The most efficient engine allowed by physics. Two isotherms and two adiabats trace the Carnot cycle — and set the ceiling no real engine can exceed.
Carnot CycleLive
the ideal heat engine
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The Carnot cycle — two isothermal and two adiabatic steps — is the most efficient possible heat engine between two temperatures. Its efficiency depends only on the reservoir temperatures: η = 1 − Tc/Th. No real engine can beat it, which is why raising the hot temperature or lowering the cold one is the only path to higher efficiency.
Reading this result: Efficiency here is 50.0% and is fixed by the temperature ratio alone — widening the expansion ratio enlarges the enclosed work loop but can never push past the 50.0% Carnot ceiling, and each kelvin removed from the cold side buys a bit more than each kelvin added to the hot side.
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How it works
The Carnot cycle alternates isothermal and adiabatic steps between a hot and cold reservoir. Its efficiency, η = 1 − Tc/Th, depends only on the temperatures, not the working fluid. It defines the absolute upper limit for converting heat to work, which is why engineers chase higher combustion temperatures and colder exhausts.
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The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
Is this Carnot cycle efficiency tool really free?▾
Yes. Carnot Cycle runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?▾
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
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How accurate are the results?▾
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.