The exothermic, elementary, second order reaction of $A+BC+D$ is carried out

in a jacketed batch reactor. The volume of the reaction mixture is $0\mathrm{.}5m^3$ and

initial temperature is $40C.$ Initial moles of A and B are $0\mathrm{.}04$ and $0\mathrm{.}02$kmol,

respectively. The cooling water pass around the reactor at a constant flow rate

and at a temperature of $15C.$

a$.$ Develop the model equations describing the change of concentrations of all

components and temperature of reaction mixture with reaction time for given

non$-$isothermal batch reactor

b$.$ Calculate the concentrations of all components and the temperature of

reaction mixture at the end of $10$ second of reaction using Euler's formula.

Additional Data:

Reaction rate constant, $k=7{10}^5$exp$(\frac{-5000}{T})\frac{m^3}{\text{k}\text{m}\text{o}\text{l}\text{s}}$

where $T[K]$

Heat of reaction $=-5000k\frac{J}{k}$mol

it Heat capacity of reaction mixture $=6k\frac{J}{k}$molK

$U.A=0\mathrm{.}02k\frac{J}{s}K$

$t=5$ seconds