The Stirling Cycle

The Stirling cycle is a closed, regenerative thermodynamic cycle that uses a fixed mass of gas (typically air, helium, or hydrogen) sealed inside the machine. The Scottish minister Robert Stirling patented it in 1816, and an engine built on it was pumping water at an Ayrshire quarry by 1818. The idealized cycle has four steps. First, isothermal expansion: the gas absorbs heat from the hot reservoir and expands at constant temperature, doing work. Second, constant-volume (isochoric) cooling: the gas passes through the regenerator, depositing heat into it as its temperature falls. Third, isothermal compression: the gas is compressed at the low temperature while rejecting heat to the cold reservoir. Fourth, constant-volume heating: the gas passes back through the regenerator and recovers the heat stored earlier, returning to the hot temperature to begin again. The regenerator, which Stirling called the 'economiser,' is the cycle's defining innovation. Acting as an internal heat store, it captures heat during cooling and gives it back during heating instead of dumping it to the sink. Because heat is added and rejected isothermally, the ideal cycle is fully reversible and reaches the same theoretical limit as Carnot Efficiency: The Theoretical Maximum for Any Heat Engine between the same two temperatures. Real machines fall well short, achieving roughly half the ideal efficiency due to heat-transfer losses and imperfect regeneration. The cycle is symmetric: supply heat and it produces shaft work as a Stirling engine using any external heat source; supply shaft work and it pumps heat the other way as a Stirling cryocooler. Philips ran a Stirling engine in reverse in 1949 and found it liquefied air at the cold tip, launching a line of cryocoolers used to reach cryogenic temperatures and liquefy gases. Stirling cryocoolers compete with other regenerative coolers such as Pulse Tube Cryocoolers: Trading Efficiency for Zero Vibration and The Gifford-McMahon Refrigeration Cycle, and the broader family of gas-based cooling is covered in Gas-Cycle Refrigeration: The Seventh Fundamental Cooling Approach.