Carnot Efficiency – Effect of Highest Temperature on Performance Statement check: 'By decreasing the highest temperature in the Carnot cycle, its efficiency is increased.' Determine its correctness.

Introduction / Context:
The Carnot cycle sets the theoretical upper limit of heat-engine efficiency: eta_C = 1 − T_L/T_H, where T_H is the high-temperature reservoir and T_L is the low-temperature reservoir. Understanding parameter effects avoids design misconceptions.

Given Data / Assumptions:

• Reversible cycle exchanging heat only at T_H and T_L.
• Absolute temperatures (Kelvin scale).
• No internal irreversibilities or pressure losses.

Concept / Approach:

From eta_C = 1 − T_L/T_H, efficiency increases when T_H increases or when T_L decreases (or both). Therefore, decreasing the highest temperature T_H while keeping T_L fixed decreases eta_C, not increases it. The given statement is false unless T_L decreases proportionally more, which is not stated.

Step-by-Step Solution:

Verification / Alternative check:

Numerical example: T_L = 300 K. If T_H drops from 1200 K to 900 K, eta_C falls from 1 − 300/1200 = 0.75 to 1 − 300/900 = 0.667.

Why Other Options Are Wrong:

Adding regeneration does not change the Carnot limit; the law holds for any working substance, not only ideal gases.

Common Pitfalls:

Confusing effects of increasing temperature difference ΔT with separately changing T_H or T_L; using Celsius instead of Kelvin.

Final Answer:

False