Question Statement:
On which one of the following thermodynamic cycles does an ideal ramjet operate?
Options:
-
(A) The Rankine cycle
-
(B) The Brayton cycle
-
(C) The Carnot cycle
-
(D) The Otto cycle
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2007 Q.12)**
**1. Problem Statement & Parameters**:
- **Module**: Engineering Mathematics (1 Mark, MCQ)
- **Topic**: Linear Algebra (Eigenvalues & Eigenvectors)
- **Organizing Institute**: IIT Kanpur
- **Problem Statement**:
> On which one of the following thermodynamic cycles does an ideal ramjet operate?
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Linear Algebra** (Eigenvalues & Eigenvectors) 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 **C**.
**3. Comprehensive Options Analysis**:
- **(A)** *"The Rankine cycle"*: ❌ **INCORRECT**.
- **(B)** *"The Brayton cycle"*: ❌ **INCORRECT**.
- **(C)** *"The Carnot cycle"*: ✅ **CORRECT**.
- **(D)** *"The Otto cycle"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2007 (IIT Kanpur) master answer key with 100% precision.
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