$($a$)$

Consider a box model for an air shed over a city $\backslash (1*10^\{5\}\backslash$mathrm$\{$~m$\}\backslash )$ on a side with a mixing depth of $1200$ m $.$ Winds with no $\backslash (\backslash$mathrm$\{$SO$\}\_\{2\}\backslash )$ blow at $4\backslash (\backslash$mathrm$\{$m$\}/\backslash$mathrm$\{$s$\}\backslash )$ against one side of the box. $\backslash (\backslash$mathrm$\{$SO$\}\_\{2\}\backslash )$ is emitted in the box at a rate of $\backslash (20\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ).$ If $\backslash (\backslash$mathrm$\{$SO$\}\_\{2\}\backslash )$ is considered to be conservative, estimate the steady$-$state concentration in the air shed.

$($b$)$

With the same air shed and ambient conditions as given in $($a$),$ above, assume that emissions occur only on weekdays. If emissions stop at $5$ pm on Friday, estimate the $\backslash (\backslash$mathrm$\{$SO$\}\_\{2\}\backslash )$ concentration at midnight. If they start up again on Monday at $8$ am$,$ what would the concentration be by $5$ pm $($on Monday$).$