A heat engine turns heat into work, but the laws of thermodynamics cap how much. Drag the sliders below to set the hot and cold reservoir temperatures and the heat supplied, and watch the work out and the Carnot efficiency limit, 1 - Tc/Th, respond.
You are up against two rules at once here, and together they box in every engine ever built. The first law says you cannot win: over a full cycle the working substance comes back to its starting state, so the work you extract is exactly the heat you put in minus the heat you throw away, W = Qh - Qc. Nothing is created. The second law is harsher still — it says you cannot even break even. Some heat Qc must always be dumped into the cold reservoir, so the efficiency η = W/Qh = 1 - Qc/Qh stays stubbornly short of 1.
Drag the sliders and watch the ceiling reveal itself. What sets it is the ratio of the two temperatures: the unbeatable Carnot limit is 1 - Tc/Th with both in kelvin, so raising the hot reservoir Th or lowering the cold reservoir Tc pushes the maximum efficiency higher. Reaching 100% would demand Tc = 0 K — absolute zero — which no cold sink offers.
Notice that the cap depends only on that temperature ratio, not on clever mechanics; a real engine leaks and rubs its way below the ideal, never above it. To pin down that ceiling for any pair of reservoirs, open the Carnot efficiency calculator or keep testing intuition against the physics in our interactive simulations.
Energy is conserved. For an engine running a cycle, the work out equals the heat in minus the heat rejected: W = Qh − Qc. You cannot get out more energy than you put in.
Some heat must always be rejected to a cold reservoir, so no engine can turn all its input heat into work. Its efficiency, η = 1 − Qc/Qh, is always less than 1.
The Carnot efficiency, 1 − Tc/Th, with the temperatures in kelvin. It depends only on the ratio of the cold to the hot reservoir temperature, and no real engine can beat it.
Reaching 100% would require the cold reservoir to be at absolute zero (0 K), which is unattainable. In practice some heat is always dumped to the surroundings.