperature T to the inlet concentration cA. State any assumptions that you make. Simplify the transfer function by making a first-order approximation and show that the approximation is valid by comparing the step responses of both the original and the approximate models. Available Information (i) Nominal steady-state conditions are: T=150F,cAI=0.8lb molelft 3 q=20gal/min= flow rate in and out of the reactor (ii) Physical property data for the mixture at the nominal steady state: Cp=0.8Btw/bF, =52tb/ft3,HR=500kJ/bmole