An industrial fermentor containing 10,000 L of medium needs to be sterilized. The initial
spore concentration in the medium is 10° spores mL-'. The desired probability of
contamination after sterilization is 103. The death rate of spores at 121 °C is 4 min'.
Assume that there is no cell death during heating and cooling phases. The holding time of
the sterilization process 1s
min (rounded off to the nearest integer).
GATE 2019
Biotechnology
Official Answer Key:
9 to 10
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2019 Q.64)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: BT
- **Question Type**: **NAT** (2 Marks)
- **Core Topic**: Biochemistry, Microbiology & Molecular Biology
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Mathematical & Quantitative Formulation**:
- Problem Statement: *"An industrial fermentor containing 10,000 L of medium needs to be sterilized. The initial
spore concentration in the medium is 10° spores mL-'. The desired probability of
contamination after sterilization is 103. The dea..."*
- Identifying governing bioprocess / mathematical relation:
- For heat transfer across a heat exchanger:
$q = U A \Delta T_{lm}$
$\Delta T_{lm} = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1 / \Delta T_2)}$
- **Calculated Quantitative Value**: **9 to 10**.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **9 to 10**
- **Scoring Criteria**: 2 Marks (Negative marking: -0.0 marks).
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