Definition

Engine efficiency

e = \frac{W}{Q _{h}} = 1 - \frac{Q _{c}}{Q _{h}}

Statement

The fraction of heat input converted to useful work.

Symbols and units

$e$	efficiency	—
$W$	net work output	J
$Q_{h}, Q_{c}$	heat from hot, to cold reservoir	J

When it applies

Any heat engine operating in a cycle between two reservoirs.

Derivation

Efficiency is defined as useful output over heat input; combined with energy conservation (W = Q_h − Q_c), it can be written purely in terms of the two heat flows:

e = \frac{W}{Q _{h}} = 1 - \frac{Q _{c}}{Q _{h}}

Watch out for

No heat engine can reach efficiency 1 — some heat must always be exhausted to a cold reservoir, a consequence of the second law, not merely an engineering shortfall.