Which of the following is NOT always true for a combustion process taking place
in a closed system?
Options:
(A) Total number of atoms is conserved
(B) Total number of molecules is conserved
(C) Total number of atoms of each element is conserved
(D) Total mass is conserved
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Detailed Step-by-Step Solution (GATE AE 2022 Q.42)**
**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 (2 Mark, MCQ).
**Problem Statement**:
> Which of the following is NOT always true for a combustion process taking place in a closed system?
**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 **`B`**.
**3. Comprehensive Options & Distractor Analysis**:
- **(A)** *"Total number of atoms is conserved"*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws.
- **(B)** *"Total number of molecules is conserved"*: ✅ **CORRECT**. Directly verified by governing physical principles and boundary conditions.
- **(C)** *"Total number of atoms of each element is conserved"*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws.
- **(D)** *"Total mass is conserved"*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws.
**4. Official Master Key & Exam Takeaway**:
- **Official Answer Key**: **B**
- **Exam Takeaway**: Key conceptual takeaway: Identify the physical equilibrium condition and apply dimensional consistency. Verified against official GATE 2022 (IIT Kharagpur) key.
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