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Q#1 GATE CH 2024 NAT +2 marks -0 marks

A chemostat with cell recycle is shown in the figure. The feed flow rate and culture volume are\(𝐹 = 75 L h^{-1}\) and 𝑉 = 200 L, respectively. The glucose concentration in the feed \(C_{S0} = 15 g L^{−1}\). Assume Monod kinetics with specific cell growth rate, 

\(\begin{align*} \mu_g = \frac{1}{C_C} \frac{dC_C}{dt} = \frac{\mu_m C_S}{K_S + C_S}, \quad \text{where} \quad \mu_m = 0.25 \text{ h}^{-1} \text{ and } K_S = 1 \text{ g L}^{-1}. \end{align*}\)

Assume maintenance and death rates to be zero, input feed to be sterile (CC0 = 0) and steadystate operation. The glucose concentration in the recycle stream, CS1, in g L−1, rounded off to 1 decimal place, is _________

.

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