# DBT JRF 2022 — Question 99

Exam: DBT JRF 2022 · Section: B · Topic: Bioprocess Engineering › CSTR Steady State Characteristics · Difficulty: Easy

## Question

In an ideal Continuous Stirred Tank Reactor (CSTR) at steady state:

## Options

- **A.** All particles have the same residence time.
- **B.** Particles which enter the reactor earlier have a higher probability of leaving than those that enter later.
- **C.** Particles which enter the reactor later have a higher probability of leaving than those that enter earlier.
- **D.** All the particles have equal probability of leaving, independent of their time of entry into the reactor.

## Answer

Option D

## Explanation

CSTR (Continuous Stirred Tank Reactor) residence time distribution: An ideal CSTR is characterised by PERFECT MIXING: every element of fluid in the reactor is equally mixed at any instant. Consequence of perfect mixing: • The composition of fluid leaving the reactor equals the composition of fluid inside the reactor. • Every fluid element has an EQUAL probability of leaving the reactor at any moment (regardless of how long it has been in the reactor). • This gives an EXPONENTIAL residence time distribution (RTD): $E(t) = \frac{1}{\tau} e^{-t/\tau}$ where $\tau = V/F$ = mean residence time. • Many fluid elements leave quickly (short residence times) and fewer stay for long times. Contrast with a plug flow reactor (PFR), where all elements have exactly the same residence time $\tau$ (no mixing, delta-function RTD). Answer: Ideal CSTR: perfect mixing → each particle has equal probability of leaving at any instant → exponential RTD.

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