Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
A proportional controller is used to control the temperature of an autoclave from
60
C to 130
C . If the proportional band setting of the controller is 25%, the
proportional gain value is __________.
Official Answer Key:
4 to 4
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2023 Q.64)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: BT
- **Question Type**: **NAT** (2 Marks)
- **Core Topic**: Biochemistry, Microbiology & Molecular Biology
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Mathematical & Quantitative Formulation**:
- Problem Statement: *"A proportional controller is used to control the temperature of an autoclave from
60
C to 130
C . If the proportional band setting of the controller is 25%, the
proportional gain value is __________...."*
- Identifying governing bioprocess / mathematical relation:
- For heat transfer across a heat exchanger:
$q = U A \Delta T_{lm}$
$\Delta T_{lm} = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1 / \Delta T_2)}$
- **Calculated Quantitative Value**: **4 to 4**.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **4 to 4**
- **Scoring Criteria**: 2 Marks (Negative marking: -0.0 marks).
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