Section 4: Bioprocess Engineering and Process Biotechnology
Bioreactor types, scale-up
Subtopic: Fundamentals of Bioreactor types, scale-up
Question Statement:
The decimal reduction time of a microbe during sterilization at 120 C with a first
order thermal death rate constant of 1 min -1 will be ________ min (rounded off to
1 decimal place).
Official Answer Key:
2.3 to 2.3
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2024 Q.35)**
**1. Governing Concept & Definition**:
- **Topic**: Thermal Sterilization & Decimal Reduction Time ($D$-value)
- **Decimal Reduction Time ($D$)**: The time required at a given temperature to reduce the microbial population by 90% (i.e. one logarithmic decade, from $N_0$ to $0.1 N_0$).
**2. Detailed Step-by-Step Calculation**:
- **Given**: First-order thermal death rate constant $k = 1.0 ext{ min}^{-1}$ at $120^\circ ext{C}$.
- **Relationship between $D$ and $k$**:
$\ln\left( rac{N_0}{N}
ight) = k \cdot t$
For a 10-fold reduction ($N/N_0 = 0.1$ or $N_0/N = 10$):
$\ln(10) = k \cdot D$
$D = rac{\ln(10)}{k} = rac{2.3026}{k}$
- **Substitution**:
$D = rac{2.3026}{1.0 ext{ min}^{-1}} pprox 2.30 ext{ min}$
**3. Final Answer**:
- **Calculated Value**: **2.3**
- **Official GATE Accepted Range**: **2.3 to 2.3**
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