How is the efficiency of a heat engine defined?

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.