GATE 2022 BT – Question 58
A batch ends with 50 g biomass. Fed-batch feeding is 1 L/h of 50 g/L substrate, with maximum yield 0.4 g/g. Under quasi-steady conditions, maximum biomass after 5 h is ___________ g.
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Correct answer: 150
Explanation
In a fed-batch culture with a constant feed, under **quasi-steady state** the substrate that is fed is consumed immediately, so the biomass produced equals the yield times the substrate added.
**Step 1: substrate fed in 5 h.**
$$\text{feed rate}=1\text{ L/h}\times50\text{ g/L}=50\text{ g/h},\qquad\text{total}=50\times5=250\text{ g}.$$
**Step 2: biomass formed** with the maximum yield $Y_{X/S}=0.4$ g/g:
$$\Delta X=0.4\times250=100\text{ g}.$$
**Step 3: total biomass** (the batch phase ended with 50 g):
$$X_{max}=50+100=\mathbf{150\ g}.$$