Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
Milk flowing through a stainless steel inner tube (40 mm inner diameter) of
double tube-type heater is to be heated from 10 °C to 85 °C by saturated
steam condensing at 120°C on the outer surface of the inner tube. Total heat
transferred (Q) is 146200 kcal h-1 and the overall heat transfer
coefficient is 750 kcal h-1 m-2°C-1. The total length of the heating
tube in m (rounded off to one decimal place) is _
Official Answer Key:
23.0 - 24.0
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2021 Q.62)**
**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: *"Milk flowing through a stainless steel inner tube (40 mm inner diameter) of
double tube-type heater is to be heated from 10 °C to 85 °C by saturated
steam condensing at 120°C on the outer surface of the inner tube. Total..."*
- Identifying governing bioprocess / mathematical relation:
- For heat transfer across a heat exchanger:
$q = U A \Delta T_{lm}$
$\Delta T_{lm} = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1 / \Delta T_2)}$
- **Official Answer Key Interval**: Evaluated numerical range is **23.0 to 24.0** (Target value: **23.0 to 24.0**).
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **23.0 to 24.0**
- **Scoring Criteria**: 2 Marks (Negative marking: -0.0 marks).
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