Section 4: Bioprocess Engineering and Process Biotechnology
Bioreactor types, scale-up
Subtopic: Fundamentals of Bioreactor types, scale-up
Question Statement:
Consider a continuous culture provided with a sterile feed containing 10 mM glucose. The steady
state cell density and substrate concentration at three different dilution rates are given in the table
below.
Dilution rate (h-1)
Cell density (g L-1)
Substrate concentration (mM)
Q.05
Q.248
Q.067
Q.5
Q.208
1.667
5
0
10
The maximum specific growth rate µm (in h−1), will be _____.
Official Answer Key:
0.80
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2014 Q.41)**
**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: *"Consider a continuous culture provided with a sterile feed containing 10 mM glucose. The steady
state cell density and substrate concentration at three different dilution rates are given in the table
below.
Dilution..."*
- Identifying governing bioprocess / mathematical relation:
- In a continuous stirred tank bioreactor (chemostat) at steady state:
$\mu = D = \frac{F}{V}$
where $\mu$ is the specific growth rate ($ ext{h}^{-1}$), $D$ is the dilution rate, $F$ is volumetric feed flow rate, and $V$ is working volume.
$S = \frac{K_s D}{\mu_{max} - D}, \quad X = Y_{X/S}(S_0 - S)$
- **Official Answer Key Interval**: Evaluated numerical range is **0.795 to 0.805** (Target value: **0.795 to 0.805**).
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **0.795 to 0.805**
- **Scoring Criteria**: 1 Mark (Negative marking: -0.0 marks).
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