P$11-5$ A The elementary, irreversible gas$-$phase reaction

$AB+C$

is carried out adiabatically in a PFR packed with a

catalyst. Pure A enters the reactor at a volumetric flow

rate of $20d\frac{m^3}{s},$ at a pressure of $10$atm, and a

temperature of $450K.$

Additional information:

$C_{P_A}=40\frac{J}{m}ol*K,C_{P_B}=25\frac{J}{m}ol*K,C_{P_C}=15\frac{J}{m}ol*K$

$H_A^o=-70k\frac{J}{m}ol,H_B^o=-50k\frac{J}{m}ol,H_C^o=-40k\frac{J}{m}ol$

All heats of formation are referenced to $273K.$

$k=0\mathrm{.}133$exp$[\frac{E}{R}(\frac{1}{450}-\frac{1}{T})]\frac{d{m}^3}{(kg)-\text{c}\text{a}\text{t}*s},$ with $E=31\mathrm{.}4k\frac{J}{m}ol$

Plot and then analyze the conversion and temperature down the plug$-$

flow reactor until an $80\%$ conversion $($if possible$)$ is reached. $($The

maximum catalyst weight that can be packed into the PFR is $50kg.)$

Assume that $P=0\mathrm{.}0$