$($c$)$ Consider the perfectly mixed storage tank where a liquid phase chemical reactions is taking

place, $AB.$ The reaction is assumed to be irreversible, first order and exothermic. The heat

generated in the reactor is removed via a cooling system. The feed enters the reactor with volumetric

rate $F_f(\frac{m^3}{s}),$ density ${}_f(\frac{kg}{m^3})$ and concentration $C_{Af}(\frac{\text{m}\text{o}\text{l}\text{e}}{m^3}).$ The output comes out of the reactor

at volumetric rate $F_0,$ density ${}_0$ and concentrations $C_{A\text{@}}(mol\frac{e}{m^3})$ and $C_{Bo}(\frac{\text{m}\text{o}\text{l}\text{e}}{m^3}).$ The effluent

temperature is different from the inlet temperature due to heat generation by the exothermic reaction.

The dependence of the rate constant on the temperature is given by $k=k_0{e}^{\frac{-E}{RT}}$

In order to establish the concepts of modelling and model verification develop a model for the

variation of the volume of the reactor and the concentration of species A and $B.$