GATE 2018 CE (CE1) – Question 62
Ultimate BOD is 87% of COD, which is 300 mg/L. First-order natural-log rate constant is 0.23 day⁻¹ and temperature coefficient 1.047. BOD after three days at 27°C, to one decimal, is ______ mg/L.
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Correct answer: 154.0 to 161.0
Explanation
Ultimate BOD is $0.87(300)=261$ mg/L. Correct the conventional 20°C rate: $k_{27}=0.23(1.047)^7=0.31722$ day⁻¹. Three-day exerted BOD is $261[1-e^{-3k_{27}}]=160.2267$ mg/L, or 160.2 mg/L.