Result

Carnot efficiency

e_{Carnot} = 1 - \frac{T _{c}}{T _{h}}

Statement

The maximum possible efficiency for any engine operating between reservoirs at temperatures T_h and T_c.

Symbols and units

$e_{Carnot}$	maximum possible efficiency	—
$T_{h}, T_{c}$	hot, cold reservoir temperature	K

When it applies

An idealized, fully reversible cycle — an upper bound, not a value any real engine reaches.

Don't use when

A theoretical upper bound only — no real engine reaches it, since it requires an idealized, infinitely slow reversible cycle.

Derivation

A consequence of the second law (Carnot's theorem): a reversible engine sets the upper bound on efficiency for any engine operating between the same two reservoirs.

e_{Carnot} = 1 - \frac{T _{c}}{T _{h}}

Worked examples

An idealized engine between 300 K and 600 K

e_{Carnot} = 1 - \frac{300}{600} = 0.50

Even a perfectly reversible engine caps out at 50% here — doubling the hot reservoir's temperature does not remotely double the efficiency; the limit is set by the ratio, not the difference.

Watch out for

This is a theoretical upper bound, reached only by an idealized, infinitely slow reversible engine — every real engine falls short of it. Doubling the hot reservoir's absolute temperature does not double the efficiency; it only halves the ratio T_c/T_h.