Heat Engine Efficiency Calculator

Actual efficiency and the Carnot (maximum) limit.

Actual efficiency

Work output W_out (J)

Heat input Q_in (J)

Heat rejected Q_out (J, optional)

Carnot limit

Hot reservoir T_h (K)

Cold reservoir T_c (K)

Results

Formulas

Actual efficiency: η = W_out / Q_in
Or: η = (Q_in − Q_out) / Q_in
Carnot maximum: η_C = 1 − T_c/T_h (temperatures in K)

Physics behind thermal efficiency

A heat engine takes in heat at high temperature, does work, and rejects waste heat at lower temperature. Energy conservation says W_out = Q_in − Q_out. Efficiency is the fraction of heat input that becomes useful work. Carnot's theorem sets a hard upper limit: any engine operating between two temperatures cannot exceed η = 1 − Tc/Th. Real engines (car petrol ≈ 30 %, modern power stations ≈ 40–60 %) sit well below this theoretical maximum.

Worked example

W_out = 400 J, Q_in = 1000 J, T_h = 600 K, T_c = 300 K

η         = 400/1000 = 40%
η_Carnot  = 1 − 300/600 = 50%
OK — actual 40% ≤ Carnot 50%

Related tools

Ideal Gas Law Heat Transfer Work & Energy

FAQs

What is Carnot efficiency?

The upper bound set by the 2nd law: η = 1 − Tc/Th.

Why can't I beat Carnot?

Because of the 2nd law of thermodynamics — any real process has irreversibility.