physics//thermodynamics//Carnot efficiency
The Carnot efficiency is the maximum fraction of heat that any heat engine working between a hot and a cold reservoir can turn into work, and it is the benchmark against which real turbines, engines and power plants are judged. It depends only on the two temperatures, in kelvin:
The Carnot efficiency is the maximum fraction of heat that any heat engine working between a hot and a cold reservoir can turn into work, and it is the benchmark against which real turbines, engines and power plants are judged. It depends only on the two temperatures, in kelvin:
ηmax=1−TcTh\eta_{\max} = 1 - \frac{T_c}{T_h}ηmax=1−ThTc
A plant that takes heat at 873 K (600 °C) and rejects it at 300 K cannot exceed 1−300/873≈66%1 - 300/873 \approx 66%1−300/873≈66%, whatever its design; real plants stay below that bound, and a modern combined-cycle gas plant reaches roughly 60% by running its hot side far hotter.
The bound limits efficiency, never power.
A plant that cannot pass two thirds can still be built twice as large, so a ceiling on efficiency says nothing about how much energy can be delivered in total.
The cold reservoir is as necessary as the hot one. With nothing colder to reject heat into, no work comes out at all, which is why plants need rivers, seas or cooling towers.
The bound follows from the second law of thermodynamics, the same law behind Landauer's principle.