GATE CE 2019 Set 2 — Question 42
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Environmental Engineering → Drinking Water Treatment → Chlorination
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Question
Chlorine is used as the disinfectant in a municipal water treatment plant. It achieves 50 percent of disinfection efficiency measured in terms of killing the indicator microorganisms (E-Coli) in 3 minutes. The minimum time required to achieve 99 percent disinfection efficiency would be
Correct answer
(C) 19.93 minutes
Solution
Disinfection kinetics typically follow Chick's Law: , where is the number of organisms at time , is the initial number, and is the rate constant.
Efficiency , so .For 50% efficiency () at minutes:For 99% efficiency ():Alternatively, using the ratio:
Efficiency , so .For 50% efficiency () at minutes:For 99% efficiency ():Alternatively, using the ratio:
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