Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
An evaporator is insulated using glass wool material of 0.15 m thickness. The
inner most surface and the outer surface of the insulation are at
700 C and
80 C
, respectively. The mean thermal conductivity of the glass wool under these
conditions is
110.29 . .W m K-- . The rate of heat loss (in
W ) through
21.2 m of the
evaporator wall surface (rounded off to the nearest integer) is __________.
Official Answer Key:
1437 to 1439
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2023 Q.63)**
**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: *"An evaporator is insulated using glass wool material of 0.15 m thickness. The
inner most surface and the outer surface of the insulation are at
700 C and
80 C
, respectively. The mean thermal conductivity of the gla..."*
- 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**: **1437 to 1439**.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **1437 to 1439**
- **Scoring Criteria**: 2 Marks (Negative marking: -0.0 marks).
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