The gas phase reaction,

$A+BC$

is carried out isothermally at $125C$ and $2$ bar pressure in a

plug$-$flow reactor. The feed contains a mixture of A and $B$ with

a ratio of $1$:$3,$ and the volumetric flowrate is $15L.h^{-1}.$ The

conversion is $80\%$ with respect to the limiting reactant. The

rate equation is given as$,$

$r=k_1{C}_A{C}_B+k_2{C}_A^{0\mathrm{.}5}{C}_B^{1\mathrm{.}5}$

where, $k_1$ and $k_2$ at the reaction conditions, are $0\mathrm{.}1L.mo{l}^{-1}.s^{-1}$

and $1\mathrm{.}5L.mo{l}^{-1}.S^{-1},$ respectively.

$($a$)$ Determine the volume of the reactor.

$($a$)$ The reactor is constructed from a uniform cylindrical

steel pipe with an internal diameter of $10cm.$ Determine

its length.