An exothermic reaction, A ~ 2B, takes place adiabati- cally 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 = 2.4 x 101se-20,000/T (min-1) where T is in oR. Using the information below, derive a transfer function relating the exit temperature T to the inlet concentration cAi· State any
An exothermic reaction, A ~ 2B, takes place adiabati-
cally 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 = 2.4 x 101se-20,000/T (min-1)
where T is in oR. Using the information below, derive a
transfer function relating the exit temperature T to the inlet
concentration cAi· 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 = 150 °F, CAi = 0.8lb mole/ft3
q = 20 gaUmin = flow rate in and out of the reactor
(ii) Physical property data for the mixture at the nominal
steady state: CP = 0.8 Btu!lb °F,
p = 52lb/ft3, -t:lHR = 500 kJ/lb mole
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