Britannica Sources used in this answer

How does the second law of thermodynamics limit heat-engine efficiency?

Created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

Study how a series of gears in a waterwheel translates a stream's energy to a millstone — energy conversion Before the Industrial Revolution, power came from three main sources: humans, draft animals, and water.
The ingenuity people used in harnessing waterpower can be seen in this medieval-style mill. The waterwheel is turned by a stream and is connected to a shaft that leads into the building. At the other end of the shaft is a gear. The connection of a series of gears translates the power from the stream to a shaft that drives a millstone, which grinds flour from grain.
(30 sec; 1.84MB)

The second law of thermodynamics dictates that a heat engine cannot convert all absorbed heat into work, establishing a fundamental limit on efficiency.12

A heat engine operating in a cycle absorbs heat $Q_{1}$ from a high-temperature reservoir ( $T_{1}$ ) and exhausts waste heat $Q_{2}$ to a lower-temperature reservoir ( $T_{2}$ ). Because the engine returns to its original state, the work done is $W = Q_{1} - Q_{2}$ . The second law requires that the net entropy change of the reservoirs must be greater than or equal to zero ( $Δ S \geq 0$ ). If $Q_{2}$ were zero, the entropy change would be negative, violating this law.12

Consequently, some heat must always be exhausted as waste, limiting the maximum possible efficiency—known as the Carnot efficiency—to:

$η = 1 - \frac{T_{2}}{T_{1}}$

This limit is a law of nature; no design improvements or reduction of mechanical imperfections like friction can surpass this theoretical maximum, as it is dictated by the temperatures of the heat reservoirs themselves.12