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GATE 2020 CE (CE2) – Question 26

Water and Waste Water Quality and Treatment · Water quality standards, parameters and water quality index · 1 mark · Multiple choice

The graph relates oxygen consumed (BOD exerted) and biodegradable organic demand remaining in a closed container. Rate obeys $dL_t/dt=-kL_t$, where $L_t$ (mg/L) is oxygen-equivalent organics remaining at t, k (day⁻¹) is decay constant and $L_0$ is initial demand. Which expression is correct?

Diagram for GATE 2020 CE (CE2) question 26
  1. $BOD_5=L_5$
  2. $BOD_t=L_0-L_t$
  3. $L_0=L_te^{-kt}$
  4. $L_t=L_0(1-e^{-kt})$

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Correct answer: (B) $BOD_t=L_0-L_t$

Explanation

First-order decay gives $L_t=L_0e^{-kt}$. Exerted demand equals initial minus remaining: **$BOD_t=L_0-L_t$, B**. The two plotted demands sum to the constant initial demand.