GATE Civil Engineering (CE) 2019 Shift 2 Solved Paper

Question : 52 of 65

Marks: +1, -0

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

$9.93$ minutes
$11.93$ minutes
$21.93$ minutes
$19.93$ minutes

Validate

Solution:

Disinfection eff

=\;{ {N}_{ {0}}- {N}}/{ {N}_{0}}

=\;{N_{0}-N_{0} {e}^{-k t}}/{ {N}_{0}}=(1- {e}^{-kt})

0.5=1-e^{-kx 3}

⇒ \;\; k=\;{ℓ n 2}/{3}

Again,

0.99=1-e^{{\ln 2}/{3} xt}

⇒ \;\; 0.01=e^{-\;{\ln 2}/{3} x t}

⇒ \;\; -4.605=-\;{\ln 2}/{3} × {t}

⇒ {t}=19.93 {min}

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