What is the thermal efficiency (in %) of an ideal Carnot heat engine operating between reservoir temperatures $T_H = 610\text{ K}$ and $T_L = 300\text{ K}$?

(A) 50.8\%

(B) 38.1\%

(C) 65.8\%

(D) 100.0\%

Answer Key:

A

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Governing Concept & Domain Context:** * This question evaluates **Brayton Cycle with Real Component Efficiencies** under *Thermodynamic Cycles of Gas Turbines* in GATE AE. 2. **Stage 2: Mathematical Derivation:** * $\eta = \frac{T_H - T_L}{T_H} = \frac{610 - 300}{610} = 50.8\%$. 3. **Stage 3: Distractor Elimination Forensics:** * The evaluated correct answer is derived using standard physical equations. * Distractor values correspond to typical unit conversion omissions or inverted formulas. 4. **Stage 4: Common Student Trap:** * *Trap:* Inverting the ratio as $1 - T_H / T_L$. *Reference: Philip G. Hill, Carl R. Peterson, Mechanics and Thermodynamics of Propulsion (Pearson).*

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