Final answer:
The effluent concentration of a conservative pollutant in a fully mixed lagoon at steady state equals the influent concentration. For a non-conservative pollutant with degradation, the effluent concentration is lower, factoring in the rate of decay. If the influent concentration changes, the concentration in the effluent will need time to adjust based on the retention time and decay rate.
Step-by-step explanation:
The question is related to the principles of environmental engineering, specifically the steady-state concentration of pollutants in a lagoon under completely mixed conditions. For a conservative pollutant, which does not undergo chemical transformation or biological degradation, the concentration in the effluent is the same as the concentration of the waste entering the lagoon.
(a) The concentration of pollutant leaving the lagoon is 10 mg/L since it reaches a steady-state under completely mixed conditions, meaning the input concentration equals the output concentration.
(b) With a new input concentration of 100 mg/L, the concentration of the effluent after 7 days can be calculated using the hydraulic retention time, which in this case is the volume of the lagoon divided by the flow rate (1200 m³ / 100 m³/day = 12 days). However, since 7 days is not enough time to reach the new steady state, the concentration in the lagoon will be a value between 10 mg/L and 100 mg/L and will depend on the inflow and mixing conditions.
(c) For a non-conservative pollutant with a decay rate k=0.2/day, the steady-state concentration can be found by balancing the inflow concentration and degradation rate using first-order kinetics. The concentration will be lower than the inflow concentration of 10 mg/L, as some of the pollutant undergoes degradation.