Statistical Physics & Thermodynamics

### **Official Solution & Step-by-Step Derivation (GATE PH 2012 Q.32)** **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**.