One mole of an ideal monatomic gas at absolute temperature T undergoes free
expansion to double its original volume , so that the entropy change is ΔS1. An
identical amount of the same gas at absolute temperature 2 T undergoes isothermal
expansion to double its original volume , so that the entropy change is ΔS2. The
value of
ΔS1
ΔS2
(in integer) is ____
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2025 Q.30)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Statistical Physics & Thermodynamics** within *Section 5: Thermodynamics and Statistical Physics* (1 Mark, NAT).
**2. Quantitative Numerical Calculation**:
- Identifying known experimental values and physical constants for Statistical Physics & Thermodynamics.
- 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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