Q$.5$ Set. $($B$)$ Suppose a lake has a volume of $3{10}^5{m}^3$ of water and is fed by a river having a flow $($discharge$)$ of $70,000\frac{m^3}{?}$ year. An agricultural farm upstream of the lake pollutes the river; hence, the river has a concentration of $6m\frac{g}{l}$ of a specific pollutant. This pollutant decays in the lake at a rate of $\frac{0\mathrm{.}10}{y}$ ear. Evaporation from the lake takes away $5000\frac{m^3}{?}$ year $($The concentration of pollutants in evaporation would be zero$).$ This river exits the lake at a downstream end. So only $65000\frac{m^3}{?}$ year of water exits the lake through the river.

a$.$ Mention the ideal reactor that we may assume this system as$?$

$[1$ Mark$]$

b$.$ Write an expression for mass balance for this situation

$[1$ Mark$]$

c$.$ Find the steady$-$state concentration in the lake by

$[1$ Mark$]$

Suppose the agricultural farm is closed down to stop pollution. This makes the concentration of pollutants in the river to be zero. Eventually, the concentration in the lake will either decay or get flushed out. For this situation

d$.$ Write down the new mass balance equation. $[1$ Mark$]$

e$.$ Derive a solution to find out the concentration of the pollutant at any time t$.$ write only the final expression $($as much as possible by typing in$)$ solution to the concentration of pollutant at any time, $t$

$[(2$Mark$]$

f$.$ How much time will it take to drop by $50\%$ of the steady$-$state concentration? $[1$ Mark$]$

g$.$ How much time will it take to drop to $0\mathrm{.}1m\frac{g}{l}$ from the steady state concentration?

$[1$ Mark$]$

h$.$ Which do you think is having have more impact in cleaning the lake: decay of the pollutant or flushing. Give clear reason.

$[2$ Mark$]$