A continuous stirred tank reactor $($CSTR$)$ is being used for biological wastewater treatment. The following parameter values apply.

$\backslash$table$[[S_{in},1000,m\frac{g}{l},$influent substrate concentration$],[Q,100,\frac{l}{h},$flow rate$],[{}_{\text{m}\text{a}\text{x}},0\mathrm{.}40,h^{-1},$maximum specific growth rate$],[K_M,120,m\frac{g}{l},$Monod half saturation coefficient$],[Y_{xs},0\mathrm{.}45,mg\frac{x}{m}{g}_S,$Yield coefficient$],[b,0\mathrm{.}007,h^{-1},$decay rate coefficient$]]$

a$)$ What size reactor would be required to reduce the soluble substrate concentration to $20m\frac{g}{1}?$

b$)$ What would the effluent substrate concentration be if the reactor volume were doubled from part $($a$)?$

c$)$ What would the effluent substrate concentration be if two reactors of the same volume as in part $($a$)$ were operated in series?