Carnot Efficiency Calculator

Carnot efficiency is the theoretical maximum efficiency any heat engine can achieve while operating between a hot reservoir at temperature Th and a cold reservoir at temperature Tc, given by η=1−Tc/Th. It is an absolute upper bound set by the second law of thermodynamics, not by any particular engine design.

η = 1 − Tc/Th, where Th and Tc are the absolute (Kelvin) temperatures of the hot and cold reservoirs respectively. Both temperatures must be in Kelvin, not Celsius or Fahrenheit, for the formula to give a correct result.

The Carnot formula derives from the thermodynamic (absolute) temperature scale, where zero represents absolute zero. Using Celsius or Fahrenheit directly (where zero is arbitrary) gives an incorrect ratio and a wrong efficiency value.

No, the Carnot efficiency assumes a perfectly reversible process with no friction, no irreversible heat transfer, and infinitely slow (quasi-static) operation, conditions no real engine can achieve. Carnot efficiency is a theoretical ceiling that real engines can only approach, never reach.

Since η=1−Tc/Th, increasing Th or decreasing Tc directly increases efficiency, this is exactly why power plant designers push for the highest practical boiler/turbine inlet temperature and seek the coldest available cooling source (like river or seawater) to maximize the temperature gap.

A power plant with a boiler at 600 K (327°C) rejecting heat to a river at 300 K (27°C) has a maximum possible Carnot efficiency of 50%, meaning even a perfect engine could convert at most half the input heat into useful work, real plants achieve considerably less due to practical losses.

Yes, remarkably, Carnot's theorem proves that the maximum efficiency between two given temperatures depends only on those two temperatures, not on the working substance or the specific engine design, a landmark result in thermodynamics.

As Tc approaches 0 K, Carnot efficiency approaches 100% (η→1). In practice, absolute zero is unreachable (third law of thermodynamics), so 100% efficiency is never actually achievable.

The same Carnot cycle run in reverse sets the maximum theoretical coefficient of performance (COP) for refrigerators and heat pumps operating between the same two temperatures, a closely related but differently expressed quantity from engine efficiency.

It provides an absolute benchmark for judging how much theoretical room for improvement exists in a real engine or power plant design, engineers compare actual efficiency against the Carnot limit to gauge how close a design comes to the physical maximum.