How is the efficiency of a heat engine defined?

How is the efficiency of a heat engine defined?

• A. ε = q_c / q_h
• B. ε = q_h / |w|
• C. ε = |w| / q_h
• D. ε = |w| + q_h

Answer: (C)

The efficiency of a heat engine is defined as the ratio of the work output of the engine to the heat input from the hot reservoir. This relationship is expressed mathematically as \( \epsilon = \frac{|w|}{q_h} \), where \( |w| \) represents the magnitude of work output and \( q_h \) is the heat absorbed from the hot reservoir. This definition captures the fundamental principle that not all of the heat energy absorbed by the engine can be converted into work; some of it is invariably rejected to a cold reservoir, in accordance with the second law of thermodynamics. Therefore, the efficiency of a heat engine reflects its ability to transform the input heat energy into useful work, thereby providing a measure of performance for comparing different heat engines. The other options do not accurately represent the efficiency of a heat engine. For instance, the comparison of heat absorbed by the cold reservoir or work done against absolute values fails to encapsulate the essence of efficiency as a measure of useful work derived from the energy input.

The efficiency of a heat engine is defined as the ratio of the work output of the engine to the heat input from the hot reservoir. This relationship is expressed mathematically as ( \epsilon = \frac{|w|}{q_h} ), where ( |w| ) represents the magnitude of work output and ( q_h ) is the heat absorbed from the hot reservoir.

This definition captures the fundamental principle that not all of the heat energy absorbed by the engine can be converted into work; some of it is invariably rejected to a cold reservoir, in accordance with the second law of thermodynamics. Therefore, the efficiency of a heat engine reflects its ability to transform the input heat energy into useful work, thereby providing a measure of performance for comparing different heat engines.

The other options do not accurately represent the efficiency of a heat engine. For instance, the comparison of heat absorbed by the cold reservoir or work done against absolute values fails to encapsulate the essence of efficiency as a measure of useful work derived from the energy input.