The following elementary irreversible reaction is in liquid phase.

A $+$ B $->$ C

An equal molar of A& B enters at $300$ K with v$0=2$ dm$3/$s$.$ For the given data below:

H$\_$A $(273$K$)=-20$ kcal$/$mol H$\_$c $(273$K$)=-41$ kcal$/$mol

H$\_$B $(273$K$)=-15$ kcal$/$mol

Activation energy, E $=10$ kcal$/$mol

k $=0\mathrm{.}01$ dm$3/$mol$.$s at $300$K CA$0=0\mathrm{.}1$ kmol$/$m$3$

CPA $=$ CPB $=15$ kcal$/$mol$.$K CPC $=30$ kcal$/$mol$.$K

Determine the PFR volumes necessary to achieve $50\%$ conversion if the system are operated adiabatically.

Plot the conversion and temperature profiles if the temperature was maintained by using heat exchanger where Ua $=20$ cal$/$m$3.$s$/$K and the coolant temperature is constant at Ta $=450$K$.$

Repeat for $($b$)$ for a co$-$current heat exchanger for a coolant flow rate of $50$ g$/$s and CP$,$C $=1$ cal$/$g$.$K$,$ and inlet coolant temperature of Ta$0=450$K$.$