A $->$ C $($r $=$ kCA, k $=1\mathrm{.}20$ h$-1)$

The liquid phase reaction represented by is performed in a tube$-$type recycling reactor.

A feedstock with a volume flow rate of v$0=4\mathrm{.}00$ m$3$ h

$-1$ with a volume flow rate of v$0=4\mathrm{.}00$ m$3$ h$-1($CA$0=2\mathrm{.}00$ kmol m$-3$

$,$ CC$0=0)$ is combined with the recirculation flow $($recirculation ratio

$\backslash$gamma $=2)$ is fed to the reactor. The product C is desired to be obtained at $6\mathrm{.}00$ kmol$/$h$.$ Find the required reactor volumeV.