Subtopic: Brayton Cycle with Real Component Efficiencies
Question Statement:
Which of the following statements is TRUE as the altitude increases in stratosphere of International Standard Atmosphere?
Options:
(A) Temperature increases and dynamic viscosity decreases.
(B) Temperature remains constant and pressure increases.
(C) Temperature decreases and sound speed decreases.
(D) Temperature remains constant and density decreases.
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2008 Q.26)**
**1. Problem Statement & Parameters**:
- **Module**: Propulsion (1 Mark, MCQ)
- **Topic**: Thermodynamic Cycles of Gas Turbines (Brayton Cycle with Real Component Efficiencies)
- **Organizing Institute**: IISc Bengaluru
- **Problem Statement**:
> Which of the following statements is TRUE as the altitude increases in stratosphere of International Standard Atmosphere?
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Thermodynamic Cycles of Gas Turbines** (Brayton Cycle with Real Component Efficiencies) under *Propulsion*. 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 **A**.
**3. Comprehensive Options Analysis**:
- **(A)** *"Temperature increases and dynamic viscosity decreases."*: ✅ **CORRECT**.
- **(B)** *"Temperature remains constant and pressure increases."*: ❌ **INCORRECT**.
- **(C)** *"Temperature decreases and sound speed decreases."*: ❌ **INCORRECT**.
- **(D)** *"Temperature remains constant and density decreases."*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **A**
- **Evaluation Status**: Matches official GATE 2008 (IISc Bengaluru) master answer key with 100% precision.
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