The elementary liquid$-$phase reaction A $+$ B $->$C takes place in a $1000$L CSTR$.$ A and B are fed equimolarly at $300$K and a volumetric flow rate of $500$L$/$min$.$ The concentration of A in the feed is $1$M$.$ When the reaction was carried out isothermally at $300$K$,$ the conversion was found to be $0\mathrm{.}18.$ When the reaction was carried out adiabatically at a temperature in the reactor of $350$K$,$ the conversion was found to be $0\mathrm{.}4.$ The heat capacities of A$,$ B and C are $25,35$ and $60$ J$/$molK$,$ respectively.

a$)$ What is Qdot for the isothermal operation? Is this energy supplied or removed from the system?

b$)$ We add a heat exchanger to the reactor with a UA of $6\mathrm{.}0$kJ$/$minK$.$ The temperature of the fluid is the same at the inlet and outlet of the heat exchanger. What is this temperature?

c$)$ What is the conversion if the reactor is operated at $345$K$?$

d$)$ What is Qdot $in$ this case $(c)?$ What will $be$ the temperature $of$ the fluid $in$ the heat exchanger $to$ maintain the temperature at $345$K in the reactor? How do Qdot and the temperature of the coolant compare to those in isothermal operation at $300$K $($see a and b$)?$