Elementary gas phase reaction $()21->2()$ is carried out in a CSTR$.$ The feed consists of pure A and is fed into the reactor at $2$ atm pressure, $80\backslash$deg C temperature and $0\mathrm{.}3$ m$3/$min volumetric flow rate. The reactor is operated at a pressure of $2$ atm. The reaction equilibrium constant at $25\backslash$deg C is known as Kp$=5030$ and the standard reaction enthalpy is $-5300$ cal$/$mol$.$ CpA and CpR values are $12\mathrm{.}5$ cal$/($mol$.$K$)$ and $7\mathrm{.}5,$ respectively. cal$/($mol$.$K$).$ Reaching $85\%$ conversion if the reactor is cooled at a steady state rate of $12000$ cal$/$min$.$ Calculate the required reactor volume. k$1=6\mathrm{.}31$x$105.$exp$(-6800/$T$),$ min$-1$ R$=1\mathrm{.}987$ cal$/($mol$.$K$)$ mCp$=12\mathrm{.}5$ cal$/($min$.$K$)$ R$=0\mathrm{.}082$ m$3.$atm$/($kmol$.$K$)$