Question $3.(30$ pts$)$ The following gas phase reversible reaction

$A+B>2C$

is taking place in a CSTR with a mounted heat exchanger. The heat exchanger has an overall heat transfer coefficient of $0\mathrm{.}01k\frac{W}{m^2}K,$ the heat transfer area of $2m^2$ and the cooling medium temperature is $290K.$ The equimolar feed of A and B at $0\mathrm{.}58$MPa and $350K$ is sent to the reactor for which the molar feed rate of A is $1200$mole$\frac{s}{m}in.$ The rate constant of the reaction is $5\mathrm{.}83{10}^{-4}d\frac{m^3}{m}ol.$s at $273K$ and the activation energy of the reaction is $70k\frac{J}{m}$ole. The enthalpy of formation values of A$,$ B and C at $298K$ are $-40000,-30000$ and $-45000\frac{J}{m}$ole, respectively. The heat capacities of A$,$ B and $C$ at $298K$ are $0\mathrm{.}025,0\mathrm{.}015$ and $0\mathrm{.}02k\frac{J}{m}$ole. $K,$ respectively. The equilibrium constant for the reaction at $298K$ is $25000.$ Determine the conversion of A which can be achieved in a $1500d{m}^3$ reactor.