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GATE 2025 MN – Question 64

Surface Environment, Mine Ventilation and Underground Hazards · Surface Environment · 2 marks · Numerical answer

Ultimate BOD is300 mg/L. The20°C rate constant is0.22/day and temperature coefficient1.05. Find5-day BOD at25°C in mg/L to two decimals.

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Correct answer: 220.00 to 230.00

Explanation

Correct the natural-exponential rate to25°C:k25=0.22×1.05⁵≈0.28078/day. BOD exerted after5 days is L₀[1−exp(−k25×5)]. Thus300[1−exp(−1.40391)]≈226.31 mg/L. The ultimate demand remains300;temperature changes the rate at which it is exerted.

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