Boneyard Tools

Heat Engine Efficiency Calculator

Calculate the maximum (Carnot) efficiency of a heat engine from its hot and cold reservoir temperatures, and the actual efficiency from the work output and heat input. Compare the two to see how close an engine gets to the ideal limit.

How to calculate heat engine efficiency

  1. For the Carnot limit, enter the hot and cold reservoir temperatures in kelvin.
  2. For the actual efficiency, enter the work output and heat input in joules.
  3. You can fill in one pair or both pairs.
  4. Read the Carnot and actual efficiencies as fractions and percentages.

Examples

Carnot limit

Th = 500 K, Tc = 300 K
Carnot efficiency = 0.4 (40%)

Actual efficiency

W = 300 J, Qin = 1000 J
Actual efficiency = 0.3 (30%)

Frequently asked questions

What is the Carnot efficiency formula?

Carnot efficiency = 1 - Tc / Th, where Tc and Th are the cold and hot reservoir temperatures in kelvin. It is the maximum possible efficiency for an engine working between those two temperatures.

What is the actual efficiency formula?

Actual thermal efficiency = work output / heat input. It is the fraction of the heat drawn from the hot reservoir that the engine converts into useful work.

Why must temperatures be in kelvin?

The Carnot formula uses absolute temperature, so the ratio Tc / Th only makes sense in kelvin. Using Celsius would give a wrong and even negative answer.

Can an engine beat the Carnot efficiency?

No. The second law of thermodynamics makes Carnot efficiency an upper limit. Real engines always fall short because of friction, heat leaks and other irreversibilities.

Why is the cold temperature limited?

The cold reservoir must be above absolute zero and below the hot reservoir, otherwise there is no temperature difference to drive the engine and the formula is undefined.

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