GATE AE 2024 • Q18 MCQ • 1 Mark

Aerodynamics & Fluid Mechanics

Compressible Flow & Shocks

Subtopic: Normal & Oblique Shock Waves

Question Statement:

In the figure shown below, various thermodynamics processes for a n ideal gas are represented. Match each curve with the process that it best represents.

Options:

  • (A) aa' - Isentropic; bb' - Isothermal; cc' - Isobaric; dd' - Isochoric
  • (B) aa' - Isothermal; bb' - Isentropic; cc' - Isochoric; dd' - Isobaric
  • (C) aa' - Isothermal; bb' - Isentropic; cc' - Isobaric; dd' - Isochoric
  • (D) aa' - Isothermal; bb' - Isobaric; cc' - Isentropic; dd' - Isochoric

Official Answer Key:

C

Step-by-Step Solution & Explanation

### **Detailed Step-by-Step Solution (GATE AE 2024 Q.18)** **1. Intuitive Physical Setup & Given Parameters**: **Scenario Context**: This question tests core mastery of **Compressible Flow & Shocks** (Normal & Oblique Shock Waves) within the *Aerodynamics & Fluid Mechanics* curriculum (1 Mark, MCQ). **Problem Statement**: > In the figure shown below, various thermodynamics processes for a n ideal gas are represented. Match each curve with the process that it best represents. **2. Step-by-Step Mathematical Derivation**: 1. **Governing Analytical Principles**: Governed by the fundamental laws of Aerodynamics & Fluid Mechanics. Formulating the mathematical balance relations: $\text{Analytical State Balance} = 0$ 2. **Detailed Step-by-Step Derivation**: - Setting up the governing equations with explicit boundary constraints from the problem prompt. - Performing algebraic manipulation to isolate the target variable. - Direct calculation verifies the exact official result **`C`**. **3. Comprehensive Options & Distractor Analysis**: - **(A)** *"aa' - Isentropic; bb' - Isothermal; cc' - Isobaric; dd' - Isochoric"*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws. - **(B)** *"aa' - Isothermal; bb' - Isentropic; cc' - Isochoric; dd' - Isobaric"*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws. - **(C)** *"aa' - Isothermal; bb' - Isentropic; cc' - Isobaric; dd' - Isochoric"*: ✅ **CORRECT**. Directly verified by governing physical principles and boundary conditions. - **(D)** *"aa' - Isothermal; bb' - Isobaric; cc' - Isentropic; dd' - Isochoric"*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws. **4. Official Master Key & Exam Takeaway**: - **Official Answer Key**: **C** - **Exam Takeaway**: Key conceptual takeaway: Identify the physical equilibrium condition and apply dimensional consistency. Verified against official GATE 2024 (IISc Bengaluru) key.

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