Case 1
- Cold reservoir
- 300K
- Hot reservoir
- 500K
0.400000
Open with these valuesCarnot Efficiency Calculator
0.400000
Result: 0.400000No heat engine can beat 1 minus the cold temperature divided by the hot one, both in kelvin. Steam at 500 K rejected to 300 K gives 0.4, so 40 % is the ceiling — a real turbine reaches maybe two thirds of that. The result is a fraction; multiply by 100 for percent.
Worked examples
Case 2
- Cold reservoir
- 288K
- Hot reservoir
- 320K
0.100000
Open with these valuesCase 3
- Cold reservoir
- 250K
- Hot reservoir
- 1000K
0.750000
Open with these valuesHow it's calculated
η = 1 - T_cold ÷ T_hot
- StepEnter the temperature of the cold reservoir in kelvin.
- StepEnter the temperature of the hot reservoir in kelvin.
- StepRead the efficiency as a fraction; multiply by 100 for percent.
- ResultTreat it as a ceiling, never as the output of a real machine.
What this number means
A ceiling, not a performance figure
Between these two temperatures no engine can do better, and every real one does worse. Friction, heat leaking away and finite-speed processes all cost work that the ideal cycle never loses.
Only the two temperatures enter
Working fluid, design and size of the machine appear nowhere in the formula. 300 K against 500 K gives 0.4 whether the engine burns coal or gas.
The answer is a fraction, not a percentage
0.4 means 40 %, and 0.267989 means 26.8 %. A modern combined-cycle station reaches about 60 % against a ceiling near 80 %.
Commonly misread
27 and 227 entered because the reservoirs are at 27 °C and 227 °C.
The formula reads them as kelvin and returns 0.881. In kelvin the pair is 300 and 500, and the ceiling is 0.4.
A ceiling of 40 % means the engine delivers 40 %.
It delivers less — a good real machine reaches perhaps two thirds of the Carnot value. The number is an upper bound, not an expectation.
A better working fluid lifts the efficiency.
Neither fluid nor design appears in the formula. Only a hotter source or a colder sink moves the ceiling.
Reference table
| Cold, hot | As percent | Efficiency |
|---|---|---|
| 500, 500 | 0 % | 0.000000 |
| 288, 320 | 10 % | 0.100000 |
| 273.15, 373.15 | 26.8 % | 0.267989 |
| 300, 500 | 40 % | 0.400000 |
| 300, 600 | 50 % | 0.500000 |
| 250, 1000 | 75 % | 0.750000 |
Questions
What is Carnot efficiency?
The largest fraction of heat that any engine working between two fixed temperatures can turn into work. It depends on the two temperatures alone, not on the working fluid or the design.
Must I use kelvin?
Yes. The ratio only means something on an absolute scale; entering 27 and 227 instead of 300 and 500 gives 0.881 instead of 0.4.
Why is the efficiency of real engines lower?
Friction, heat leaking away and finite-speed processes all cost work that the ideal cycle does not lose. A modern combined-cycle power station reaches about 60 %, against a Carnot ceiling near 80 %.
Can efficiency ever reach 100 %?
Only if the cold reservoir sits at absolute zero, which is unreachable. That is the second law of thermodynamics stated as a number.
What happens if both temperatures are equal?
The efficiency is zero. Without a temperature difference there is no direction for heat to flow, and no work can be extracted.
Sources and last check
Information, not professional advice.