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Carnot Efficiency

Also known as maximum theoretical efficiency

η=1−TcTh\eta = 1 - \frac{T_c}{T_h}

Worked example: 500 K hot, 300 K cold → η = 0.4 — press Try an example to run it live, then adjust anything.

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Carnot Efficiency explained

ThηTc

In 1824 the 28-year-old French engineer Sadi Carnot proved a startling result: no heat engine, however ingenious, can beat an efficiency ceiling set purely by the absolute temperatures of its hot source and cold sink. His short book went almost unnoticed in his lifetime, yet it founded thermodynamics and anticipated the second law. The formula demands kelvin — formula.expert converts °C and °F inputs — and it only makes sense when 0 < TcT_c < ThT_h.

A steam plant running between 800 K boiler steam and a 300 K cooling river can never exceed η = 1 − 300/800 = 62.5%; real plants manage about 40% after friction and other irreversibilities take their share. The lesson is practical: to buy efficiency, raise ThT_h or lower TcT_c. That is why power stations chase ever-hotter turbine materials — and why waste heat is not an engineering failure but a law of nature.

Carnot Efficiency formula

η=1−TcTh\eta = 1 - \frac{T_c}{T_h}
Where
  • η\eta= Maximum efficiency
  • TcT_c= Cold reservoir temperature (°C)
  • ThT_h= Hot reservoir temperature (°C)

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