# DBT JRF 2020 — Question 105

Exam: DBT JRF 2020 · Section: B · Topic: Bioprocess Engineering · Difficulty: Hard

## Question

At what condition does the specific growth rate of the microorganisms decline in a constant volume fed-batch culture

## Options

- **A.** cell biomass remains constant
- **B.** cell biomass is equal to zero
- **C.** cell biomass decreasing
- **D.** cell biomass increasing

## Answer

Option D

## Explanation

In a constant-volume fed-batch culture, substrate feed rate $F$ (L/h) is fixed and feed substrate concentration $S_f$ is constant. Substrate mass balance: $\dfrac{dS}{dt} = \dfrac{F S_f}{V} - \dfrac{\mu X}{Y_{X/S}}$ . As fermentation proceeds, cell biomass $X$ (g/L) increases. With fixed $F S_f / V$ , the substrate consumption term $\mu X / Y_{X/S}$ increases with increasing $X$ . To maintain mass balance, $S$ falls → from Monod kinetics $\mu = \dfrac{\mu_{\max} S}{K_s + S}$ , decreasing $S$ → decreasing $\mu$ . Therefore, as BIOMASS INCREASES in a constant-volume fed-batch culture, the specific growth rate DECLINES. This is a controlled growth strategy used to reduce oxygen demand, minimise acetate overflow in E. coli, and produce dense cultures.

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