Section 4: Bioprocess Engineering and Process Biotechnology
Bioreactor types, scale-up
Subtopic: Fundamentals of Bioreactor types, scale-up
Question Statement:
If the doubling time of a bacterial population is 3 hours, then its average specific
growth rate during this period is _____ h-1.
(Round off to two decimal places)
Official Answer Key:
0.20 to 0.25
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2025 Q.28)**
**1. Governing Concept & Definition**:
- **Topic**: Microbial Growth Kinetics & Exponential Growth
- The specific growth rate ($\mu$) during the exponential growth phase is related to the doubling time ($t_d$) by:
$\mu = \frac{\ln(2)}{t_d}$
**2. Detailed Step-by-Step Calculation**:
- **Given**:
- Doubling time ($t_d$) = $3\text{ hours}$
- Natural logarithm of 2: $\ln(2) \approx 0.69315$
- **Calculation**:
$\mu = \frac{0.69315}{3\text{ h}} \approx 0.231\text{ h}^{-1}$
**3. Final Answer**:
- **Calculated Value**: **0.23 h⁻¹**
- **Official GATE Accepted Range**: **0.20 to 0.25**
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