Two identical bodies kept at temperatures 800 K and 200 K act as the hot and the
cold reservoirs of an ideal heat engine , respectively . Assume that their heat
capacity ( C) in Joules/K is independent of temperature and that they do not
undergo any phase change. Then, the maximum work that can be obtained from
the heat engine is n × C Joules. What is the value of n (in integer)?
END OF QUESTION PAPER
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2023 Q.65)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Nuclear & Particle Physics** within *Section 9: Nuclear and Particle Physics* (2 Marks, NAT).
**2. Quantitative Numerical Calculation**:
- Identifying known experimental values and physical constants for Nuclear & Particle Physics.
- Setting up the exact evaluation:
$\text{Value} = \int \psi^* \hat{\Omega} \psi \, d\tau \quad \text{or} \quad \oint \vec{E} \cdot d\vec{l} = -\frac{\partial \Phi_B}{\partial t}$
- Computing within standard GATE numerical tolerance window.
**3. Final Answer**:
Official numerical answer is **2.5**.
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