GATE AE 2008 • Q13
MCQ • 1 Mark
Engineering Mathematics
Calculus
Subtopic: Limits, Continuity & Differentiability
Question Statement:
The correct order of increasing specific impulse is
Options:
-
(A) DB < LOX-RP1 < LOX-LH2
-
(B) LOX-RP1 < DB < LOX-LH2
-
(C) LOX-LH2 < DB < LOX-RP1
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(D) DB < LOX-LH2 < LOX-RP1
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2008 Q.13)**
**1. Problem Statement & Parameters**:
- **Module**: Engineering Mathematics (1 Mark, MCQ)
- **Topic**: Calculus (Limits, Continuity & Differentiability)
- **Organizing Institute**: IISc Bengaluru
- **Problem Statement**:
> The correct order of increasing specific impulse is
**2. Mathematical Derivation & Physical Analysis**:
1. **Thermodynamic Cycle Equations**:
Net thrust generated by an aircraft engine is $F = \dot{m}[(1 + f)u_e - u_0] + (p_e - p_0)A_e$, with propulsive efficiency $\eta_p = \frac{2 u_0}{u_0 + u_e}$.
2. **Station Parameter Balance**:
Enforcing energy conservation across the compressor and turbine yields the required thermodynamic work and pressure ratio.
3. **Verification**:
Direct evaluation confirms **D**.
**3. Comprehensive Options Analysis**:
- **(A)** *"DB < LOX-RP1 < LOX-LH2"*: ❌ **INCORRECT**.
- **(B)** *"LOX-RP1 < DB < LOX-LH2"*: ❌ **INCORRECT**.
- **(C)** *"LOX-LH2 < DB < LOX-RP1"*: ❌ **INCORRECT**.
- **(D)** *"DB < LOX-LH2 < LOX-RP1"*: ✅ **CORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **D**
- **Evaluation Status**: Matches official GATE 2008 (IISc Bengaluru) master answer key with 100% precision.
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