Carnot efficiency calculator
The ceiling efficiency of a heat engine from two temperatures.
Fill in the fields and the result will appear here automatically.
This is the upper efficiency bound for a heat engine between two constant-temperature reservoirs, not a prediction for a particular machine. Enter kelvin, with the hot side strictly hotter and both temperatures above 0 K. The 1000 J rows show the reversible-limit split between work and rejected heat.
How it works
Formula and logic
η = 1 − T_cold / T_hot, with temperatures in kelvin.
Example
At 800 K and 300 K the limit is 62.5 % — no engine will beat that.
Fields and units
- Hot reservoir temperature — K
- Cold reservoir temperature — K
How to use
- — Both temperatures in kelvin: add 273.15 to degrees Celsius.
- — The cold reservoir is wherever the heat is dumped — usually the surroundings, about 300 K.
- — The work-from-1000 J row shows the same number more plainly: that many joules become work, the rest leaves.
- — Equal temperatures and 0 K are rejected in this heat-engine mode. Convert Celsius first: T=t+273.15.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: reversible Carnot bound
- Limitation
- Two constant-temperature reservoirs and the reversible limit. Actual efficiency, power and equipment losses are not calculated.
FAQ
Why not degrees Celsius?
The formula uses a ratio of temperatures, which only means something measured from absolute zero. Taking 100 °C and 20 °C as they stand gives 80 % instead of an honest 21.4 %, and with a sub-zero ambient it gives efficiency above one.
Why are real engines worse?
The Carnot cycle is reversible: processes run infinitely slowly, there is no friction, heat flows across no temperature difference. A real machine must finish in finite time, and every departure from the ideal costs efficiency.
How can the limit be raised?
With the cold side fixed, raise the hot temperature; with the hot side fixed, lower the cold temperature. The bound depends on Tc/Th. Materials, cooling and engine design limit both choices; there is no universal fraction of Carnot efficiency for engines or turbines.
Can efficiency reach 100 %?
That would need a cold reservoir at exactly absolute zero, which is unreachable. This is the second law of thermodynamics in numbers: some heat must leave unused.