Q$3.$ An exothermic, $1$st order reaction $AB$ is carried out in a jacketed, stirred$-$tank

reactor at a steady$-$state temperature of $500K.$ The feed to the reactor is $0\mathrm{.}5kmol{s}^{-1}$ of

pure $A$ at $300K$ and the jacket is at a constant temperature of $400K.$ Calculate the exit

conversion and estimate the overall heat transfer coefficient for the tank.

DATA

Rate constant: $k={10}^3$exp$(-\frac{4000}{T})s^{-1}$

Molar density of A and $B$:$20kmol{m}^{-3}$

Heat capacity of A and $B$:$250kJkmo{l}^{-1}{K}^{-1}$

Heat of reaction: $-{10}^{5}kJkmo{l}^{-1}$

Volume of reactor: $0\mathrm{.}1m^3$

Heat transfer area: $1m^2$