A complete$-$mix activated sludge process $($CMAS$)$ is to be designed to treat $10,000\frac{m^3}{?}$ day of domestic wastewater having a $BO{D}_5$ of $250m\frac{g}{L}.$ The National Pollution Discharge Elimination System $($NPDES$)$ permit requires that the effluent $BO{D}_5$ and TSS concentrations should be $20m\frac{g}{L}$ or less on an annual average basis. The following biokinetic coefficients obtained at $20C$ will be used in designing the process: $Y=0\mathrm{.}6mgVS\frac{S}{m}gBO{D}_5,k=5d^{-1},K_s=60m\frac{g}{L}$BOD$5,$ and $k_d=0\mathrm{.}06d^{-1}.$ Assume that the MLVSS concentration in the aeration basin is maintained at $3,000m\frac{g}{L}$ and the VSS: TSS ratio is $0\mathrm{.}80.$ The temperature of the wastewater during the winter months is expected to remain at $18C$ for extended periods. During the summer, the wastewater temperature may reach $25C$ for several weeks.

Hint: Take the temperature correction coefficients $()$ of $1\mathrm{.}07,1\mathrm{.}00,$ and $1\mathrm{.}04$ will be used to correct $k,K_s,$ and $k_d,$ respectively.

Determine the following:

a$)$ Volume of the aeration basin in $m^3.$

b$)$ Mean cell residence time necessary to meet the NPDES permit during the summer months. $(15$ points$)$