The ideal Stirling cycle simply explained (volume-pressure diagram)

In this video, we examine the idealized Stirling cycle. This cycle consists of two isothermal and two isochoric processes. The efficiency of the Stirling cycle represents the maximum possible efficiency achievable for a given minimum and maximum temperature. This efficiency is also referred to as the Carnot efficiency. The Carnot efficiency provides a way to express the second law of thermodynamics.

The thermodynamic processes in a Stirling engine are relatively complex. However, under idealized conditions, a simplified process description can be derived.

Ideally, during the compression process, the entire gas mass would be cooled and would assume the minimum possible temperature of the cooled cylinder. In this ideal case, no heating of the gas due to compression would occur, as maximum cooling would be applied. This approach would result in the minimum possible pressure increase during compression. In such a theoretical process, the compression of the gas would correspond to an isothermal compression process at the constant temperature of the cooled cylinder.

Subsequently, the fully cooled gas would now be passed through the regenerator. Ideally, the gas would completely absorb the heat previously released to the regenerator during the preceding process cycle. In this ideal case, the gas would instantly heat up to the maximum temperature level of the heated cylinder. The flow through the regenerator would occur without delay, i.e., without piston movement, so that the gas would be fully heated and immediately available for the subsequent expansion process. The gas volume would remain unchanged and would merely be heated as a whole through the regenerator. The constant gas volume during heat absorption by the regenerator thus corresponds to an isochoric heating of the gas.

Subsequently, the fully heated gas would be ready for expansion. Ideally, this expansion phase would involve no cooling, which would otherwise result in a pressure drop. This approach would ensure a maximum pressure profile during expansion. In the ideal case, the gas would remain fully heated and always exhibit the temperature of the heated cylinder. Therefore, this process represents an isothermal expansion in the ideal case.

To restart the cycle, the heated gas must now be cooled again for the compression process. Ideally, this cooling would also occur through the regenerator, which would extract the necessary amount of heat from the gas. The regenerator would fully store the extracted heat and release it back to the gas during the next cycle before compression to reheat it. This cooling of the gas in the regenerator would also ideally occur without time loss, ensuring that the fully cooled gas is immediately available for the compression process after expansion. In the ideal case, this heat transfer from the gas to the regenerator would again correspond to an isochoric cooling process.

It is important to note that only the heat transfers during expansion and compression have an external effect, as these maintain constant temperatures. The heat required for isochoric heating and cooling is transferred internally via the regenerator and does not affect the external system. Therefore, only the isothermal processes are relevant for the calculation of the net work based on the difference between the heat supplied and removed.

In the 19th century, physicist Nicolas Carnot demonstrated through theoretical considerations that the thermal efficiency of the idealized Stirling cycle represents the maximum possible efficiency achievable at a given minimum and maximum temperature. This principle applies to all heat engines operating between a minimum and a maximum temperature. The minimum temperature is typically the ambient temperature, as active cooling would otherwise require additional work. The maximum temperature is generally limited by the thermal durability of the materials used.

00:00 Structure and Operation
01:05 Idealized Stirling cycle
01:19 Isothermal Compression
02:01 Isochoric heating
02:40 Isothermal Expansion
03:05 Isochoric cooling
03:41 External heat transfers (regenerator)
05:20 Thermal Efficiency
06:31 Carnot Efficiency (2nd law of thermodynamics)