GATE 2026 BT – Question 56
A CSTR with a volume of 100 m$^3$ is operated in cell recycle mode. At a volumetric flow rate of 10 m$^3$ day$^{-1}$ and effluent biomass of 20 mg L$^{-1}$, the steady state biomass concentration is 200 mg L$^{-1}$. The mean cell retention time in the reactor is ____ days. (answer in integer)
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Correct answer: 100 to 100
Explanation
The mean cell retention time is the biomass in the reactor divided by the rate at which biomass leaves: $\theta_c = \frac{VX}{QX_e} = \frac{100 \times 200}{10 \times 20} = 100$ days.
Official GATE 2026 answer key: https://gate2026.iitg.ac.in/doc/download/2026/Keys/BT_Keys.pdf