Use POLYMATH or MATLAB to solve this problem.

The following $E(t)$ curve was obtained from a tracer test on a $20d{m}^3$ reactor.

$E(t)=0\mathrm{.}4(t)+0\mathrm{.}6(t-2)$

A second$-$order reaction $(AkB)$ is to be carried out in this reactor, with $v_0=10d\frac{m^3}{m}in,C_{A0}=2mo\frac{l}{d}{m}^3,$ and $k=0\mathrm{.}2d\frac{m^3}{m}ol*min,$

$($i$)$ What is the mean residence time $t_m?$

$($j$)$ What is the variance ${}^2?$

$($k$)$ What conversions do you expect from an ideal PFR and an ideal CSTR in a real reactor $t_m?$

$($I$)$ Find the conversion predicted by the segregation model.

$($m$)$Find the conversion predicted by the maximum mixedness model.

$($n$)$ What conversion is predicted by the tanks$-$in$-$series model?

$($o$)$ Suggest a two$-$parameter model $($combination of ideal reactors with bypass and$/$or dead volume$)$ consistent with the data; evaluate the model parameters, $$ and $,$ and the expected conversion.

$($p$)$ Compare and discuss the results of the four models.