Media Sterilization and Stoichiometry

### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2021 Q.32)** **1. Governing Concept & Definition**: - **Topic**: Bioprocess Sterilization & Decimal Reduction Time ($D$-value) - The decimal reduction time ($D$) is the time required at a given temperature to reduce the viable microbial population by $90\%$ (one logarithm base 10): $k_d = \frac{\ln(10)}{D} = \frac{2.3026}{D}$ where $k_d$ is the first-order specific thermal death rate constant. **2. Detailed Step-by-Step Calculation**: - **Given**: - Decimal reduction time $D = 20\text{ min}$ - $\ln(10) \approx 2.302585$ - **Calculation of $k_d$**: $k_d = \frac{2.302585}{20\text{ min}} \approx 0.1151\text{ min}^{-1} \approx 0.12\text{ min}^{-1}$ **3. Final Answer**: - **Calculated Value**: **0.12 min⁻¹** - **Official GATE Accepted Range**: **0.10 to 0.13**