How to use the Carnot Efficiency Calculator
- 1. Pick the unitEnter temperatures in °C or kelvin.
- 2. Enter T_H and T_LSource (hot) and sink (cold) temperatures, plus heat supplied if you want work output.
- 3. See the limitEfficiency, work, heat rejected and the matching refrigerator and heat pump COP.
Carnot efficiency formula
A reversible (Carnot) engine working between a hot reservoir TH and a cold reservoir TL has efficiency η = 1 − TL / TH, with both temperatures in kelvin. No real engine between the same temperatures can do better (Carnot's theorem).
Reversed, the same cycle gives refrigerator COP = TL / (TH − TL) and heat pump COP = TH / (TH − TL).
Worked example and exam tips
An engine takes heat at 500 °C and rejects it at 30 °C. TH = 773.15 K, TL = 303.15 K. η = 1 − 303.15 / 773.15 = 60.8%. From 1000 kJ of heat, at most 608 kJ becomes work and 392 kJ is rejected.
- The most common mistake is using °C in the ratio. Always add 273.15.
- Raising TH or lowering TL both raise efficiency.
- If a question claims an efficiency above the Carnot value, the claim is impossible.
Frequently asked questions
Why must I use kelvin?
The formula comes from the absolute temperature scale. Using °C gives wrong, sometimes negative, answers.
Can a real engine reach Carnot efficiency?
No. Friction, heat transfer across finite temperature differences and other losses keep real engines below it.
How is Carnot COP related to efficiency?
Heat pump COP = 1 / η for the same two temperatures, and refrigerator COP = heat pump COP − 1.
Is this calculator free?
Yes. You enter your name and WhatsApp number once to see your result, and all other Uncodemy tools then open without the form. Everything is calculated in your browser.