GATE 2023 BT – Question 48
E. coli is cultivated in a chemostat at dilution rate $0.2\ \mathrm{h^{-1}}$. Biomass yield due to oxygen consumption is $0.2\ \mathrm{g/g}$ and steady biomass concentration is $10\ \mathrm{g/L}$. The oxygen transfer rate (in $\mathrm{g\ L^{-1}h^{-1}}$) is ___________.
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Correct answer: 10
Explanation
In a chemostat at steady state, the biomass is produced at the same rate it is washed out, so the specific growth rate equals the dilution rate, $\mu=D$.
**Step 1: biomass production rate.**
$$r_X=D\,X=0.2\ \text{h}^{-1}\times10\ \text{g/L}=2\ \text{g L}^{-1}\text{h}^{-1}.$$
**Step 2: oxygen uptake rate.** The yield on oxygen is $Y_{X/O_2}=0.2$ g biomass per g $O_2$, so
$$OUR=\frac{r_X}{Y_{X/O_2}}=\frac{2}{0.2}=10\ \text{g L}^{-1}\text{h}^{-1}.$$
**Step 3: transfer rate.** At steady state, oxygen is supplied exactly as fast as it is consumed, so
$$OTR=OUR=\mathbf{10\ g\,L^{-1}h^{-1}}.$$