Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
Consider a piston-cylinder assembly shown in the figure below. The walls of the
cylinder are insulated. The cylinder contains 1 mole of an ideal gas at 300 K and
the piston is held initially at the position z1 using a stopper. After the stopper is
removed, the piston suddenly rises against atmospheric pressure (1.013Γ105 Pa)
to the new position z2 where it is held by another stopper.
The heat capacity (Cv) of the gas is 12.5 J mol-1 K-1. The cross-sectional area of
the cylinder is 10-3 m2. Assume the piston is weightless and frictionless.
If π§ΰ¬Άβ π§ΰ¬΅ = 1 m, the final temperature of the gas (rounded off to nearest integer)
is ___________K.
Official Answer Key:
291 to 293
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2022 Q.61)**
**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: *"Consider a piston-cylinder assembly shown in the figure below. The walls of the
cylinder are insulated. The cylinder contains 1 mole of an ideal gas at 300 K and
the piston is held initially at the position z1 using a ..."*
- 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**: **291 to 293**.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **291 to 293**
- **Scoring Criteria**: 2 Marks (Negative marking: -0.0 marks).
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