The efficiency of the Carnot cycle is maximum when the engine operates in a perfectly reversible manner and there are no incidental wasteful processes such as friction or heat conduction between parts at different temperatures. Specifically, the Carnot cycle efficiency is maximized when the engine operates between two thermal reservoirs at constant temperatures, and the efficiency depends on the temperatures of the hot and cold reservoirs. The efficiency is given by:
Efficiency=1−TCTH\text{Efficiency}=1-\frac{T_C}{T_H}Efficiency=1−THTC
where THT_HTH is the absolute temperature of the hot reservoir and TCT_CTC is the absolute temperature of the cold reservoir. From this, the efficiency is maximum when the temperature difference between the hot reservoir and the cold reservoir is the greatest and the processes are reversible with no entropy generation. This principle means no engine operating between two heat reservoirs can be more efficient than a Carnot engine operating between those same reservoirs. Also, lowering the temperature of the cold reservoir has a greater impact on increasing efficiency than raising the temperature of the hot reservoir by the same amount.
In summary:
- Maximum efficiency is achieved by a reversible Carnot cycle.
- Efficiency depends on the temperature difference between hot and cold reservoirs.
- Efficiency formula: η=1−TCTH\eta =1-\frac{T_C}{T_H}η=1−THTC.
- The larger the temperature difference and the more reversible the process, the higher the efficiency.
This is why Carnot cycle efficiency is considered the theoretical upper limit for heat engine efficiency operating between two thermal reservoirs.
