Three stirred-tanks in series are used in a reactor train (see Fig. E3.20). The flow rate into the system of some inert species is maintained constant while tracer tests are conducted. Assuming that mixing in each tank is perfect and the volumes are constant:

(a) Derive expressions for the concentration of tracer leaving each tank; c_i is the concentration of tracer entering the first tank.(b) If c_i 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

1. V₁ = V₂ = V₃2. V₁ ?  V₂ ?  V₃.(c) If the amount of tracer injected is unknown, is it possible to back-calculate it from experimental data? How would you do it?

M Ci M c3 V1 V2 V3 O