PLEASE SOLVE THIS PROBLEM WITHOUT USING AI OR ANYOTHER SOFTWARE.

The following liquid phase reactions take place in a batch reactor:

$(1)$

$(2)$

$(3)$

$A+2BC{r}_{1A}=-0\mathrm{.}001C_A{C}_B^2$

$3C+2AD{r}_{2A}=-0\mathrm{.}0003333C_{A}Cc$

$B+3CE{r}_{3C}=-0\mathrm{.}0006k_3{C}_{B}Cc$

Initial Concentrations and Temperature:

$C_{A0}=1mo\frac{l}{l}it$

$C_{B0}=0\mathrm{.}5mo\frac{l}{i}t$

$C_{C_0}=0\mathrm{.}2mo\frac{l}{l}it$

$C_{D0}=0\mathrm{.}0$

$C_{00}=0\mathrm{.}0$

$T_0=450K$

The heat of reactions:

$Hr{x}_{1B}=-5000ca\frac{l}{m}ol$

$Hr{x}_{2C}=-10000ca\frac{l}{m}ol$

$Hr{x}_{3B}=-50000ca\frac{l}{m}ol$

Heat exchanger:

$UA=100ca\frac{l}{s}-K$

$Ta,in=Ta,$out $=Ta=400K$

The volume of reacting fluid:

$V=2000$ lit

$($a$)$ Determine $Q_r,$ at $t=0.$

$($b$)$ Determine Qgen., at $t=0.$

$($c$)$ Determine $d\frac{T}{d}t$ at $t=0.$