Section 4: Bioprocess Engineering and Process Biotechnology
Media Sterilization and Stoichiometry
Subtopic: Thermal Sterilization & Stoichiometry
Question Statement:
A batch sterilizer is being operated at 121 oC for sterilizing a medium containing
microbial cells. Assume that the thermal deactivation of cells is a first order process
with a death rate constant of 0.69 min-1 at 121 oC. If the initial concentration of
microbes in the medium is 1010 cells m-3, the time taken to reduce the microbial load
to a final concentration of 10 cells m-3 is _________ min. (rounded off to the nearest
integer)
Official Answer Key:
30 to 30
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2026 Q.59)**
**1. Governing Concept & Definition**:
- **Topic**: Bioprocess Sterilization Kinetics & Thermal Death
- Thermal deactivation follows first-order kinetics:
$\ln\left(\frac{N_0}{N}\right) = k_d \cdot t \implies t = \frac{\ln(N_0/N)}{k_d}$
where $\nabla = \ln(N_0/N)$ is the Del factor.
**2. Detailed Step-by-Step Calculation**:
- **Given**:
- Initial microbial concentration $N_0 = 10^{10}\text{ cells m}^{-3}$
- Final target concentration $N = 10\text{ cells m}^{-3}$
- Specific death rate constant $k_d = 0.69\text{ min}^{-1}$
- **Step 1: Calculate Del factor ($\nabla$)**:
$\nabla = \ln\left(\frac{10^{10}}{10}\right) = \ln(10^9) = 9 \times \ln(10) \approx 9 \times 2.302585 = 20.723$
- **Step 2: Calculate sterilization time ($t$)**:
$t = \frac{20.723}{0.69\text{ min}^{-1}} \approx 30.03\text{ min} \approx 30\text{ min}$
**3. Final Answer**:
- **Calculated Value**: **30 min**
- **Official GATE Accepted Range**: **30 to 30**
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