What Carnot Efficiency Means
Carnot efficiency is the maximum theoretical efficiency possible for a reversible heat engine operating between a hot reservoir and a cold reservoir. It is an upper limit, not the efficiency of a real engine.
The temperatures must be absolute temperatures in Kelvin. Celsius and Fahrenheit must be converted before using the formula.
Temperature Inputs Must Be Absolute
The calculator accepts Kelvin, Celsius, and Fahrenheit, but it converts everything to Kelvin internally. This matters because the Carnot formula depends on absolute temperature ratios, not temperature differences in Celsius or Fahrenheit.
| Unit | Conversion to Kelvin |
|---|---|
| Kelvin | K = K |
| Celsius | K = °C + 273.15 |
| Fahrenheit | K = (°F − 32) × 5 / 9 + 273.15 |
Heat, Work, and Rejected Heat
If heat input QH is provided, the calculator also estimates the ideal maximum work output and the rejected heat.
QC = QH − Wmax
The Four Carnot Cycle Processes
- Isothermal expansion: the working fluid absorbs heat from the hot reservoir at TH.
- Adiabatic expansion: the fluid expands without heat transfer and cools from TH to TC.
- Isothermal compression: the fluid rejects heat to the cold reservoir at TC.
- Adiabatic compression: the fluid compresses without heat transfer and returns to TH.
Example Calculation
Hot reservoir: 600 K Cold reservoir: 300 K η = 1 − TC / TH η = 1 − 300 / 600 η = 0.5 Carnot efficiency = 50%
Why Real Engines Are Less Efficient
Real heat engines cannot reach Carnot efficiency because they are not perfectly reversible. Losses occur through friction, finite temperature differences, pressure drops, heat leakage, fluid losses, and non-ideal combustion or heat transfer.
Common Mistakes
- Using Celsius directly inside the Carnot formula.
- Using Fahrenheit directly inside the Carnot formula.
- Entering a cold reservoir temperature higher than the hot reservoir temperature.
- Assuming a real engine can reach Carnot efficiency.
- Confusing Carnot efficiency with mechanical efficiency or combustion efficiency.
Frequently Asked Questions
What is the Carnot Cycle Calculator used for?
It calculates the ideal maximum efficiency of a reversible heat engine operating between two temperature reservoirs.
Why must temperatures be in Kelvin?
Carnot efficiency uses a ratio of absolute temperatures. Kelvin is the absolute temperature scale used for this formula.
Can Carnot efficiency be 100%?
Only if the cold reservoir were at absolute zero, which is not physically achievable in a real heat engine. Real engines always have lower efficiency.
What happens if TC is greater than TH?
Then the setup is not a heat engine operating in the intended direction. For a heat engine, TH must be greater than TC.
Does this calculate real engine efficiency?
No. It calculates the ideal upper limit. Real engine efficiency requires additional losses and design details.