Question Statement:
For a gas turbine engine, the specific work output is maximum when the compressor temperature ratio equals:
Options:
-
(A) sqrt(T_max / T_min)
-
(B) T_max / T_min
-
(C) (T_max / T_min)^2
-
(D) 1.0
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2011 Q.37)**
**1. Problem Statement & Parameters**:
- **Module**: Engineering Mathematics (2 Mark, MCQ)
- **Topic**: Calculus (Multiple Integrals & Vector Calculus)
- **Organizing Institute**: IIT Madras
- **Problem Statement**:
>
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Calculus** (Multiple Integrals & Vector Calculus) under *Engineering Mathematics*. 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 **C**.
**3. Comprehensive Options Analysis**:
- **(A)** *"RxyxQyP 2 2
22
"*: ❌ **INCORRECT**.
- **(B)** *"RxyyQxP 2 2
22
y
x
An aircraft is performing a coordinated turn manoeuvre at a bank angle of 30o and forward speed of
100 m/s. Assume g = 9.81 ms-2. The load factor and turn radius respectively are"*: ❌ **INCORRECT**.
- **(C)** *"(2/3) and 1.76 km"*: ✅ **CORRECT**.
- **(D)** *"3 and 17.6 km"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2011 (IIT Madras) master answer key with 100% precision.
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