Irreversibke consecutive reactions $ABC$ occur in a jacketed, stirred$-$tank reactor as shown in diagram. Derive a dynamic model based on the following assumptions:

i$)$ The contents of the tank and cooling jacket are well mixed. The volumes of material in the jacket and in the tank do not vary with time.

ii$)$ The reaction rates are given by $r_1=k_1{e}^{-\frac{E_1}{kT}}{C}_A$;$[mol\frac{A}{h}L]$

$r_2=k_2{e}^{-\frac{E_2}{k_T}}{C}_B[mol\frac{B}{h}L]$

iii$)$ The thermal capacitances of the tank contents and the jacket contents are significant relative to the thermal capacitances of the jacket and tank walls, which can be neglected.

iv$)$ Constant physical properties and heat transfer coefficients can be assumed.