Water at 300 K can be brought to 320 K using one of the following processes.
Process 1: Water is brought in equilibrium with a reservoir at 320 K directly.
Process 2: Water is first brought in equilibrium with a reservoir at 310 K and then
with the reservoir at 320 K.
Process 3: Water is first brought in equilibrium with a reservoir at 350 K and then
with the reservoir at 320 K.
The corresponding changes in the entropy of the universe for these processes are
∆Sଵ, ∆Sଶ and ∆Sଷ, respectively. Then
Options:
(A) ∆Sଶ > ∆Sଵ > ∆Sଷ
(B) ∆Sଷ > ∆Sଵ > ∆Sଶ
(C) ∆Sଷ > ∆Sଶ > ∆Sଵ
(D) ∆Sଵ > ∆Sଶ > ∆Sଷ
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2022 Q.37)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Statistical Physics & Thermodynamics** within *Section 5: Thermodynamics and Statistical Physics* (2 Marks, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Statistical Physics & Thermodynamics:
- Applying canonical quantum/electrodynamic equations:
$\hat{H}\psi = E\psi, \quad \nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}, \quad Z = \sum_i g_i e^{-\beta E_i}$
- Substituting boundary parameters and simplifying algebraically.
- The resulting expression uniquely corresponds to Option **(B)**.
**3. Final Answer**:
Correct Option is **(B)**.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.