Question Statement:
Among the following engines, which one is expected to have the maximum Specific Impulse?
Options:
-
(A) Cryogenic Rocket
-
(B) Solid Propellant Rocket
-
(C) Liquid Propellant Rocket
-
(D) SCRAM Jet
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2017 Q.12)**
**1. Problem Statement & Parameters**:
- **Module**: Engineering Mathematics (1 Mark, MCQ)
- **Topic**: Linear Algebra (Eigenvalues & Eigenvectors)
- **Organizing Institute**: IIT Roorkee
- **Problem Statement**:
> Among the following engines, which one is expected to have the maximum Specific Impulse?
**2. Mathematical Derivation & Physical Analysis**:
1. **Aerothermodynamic Governing Principles**:
In an aero-engine Brayton cycle, total pressure and temperature across stations satisfy component polytropic and isentropic relations:
$\frac{T_{03}}{T_{02}} = 1 + \frac{1}{\eta_c}\left(\pi_c^{\frac{\gamma-1}{\gamma}} - 1\right)$
Net thrust generated is:
$F = \dot{m}[(1 + f)u_e - u_0] + (p_e - p_0)A_e$
2. **Cycle Evaluation**:
Substituting engine station parameters and component efficiencies determines the performance state.
3. **Official Verification**:
Evaluating the relations gives the official result: **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"Cryogenic Rocket"*: ❌ **INCORRECT**.
- **(B)** *"Solid Propellant Rocket"*: ✅ **CORRECT**.
- **(C)** *"Liquid Propellant Rocket"*: ❌ **INCORRECT**.
- **(D)** *"SCRAM Jet"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2017 (IIT Roorkee) master answer key with 100% precision.
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