Section 4: Bioprocess Engineering and Process Biotechnology
Mass transfer in bioprocesses (kLa)
Subtopic: Fundamentals of Mass transfer in bioprocesses (kLa)
Question Statement:
To facilitate mass transfer from a gas to a liquid phase, a gas bubble of radius r is
introduced into the liquid. The gas bubble then breaks into 8 bubbles of equal
radius. Upon this change, the ratio of the interfacial surface area to the gas phase
volume for the system changes from 3/r to 3n/r. The value of n is
Official Answer Key:
2 to 2
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2020 Q.32)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: BT
- **Question Type**: **NAT** (1 Mark)
- **Core Topic**: Biochemistry, Microbiology & Molecular Biology
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Mathematical & Quantitative Formulation**:
- Problem Statement: *"To facilitate mass transfer from a gas to a liquid phase, a gas bubble of radius r is
introduced into the liquid. The gas bubble then breaks into 8 bubbles of equal
radius. Upon this change, the ratio of the interfacial ..."*
- Identifying governing bioprocess / mathematical relation:
- Evaluating volumetric mass transfer rate for oxygen in aerobic fermentation:
$\text{OTR} = k_L a (C^* - C_L)$
where $k_L a$ is volumetric mass transfer coefficient, $C^*$ is equilibrium saturation dissolved oxygen concentration, and $C_L$ is actual bulk liquid concentration.
- **Calculated Quantitative Value**: **2 to 2**.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **2 to 2**
- **Scoring Criteria**: 1 Mark (Negative marking: -0.0 marks).
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.