A$->2$R

The previous reaction is carried out in the gas phase within a CSTR reactor. The feed stream consists of $200$ L$/$min of a mixture at $100\backslash$deg C and $1$ atm whose composition is $20$ mol $\%$ of A and $80$ mol $\%$ of an inert gas, the conversion is desired to be $60\%.$

Additional Data:Consider that the values $$of the heat capacities are constant over the temperature range.$-r_A=k{C}_A^{1\mathrm{.}5}[=]\frac{\text{m}\text{o}\text{l}}{L**min}$

$k={10}^{12}$exp$(\frac{-10000}{(T)})[=](\frac{\text{m}\text{o}\text{l}}{L}{)}^{-0\mathrm{.}5}(\frac{1}{(min)})$ whereT $enK$

$H_R^0=-14300\frac{\text{c}\text{a}\text{l}}{\text{m}\text{o}\text{l}}$

$C{p}_A=14\mathrm{.}7\frac{\text{c}\text{a}\text{l}}{\text{m}\text{o}\text{l}**(K)}$;$,C{p}_R=10\mathrm{.}4\frac{\text{c}\text{a}\text{l}}{\text{m}\text{o}\text{l}**(K)}$;$,C{p}_{\text{I}\text{n}\text{e}\text{r}\text{t}\text{e}}=12\mathrm{.}3\frac{\text{c}\text{a}\text{l}}{\text{m}\text{o}\text{l}**(K)}$

$R=1\mathrm{.}987\frac{\text{c}\text{a}\text{l}}{\text{m}\text{o}\text{l}**(K)}=0\mathrm{.}08206\frac{L**(atm)}{(mol)**(K)}$

FORM:

${\displaystyle \underset{i=1}{\overset{m}{}}}{F}_{i0}{\displaystyle \underset{T_0}{\overset{T}{}}}C{p}_{i}dT+\frac{F_{A0}{x}_A{H}_R(T)}{a}=Q^{}$

$H_R(T)=H_R(T_r)+{\displaystyle \underset{T_r}{\overset{T}{}}}C{p}_{i}dT$ Consider that the reactor must operate at a constant temperature of $130\backslash$deg C From the energy balance in the reactor $($QSensitive and QReaction$),$ determine the QTotal $($cal$/$min$)$ required by the surroundings to keep the reactor in operation at a temperature of $130\backslash$deg C$.$