GATE 2022 CE (CE1) – Question 60
A 2 % sewage sample (in distilled water) was incubated for 3 days at 27 °C temperature. After incubation, a dissolved oxygen depletion of 10 mg/L was recorded. The biochemical oxygen demand (BOD) rate constant at 27 °C was found to be 0.23 day-1 (at base e). The ultimate BOD (in mg/L) of the sewage will be_____________. (round off to the nearest integer)
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Correct answer: 1003
Explanation
The observed 10 mg/L depletion occurs in a 2% sample, so the sewage’s three-day BOD is $10/0.02=500$ mg/L.
For a base-e rate constant, $BOD_t=L_0(1-e^{-kt})$. Thus $L_0=500/(1-e^{-0.23(3)})=1002.985$ mg/L, rounded to **1003 mg/L**.