What is the formula for Carnot efficiency?

The Carnot efficiency of a heat engine is a measure of the maximum possible efficiency with which an engine can convert heat into work. This value is determined by the temperatures of the thermal reservoirs between which the engine operates.

The formula for Carnot efficiency is expressed as 1 minus the ratio of the cold reservoir temperature (T_c) to the hot reservoir temperature (T_h). This reflects the idea that the efficiency increases as the temperature difference between the hot and cold reservoirs increases.

This relationship arises from the second law of thermodynamics, which states that no engine operating between two temperature reservoirs can be more efficient than a Carnot engine operating between the same temperatures. Thus, as the temperature of the hot reservoir increases or the temperature of the cold reservoir decreases, the fraction of energy converted into work approaches one.

In summary, the formula ε_rev = 1 - T_c / T_h captures the essence of Carnot efficiency by demonstrating that maximum efficiency depends directly on the temperatures of the two reservoirs involved in the thermodynamic process.