The GATE Grind

GATE 2025 CH – Question 23

Chemical Reaction Engineering · Non-ideal reactors and residence time distribution · 1 mark · Multiple choice

Choose the CORRECT statement that describes the dependence of the variance ($\sigma_\Theta^2$) of the residence time distribution (RTD) with respect to the number of tanks ($n$) in the Tanks-in-Series model of non-ideal reactors.

  1. $\sigma_\Theta^2$ monotonically increases with $n$
  2. $\sigma_\Theta^2$ first increases and then decreases with $n$
  3. $\sigma_\Theta^2$ first decreases and then increases with $n$
  4. $\sigma_\Theta^2$ monotonically decreases with $n$

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Show answer and explanation

Correct answer: (D) $\sigma_\Theta^2$ monotonically decreases with $n$

Explanation

For $n$ equal tanks in series the dimensionless variance is $\sigma_\Theta^2 = \frac{1}{n}$. It falls steadily as $n$ rises, from 1 for one tank (mixed flow) towards 0 for plug flow.