The elementary irreversible gas$-$phase reaction Alongrightarrow$2B+C$ is carried out in a packed bed reactor. Pure A enters the reactor at a volumetric flow rate of $v_{0}d\frac{m^3}{s},$ and pressure $P_0$ atm and temperature $T_{0}C.$ The maximum catalyst weight that can be packed into the reactor is $Wkg.$ Heat is removed by a heat exchanger jacketing the reactor. The flow rate of the coolant through the jacket is sufficiently high that the ambient exchanger temperature is constant at $T_{a}C$

The overall heat transfer coefficient is given by:

$\frac{Ua}{{}_b}=U\frac{J}{(s)*kgcat*K}$

Where $U=$ overall heat$-$transfer coefficient $(\frac{J}{s}*m^2*K)$

$a=$ heat$-$exchange area per unit volume of reactor $(\frac{m^2}{m^3})$

${}_b=$ bulk density of the catalyst $(k\frac{g}{m^3})$

The rate constant $k$ is given by $3\mathrm{.}2e^{[\frac{35,600}{R}(\frac{1}{T_0}-\frac{1}{T})]}\frac{d{m}^3}{(s)*kgcat}$

The specific heat capacities for each component are:

$Cp{A}_A=70\frac{J}{m}ol*K,Cp{B}_p=45\frac{J}{m}ol*K,Cpc=25\frac{J}{m}ol*K$

The heat of formations for each component are:

$H_A^0=-60\frac{kJ}{\text{m}\text{o}\text{l}},H_B^0=-30\frac{kJ}{\text{m}\text{o}\text{l}},H_C^0=-55\frac{kJ}{\text{m}\text{o}\text{l}}$

All heats of formation are referenced to $273K$

a$)$ Using polymath, plot the temperature and conversion profiles.

b$)$ How would the profiles change if there is a pressure drop with $k{g}^{-1}?$

$\backslash$table$[[,,,,,,,],[$Group $3,W=74kg,v_0=12\mathrm{.}1d\frac{m^3}{s},P_0=10\mathrm{.}4$atm,$T_0=289C,U=0\mathrm{.}015,T_a=23C,=0\mathrm{.}01$