GATE AE 2008 • Q13 MCQ • 1 Mark Propulsion

Propulsion

Rocket Propulsion

Subtopic: Tsiolkovsky Rocket Equation & Specific Impulse

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
  • (D) DB < LOX-LH2 < LOX-RP1

Official Answer Key:

D

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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