Q7/ An exothermic reaction, A 2B, takes place adiabatically in a stirred-tank reactor. This liquid reaction occurs at constant volume in a 1000-gal reactor. The reaction can be considered to be...

Extracted text: Q7/ An exothermic reaction, A 2B, takes place adiabatically in a stirred-tank reactor. This liquid reaction occurs at constant volume in a 1000-gal reactor. The reaction can be considered to be second-order and irreversible with the rate constant given by k = 2.4 x 1015e20.000(min-) where Tis in R. (a) Using the information below, derive a transfer function relating the exit temperature T to the inlet concentration CA. State all assumptions that you make. (b) How sensitive is the transfer function gain K to the operating conditions? Find an expression for the gain in terms of, , and, and evaluate the sensitivities (aKa, (aKa, and (aK/a). Available Information (1) Nominal steady-state conditions are = 150 F,= 0.8 mol/ft', 20 gal/min = flow in and out of the reactor (ii) Physical property data for the mixture at the nominal steady state: C= 0.8 Btu/(1b F), p= 52 lb/ft', -AH, = 500 Kj/mol