GATE BT 2026 • Q55 NAT • 2 Marks

Section 4: Bioprocess Engineering and Process Biotechnology

Bioreactor types, scale-up

Subtopic: Fundamentals of Bioreactor types, scale-up

Question Statement:

A microbial culture (following Monod model for growth) has a maximum specific growth rate of 0.1 h -1, Monod constant of 1 mg L -1 and endogenous decay rate of Q.1 day-1. At limiting substrate concentration of 23 g L-1, the net specific growth rate will be ________day-1. (rounded off to one decimal place)

Official Answer Key:

2.2 to 2.4

Step-by-Step Solution & Explanation

### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2026 Q.55)** **1. Governing Concept & Definition**: - **Topic**: Microbial Kinetics & Net Specific Growth Rate - Net specific growth rate ($\mu_{\text{net}}$) accounts for endogenous decay ($k_d$): $\mu_{\text{net}} = \mu - k_d = \frac{\mu_{\max} S}{K_s + S} - k_d$ **2. Detailed Step-by-Step Calculation**: - **Given**: - $\mu_{\max} = 0.1\text{ h}^{-1} = 0.1 \times 24\text{ day}^{-1} = 2.4\text{ day}^{-1}$ - $K_s = 1\text{ mg L}^{-1} = 0.001\text{ g L}^{-1}$ - Limiting substrate concentration $S = 23\text{ g L}^{-1}$ - Since $S \gg K_s$ ($23\text{ g L}^{-1} \gg 0.001\text{ g L}^{-1}$): $\frac{S}{K_s + S} \approx 1.000$ $\mu \approx \mu_{\max} = 2.4\text{ day}^{-1}$ - Endogenous decay rate $k_d = 0.1\text{ day}^{-1}$ - **Step 1: Calculate $\mu_{\text{net}}$**: $\mu_{\text{net}} = 2.4\text{ day}^{-1} - 0.1\text{ day}^{-1} = 2.3\text{ day}^{-1}$ **3. Final Answer**: - **Calculated Value**: **2.3 day⁻¹** - **Official GATE Accepted Range**: **2.2 to 2.4**

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