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How does a piston-and-cylinder system demonstrate the first law of thermodynamics?

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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 piston-and-cylinder system serves as a classic model for demonstrating the first law of thermodynamics, which states that the change in a system's internal energy ( $Δ U$ ) equals the heat ( $Q$ ) added to the system minus the work ( $W$ ) done by the system on its surroundings: $Δ U = Q - W$ .12

In this system, the cylinder walls act as a boundary, and the movable piston allows the gas to perform work by expanding against a restraining force. The law functions as an energy accounting system:1

Energy Conservation: If the gas absorbs heat and performs work, the internal energy changes to balance the net flow of energy.1
Adiabatic Processes: In a perfectly insulated cylinder, no heat flows ( $Q = 0$ ). If the gas expands, it must perform work at the expense of its own internal energy, causing the gas to cool ( $Δ U = - W$ ).3
Cyclic Processes: In heat engines, the system returns to its initial state, meaning $Δ U = 0$ . Consequently, the net work done over a cycle is exactly equal to the net heat absorbed ( $W = Q_{1} - Q_{2}$ ).4