What is Carnot efficiency?

Carnot efficiency is the maximum possible efficiency any heat engine operating between two temperature reservoirs can achieve. It is given by η = 1 − T_C / T_H, where temperatures are in Kelvin. No real engine can exceed this limit.

Why must temperatures be in Kelvin?

The Carnot formula requires absolute temperatures. Kelvin starts at absolute zero (−273.15 °C), so ratios of Kelvin temperatures are physically meaningful. Using Celsius or Fahrenheit directly gives wrong results.

What happens if T_C equals T_H?

Efficiency becomes 0%. No work can be extracted when both reservoirs are at the same temperature — there is no temperature difference to drive the cycle.

Can any real engine reach Carnot efficiency?

No. The Carnot cycle is a theoretical ideal requiring perfectly reversible processes with no friction, heat losses, or irreversibilities. Real engines are always less efficient due to these practical limitations.

What is COP for a Carnot refrigerator?

When the cycle runs in reverse as a refrigerator, its Coefficient of Performance (COP) = T_C / (T_H − T_C). This tool shows the COP alongside efficiency when T_C < T_H.

Carnot Efficiency Calculator

Name: Carnot Efficiency Calculator
Availability: InStock
Author: Nham Vu

Enter hot and cold reservoir temperatures to calculate the maximum possible efficiency of a Carnot heat engine.

Reservoir Temperatures

Temperature Unit

Hot Reservoir Temperature (T_H)

Cold Reservoir Temperature (T_C)

Quick Presets

Results

Enter temperatures and click Calculate

Summary

Enter hot and cold reservoir temperatures to calculate the maximum possible efficiency of a Carnot heat engine.

How it works

Enter the hot reservoir temperature (T_H) — the heat source.
Enter the cold reservoir temperature (T_C) — the heat sink.
Select the temperature unit: Kelvin, Celsius, or Fahrenheit.
The calculator converts inputs to Kelvin internally and applies η = 1 − T_C / T_H.
Results show efficiency as a percentage plus the work output per unit of heat input.

Use cases

Determine the theoretical upper limit for steam turbine efficiency.
Compare real engine performance against the Carnot ideal.
Solve thermodynamics homework problems on heat engine cycles.
Evaluate efficiency trade-offs when varying boiler or condenser temperatures.
Understand why higher temperature differentials yield better efficiency.
Validate power plant design calculations.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu