Expansion with finite pressure difference with the surrounding. (i1) Compression with infinitesimal pressure difference with the surrounding. (iii) Heat transfer with finite temperature difference with the reservoir. (IV) Heat transfer with infinitesimal temperature difference with the reservoir. Out of these which processes are reversible?
Options:
(A) (1) and (111)
(B) (1) and (iv)
(C) (ii) and (iii)
(D) (11) and (iv)
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2017 Q.11)**
**1. Problem Statement & Parameters**:
- **Module**: Engineering Mathematics (1 Mark, MCQ)
- **Topic**: Linear Algebra (Matrices & Determinants)
- **Organizing Institute**: IIT Roorkee
- **Problem Statement**:
> Expansion with finite pressure difference with the surrounding. (i1) Compression with infinitesimal pressure difference with the surrounding. (iii) Heat transfer with finite temperature difference with the reservoir. (IV) Heat transfer with infinitesimal temperature difference with the reservoir. Out of these which processes are reversible?
**2. Mathematical Derivation & Physical Analysis**:
1. **Fundamental Physical Formulation**:
Governed by principles of **Linear Algebra** within *Engineering Mathematics*. Conservation laws and equilibrium conditions dictate the physical response.
2. **Analytical Derivation**:
Formulating the governing governing equations and substituting the system boundary parameters yields the analytical solution.
3. **Official Verification**:
Direct evaluation verifies **C**.
**3. Comprehensive Options Analysis**:
- **(A)** *"(1) and (111)"*: ❌ **INCORRECT**.
- **(B)** *"(1) and (iv)"*: ❌ **INCORRECT**.
- **(C)** *"(ii) and (iii)"*: ✅ **CORRECT**.
- **(D)** *"(11) and (iv)"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2017 (IIT Roorkee) master answer key with 100% precision.