A reaction of the type:

$A+2B2C+D,H_r=-330\mathrm{.}21k\frac{J}{m}ol$

Needs to be evaluated in order to determine the best processing condition for it$.$ The effects of density variation due to the reaction can be neglected. It is known that the heat capacities of the compounds are:

$($:$C_{PA}=84\mathrm{.}5\frac{J}{\text{m}\text{o}\text{l}\text{.}k}$;$C_{PB}=130\frac{J}{m}ol.K\}$

The kinetic constant $k$ is dependent on the reaction temperature with an Arrhenius equation$-$type relationship given by:

$k=0,0883$exp$[\frac{(51(\frac{kJ}{m}ol))}{R}(\frac{1}{T_0}-\frac{1}{T})],(\frac{L}{m}ol{)}^2(min{)}^{-1}$

Knowing that the initial operating temperature of the system is $25C,$ that the molar feed flow rates of A and $B$ are $10mo\frac{l}{m}in$ and $30mo\frac{l}{m}in,$ respectively, and that the volumetric feed flow rate is $150\frac{L}{m}in$ :

$($a$)$ Determine the volume and space time required to achieve a $25\%$ conversion of the compound $A$ in an adiabatic CSTR reactor;

$($b$)$ Determine the volume and space time required to achieve a $25\%$ conversion in a cooled CSTR reactor knowing that for this cooling system, the value of the $U{A}_H$ product is $8450\frac{J}{?}($min$.$K$)$ and the temperature of the coolant is $323K($constant$).$ Comment on the effect observed on the temperature due to the inclusion of the cooling jacket. Was this the expected behavior? Discuss your results.