What is Carnot efficiency?

Carnot efficiency is the maximum possible thermal efficiency any heat engine can achieve when operating between two temperature reservoirs. It is given by η_Carnot = 1 − (T_C / T_H), where temperatures must be in Kelvin. No real engine can exceed this limit because it assumes perfectly reversible (ideal) processes.

How is actual thermal efficiency calculated?

Actual thermal efficiency is η = W_net / Q_H = 1 − (Q_C / Q_H), where Q_H is the heat absorbed from the hot reservoir, Q_C is the heat rejected to the cold reservoir, and W_net = Q_H − Q_C is the net work output. Real engines are always less efficient than the Carnot limit due to irreversibilities such as friction and heat loss.

Why must temperatures be in Kelvin for Carnot efficiency?

Thermodynamic temperature ratios require an absolute scale. Kelvin starts at absolute zero (−273.15 °C), ensuring T_C / T_H is always between 0 and 1. Using Celsius or Fahrenheit directly would give incorrect ratios and meaningless results.

What happens if T_C equals T_H?

If both reservoirs are at the same temperature, Carnot efficiency is 0 %. This reflects the second law of thermodynamics: no net work can be extracted from a single temperature reservoir. A temperature difference is mandatory for any heat engine to operate.

Can efficiency exceed 100 %?

No. The first law of thermodynamics prohibits it. Efficiency above 100 % would imply more work out than heat in, which violates energy conservation. If your inputs give η > 100 %, check that Q_C < Q_H and that T_C < T_H.

What is net work output?

Net work output W_net = Q_H − Q_C is the useful mechanical energy the engine delivers per cycle. In the actual efficiency mode this calculator derives W_net from the heat values you enter and shows it alongside efficiency.

Heat Engine Efficiency Calculator

Enter hot and cold reservoir temperatures or heat input/output values to calculate Carnot and actual thermal efficiency of a heat engine.

Calculation Mode

Enter hot and cold reservoir temperatures to find the maximum (Carnot) efficiency.

Hot Reservoir Temperature (T_H)

Cold Reservoir Temperature (T_C)

Results

Select a mode, enter values, and click Calculate

Typical Engine Efficiencies

Real-world reference values for common heat engines.

Summary

The Heat Engine Efficiency Calculator computes both the theoretical Carnot efficiency and the actual thermal efficiency of a heat engine. Carnot efficiency sets the upper limit on performance and depends only on the hot and cold reservoir temperatures (in Kelvin). Actual thermal efficiency is calculated from the heat absorbed from the hot reservoir (Q_H) and the heat rejected to the cold reservoir (Q_C), letting you compare real engine performance against the ideal Carnot limit.

How it works

Choose a calculation mode: Carnot Efficiency (from temperatures) or Actual Thermal Efficiency (from heat values).
For Carnot mode, enter the hot reservoir temperature T_H and cold reservoir temperature T_C in Kelvin or Celsius.
For Actual mode, enter the heat input Q_H and heat rejected Q_C, then select energy units.
Click Calculate to see efficiency as a percentage and key derived values.
The results panel shows work output, coefficient of performance comparison, and step-by-step working.
Switch modes to compare actual performance against the Carnot ideal limit.

Use cases

Determine the theoretical maximum efficiency of a steam turbine power plant.
Evaluate how close a real heat engine is to the Carnot ideal.
Solve thermodynamics homework involving heat engine cycles.
Compare efficiencies of engines operating between different temperature reservoirs.
Calculate net work output from given heat input and efficiency.
Analyze refrigerator or heat pump performance using reversed Carnot logic.
Understand the impact of raising or lowering the hot reservoir temperature.
Cross-check results from measured Q_H and Q_C against theoretical Carnot efficiency.

Frequently Asked Questions

Last updated: 2026-09-30 · Reviewed by Nham Vu