A wastewater is to be disinfected using ultraviolet $($UV$)$ light. Batch experiments find that the

bacterial concentration decays under UV light with first$-$order kinetics, with a half of the initial

bacteria killed after $5\mathrm{.}1$ minutes of illumination. You need to design a reactor than can kill $99\%$

of bacteria in a stream having a flow rate of $650,000ga\frac{l}{d}.$ Assume that regardless of the

reactor type it will be possible to have UV illumination conditions identical to those of the

batch experiment.

a$.$ If a PFR is used for the reactor, what reactor volume is required, in gallons?

b$.$ If a CMFR is used for the reactor, what reactor volume is required, in gallons?