If you're studying thermodynamics and are searching for how to calculate the Carnot efficiency, you're in the right place! With this tool, you can calculate the efficiency of a Carnot engine by just inputting the cold and hot reservoir temperatures.
Keep reading the rest of this article to learn more about the Carnot heat engine and the Carnot efficiency formula.
Carnot heat engine
Heat engines are devices that receive heat from a high-temperature or hot reservoir and convert it into work. The main characteristic of heat engines is that they can convert only a portion of their heat energy into work and reject the remaining heat to a low-temperature or cold reservoir. The efficiency of these engines is limited, as they only allow the conversion of a part of the heat into work.
The Carnot heat engine is a theoretical heat engine that operates under the Carnot cycle, the most efficient heat engine process possible. This maximum efficiency of the Carnot cycle occurs as it is executed as a reversible process (no irreversibilities).
For example, for a piston-cylinder device using air as the working fluid and assuming no friction, the Carnot cycle consists of the following four reversible processes:
- Reversible isothermal expansion (A-B): the gas inside the cylinder receives the heat Q₁ from a hot reservoir at temperature TH. The gas performs work by expanding itself while diminishing its pressure at constant temperature TH (Boyle's law). The fact that the gas receives heat at the same temperature as the reservoir avoids the irreversibility associated with transferring heat through a finite temperature difference.
- Reversible adiabatic expansion (B-C): the gas is thermally insulated from its surroundings so that the process becomes adiabatic. The gas continues to perform work by expanding itself very slowly (quasi-static expansion), avoiding the irreversibility of fast expansion.
- Reversible isothermal compression (C-D): this process is analogous to but opposite to the A-B process. An external force performs work on the gas, compressing it at a constant temperature TC. Again, the process is reversible thanks to its isothermal nature.
- Reversible adiabatic compression (D-A): this process is analogous to but opposite to the B-C process. The external force keeps performing work on the gas, but this time, in an adiabatic way.
As said before, the Carnot cycle efficiency is the highest a heat engine can achieve. The efficiency is lower in real heat engines, like internal combustion engines or thermal plants.
How to calculate the Carnot efficiency
The formula for the efficiency of a Carnot engine is:
η = 1 - TL/TH
- η — Carnot efficiency, calculated as a fraction.
- TL — Temperature of the cold reservoir, in absolute temperature units (kelvin or Rankine degrees).
- TL — Temperature of the hot reservoir, also expressed in absolute temperature units. (using °C or °F to calculate the Carnot efficiency would provide wrong results).
To calculate the Carnot engine efficiency as a percentage, multiply η by 100%.