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QUESTION 7 . Deriving and solving a model with Laplace transforms. ( 2 3 pts ) Three stirred - tanks in series are used in

QUESTION 7. Deriving and solving a model with Laplace transforms. (23 pts)
Three stirred-tanks in series are used in a reactor train.
The flow rate into the system of some inert species is maintained constant while tracer test are
conducted. Assuming that mixing in each tank is perfect and the volumes are constant:
a) Derive expressions for the concentrations of tracer leaving each tank. Here, ci is the
concentration of tracer entering the first tank. You can do this by developing an ODE-
based model for this system (do not solve it yet). Note in the image, q=v for what I used
in CHEM E 465(volumetric flow rate).
b) If ci has been constant and equal to zero for a long time and an operator suddenly injects
a large amount of tracer material in the inlet to tank 1, what will be the form of c3(t)(i.e.,
what types of time functions will be involved) if:
i.,V1=V2=V3
ii.,V1V2V3
c) If the amount of tracer injected is unknown, is it possible to back-calculate it from
experimental data? How would you do it? This is a short, conceptual answer (i.e., imagine
that you have a fully expression for {:c3(t)).
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