Britannica Sources used in this answer

How does a heat engine complete a cycle while returning to its original internal energy?

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

Engraved portrait of Rudolf Julius Emanuel Clausius, a bearded man in formal attire with sideburns, facing forward. — thermodynamics Rudolf Clausius (1822 - 1888) is considered one of the central founders of the science of thermodynamics.

A heat engine completes a cycle by returning to its initial thermodynamic state, meaning its internal energy ( $U$ ) remains unchanged ( $Δ U = 0$ ) at the end of each cycle.1

Internal energy is a state function, meaning its value depends solely on the current condition of the system—defined by properties like temperature, pressure, and volume—rather than the path taken to reach that state. Because the engine returns to its starting state, the net change in internal energy over one full cycle is zero.231

According to the first law of thermodynamics, the change in internal energy is equal to the heat ( $Q$ ) absorbed minus the work ( $W$ ) done by the system. For a complete cycle, this relationship simplifies to:3
$W = Q_{1} - Q_{2}$
where $Q_{1}$ is the heat absorbed from a high-temperature source and $Q_{2}$ is the heat exhausted to a lower-temperature sink. By exhausting the remaining heat, the engine resets its state, allowing the process to repeat while adhering to the conservation of energy.1