Consider a system of 3 fermions, which can occupy any of the 4 available energy states with equal
probability. The entropy of the system is
(A) kkBBln2 (B) 2kkBBln2 (C) 2kkBBln4 (D) 3kkBBln4
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2014 Q.47)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Statistical Physics & Thermodynamics** within *Section 5: Thermodynamics and Statistical Physics* (2 Marks, 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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