In a turbojet engine, the compressor outlet temperature increases with decreasing efficiency of the compressor. If the turbine inlet temperature remains constant, with decreasing efficiency of the compressor, the thrust specific fuel consumption of the engine
Options:
(A) decreases, as the heat input is lower.
(B) remains unchanged.
(C) increases, as the compressor needs more work input from the turbine.
(D) decreases, as the thrust produced is higher.
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2019 Q.22)**
**1. Problem Statement & Parameters**:
- **Module**: Flight Mechanics & Space Dynamics (1 Mark, MCQ)
- **Topic**: Atmospheric Flight Mechanics (Climb, Glide, Ceiling & Turn Performance)
- **Organizing Institute**: IIT Madras
- **Problem Statement**:
> In a turbojet engine, the compressor outlet temperature increases with decreasing efficiency of the compressor. If the turbine inlet temperature remains constant, with decreasing efficiency of the compressor, the thrust specific fuel consumption of the engine
**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)** *"decreases, as the heat input is lower."*: ❌ **INCORRECT**.
- **(B)** *"remains unchanged."*: ✅ **CORRECT**.
- **(C)** *"increases, as the compressor needs more work input from the turbine."*: ❌ **INCORRECT**.
- **(D)** *"decreases, as the thrust produced is higher."*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2019 (IIT Madras) master answer key with 100% precision.
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