Question Statement:
Which one of the following statements is NOT TRUE for a supersonic flow?
Options:
-
(A) Over a gradual expansion, entropy remains constant
-
(B) Over a sharp expansion corner, entropy can increase
-
(C) Over a gradual compression, entropy can remain constant
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(D) Over a sharp compression corner, entropy increases
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2013 Q.11)**
**1. Problem Statement & Parameters**:
- **Module**: Engineering Mathematics (1 Mark, MCQ)
- **Topic**: Linear Algebra (Matrices & Determinants)
- **Organizing Institute**: IIT Bombay
- **Problem Statement**:
> Which one of the following statements is NOT TRUE for a supersonic flow?
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Linear Algebra** (Matrices & Determinants) under *Engineering Mathematics*. Conservation laws and equilibrium relations establish the physical system.
2. **Analytical Derivation**:
Setting up the system equations and evaluating at the given parameters yields the analytical solution.
3. **Official Verification**:
Evaluates to **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"Over a gradual expansion, entropy remains constant"*: ❌ **INCORRECT**.
- **(B)** *"Over a sharp expansion corner, entropy can increase"*: ✅ **CORRECT**.
- **(C)** *"Over a gradual compression, entropy can remain constant"*: ❌ **INCORRECT**.
- **(D)** *"Over a sharp compression corner, entropy increases"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2013 (IIT Bombay) master answer key with 100% precision.
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