GATE 2016 CE (CE1) – Question 62
The 2-day and 4-day BOD values of a sewage sample are 100 mg/L and 155 mg/L, respectively. The value of BOD rate constant (expressed in per day) is _________
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Correct answer: 0.29 to 0.31
Explanation
Write BODt=L0(1−exp(−kt)). Put a=exp(−2k); then BOD4/BOD2=(1−a²)/(1−a)=1+a. The given155/100=1.55 implies a=0.55. Therefore k=−ln0.55/2=**0.29892day⁻¹**; the logarithm is natural because the model is base e.