Improving Carnot Efficiency – Parameter Sensitivity For a Carnot heat engine operating between T_H (highest temperature) and T_L (lowest temperature), efficiency increases by raising T_H and/or lowering T_L. Which listed action increases efficiency?

Introduction / Context:
The Carnot cycle provides the upper theoretical efficiency bound for heat engines. Its efficiency depends only on the two reservoir temperatures, not on the working fluid or specific mechanism. Understanding sensitivity to T_H and T_L guides practical design goals for turbines and boilers.

Given Data / Assumptions:

• Carnot efficiency formula: eta_C = 1 − T_L/T_H (temperatures in Kelvin).
• Ideal reversible operation; no internal losses.
• Other variables (mass flow, pressures) are secondary to reservoir temperatures.

Concept / Approach:

From eta_C = 1 − T_L/T_H, increasing T_H (with T_L fixed) makes the ratio T_L/T_H smaller, thus increasing efficiency. Conversely, decreasing T_H reduces efficiency, and increasing T_L also reduces efficiency. Holding T_L “constant” does not by itself increase efficiency; it simply states no change. Raising both T_H and T_L by the same absolute amount does not necessarily increase efficiency; what matters is their ratio.

Step-by-Step Solution:

Verification / Alternative check:

Example: T_L = 300 K. If T_H rises from 900 K to 1200 K, eta_C increases from 1 − 300/900 = 0.667 to 1 − 300/1200 = 0.75.

Why Other Options Are Wrong:

Decreasing T_H or increasing T_L worsens efficiency; keeping T_L constant is not an action that increases it; increasing both temperatures equally may or may not change T_L/T_H beneficially.

Common Pitfalls:

Using Celsius instead of Kelvin; focusing on absolute temperature difference ΔT rather than the ratio T_L/T_H that appears in the Carnot expression.

Final Answer:

increasing the highest temperature