To increase the thermal efficiency of a reversible power...

To increase the thermal efficiency of a reversible power cycle operating between thermal reservoirs at temperatures $T_{\mathrm{H}}$ and $T_{C}$, would it be better to increase $T_{\mathrm{H}}$ or decrease $T_{\mathrm{C}}$ by equal amounts?

Key Concepts

Reversible Power Cycle

A reversible power cycle is an idealized thermodynamic process that operates between two thermal reservoirs in such a way that all the heat transfers are reversible. This means that the process can theoretically be reversed without any loss or increase in entropy, thereby attaining the maximum efficiency possible as defined by the laws of thermodynamics.

Thermal Efficiency

Thermal efficiency is a measure of how well a heat engine converts heat into work. It is expressed as the ratio of the work output to the heat input. In ideal cycles, such as the Carnot cycle, this efficiency is determined solely by the temperatures of the two reservoirs between which the engine operates.

Carnot Cycle

The Carnot cycle is a theoretical thermodynamic cycle proposed by Sadi Carnot that defines the maximum possible efficiency any heat engine can achieve when operating between two temperature reservoirs. The efficiency of a Carnot cycle is given by 1 - (T_C/T_H), where T_H and T_C are the absolute temperatures of the hot and cold reservoirs, respectively.

Effect of Temperature Variation on Efficiency

Since the efficiency of a Carnot engine is expressed as 1 - (T_C/T_H), small changes in the temperatures of the hot and cold reservoirs alter the efficiency by affecting the ratio T_C/T_H. When both reservoir temperatures are altered by equal amounts, a decrease in the cold (low) temperature has a more pronounced effect on reducing the ratio T_C/T_H than an equivalent increase in the hot (high) temperature, thereby leading to a greater improvement in thermal efficiency.

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