Formulas & tables/Physics/Thermodynamics/Carnot cycle efficiency

Carnot cycle efficiency

η=1−TzTg\eta=1-\dfrac{T_z}{T_g}

Result unit: — (dimensionless, < 1)

What it describes

The maximum theoretical efficiency of a heat engine operating between two temperatures.

Symbols

η\eta
efficiency
[—]
TzT_z
temperature of the cold reservoir
[K]
TgT_g
temperature of the hot reservoir
[K]

Where it comes from

No heat engine can convert all heat into work — the maximum efficiency is set by the ratio of the temperatures (in kelvins) of the cold and hot reservoirs. A larger temperature difference means higher efficiency.

When to use it

The upper limit of heat-engine efficiency. Temperatures always in kelvins!

Example

An engine operates between Tg=600T_g=600 K and Tz=300T_z=300 K. Calculate the maximum efficiency.
SubstitutionTz=300T_z=300 K, Tg=600T_g=600 K.
Resultη=1−300600=0.5=50%\eta=1-\dfrac{300}{600}=0.5=50\%.

Related formulas

First law of thermodynamics Efficiency

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