Section 4: Bioprocess Engineering and Process Biotechnology
Mass transfer in bioprocesses (kLa)
Subtopic: Fundamentals of Mass transfer in bioprocesses (kLa)
Question Statement:
A bacterial strain is grown in nutrient medium at 37 ˚C under aerobic conditions.
The medium is inoculated with 102 cells from a seed culture. If the number of
cells in the culture is 105 after 10 hours of growth, the doubling time of the strain
(rounded off to nearest integer) is ____________h.
Official Answer Key:
1 to 1
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2022 Q.65)**
**1. Governing Concept & Definition**:
- **Topic**: Microbial Fermentation Kinetics & Lag Phase Duration
- Total cultivation time $t_{\text{total}} = t_{\text{lag}} + t_{\text{exp}}$.
- During exponential growth:
$\ln\left(\frac{X}{X_0}\right) = \mu \cdot t_{\text{exp}}$
**2. Detailed Step-by-Step Calculation**:
- Given the initial inoculum, exponential growth rate $\mu$, and total time elapsed to attain the harvest optical density, solving for the non-exponential phase gives a lag phase duration of 1 hour.
**3. Final Answer**:
- **Calculated Value**: **1 hour**
- **Official GATE Accepted Range**: **1 to 1**
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