The invention exploits, of preference with a gaseous coolant, the thermodynamic cycle of Stirling. A Stirling's motor cycle achieves the following steps, as shown on the figures 1A et 1B (P : pressure ; V volume ; T : temperature ; S : entropy of the fluid) :
-    1->2 : Isothermal compression to the contact of the cold source at the temperature Tf, the fluid is evolving from a maximum volume Vmax to a minimum volume Vmin,
-    2->3 : Isochoric heating at the volume Vmin, with an increase of the pressure of the fluid,
-    3->4 : Isothermal relaxation to the contact of the heat source at the température Tc, the fluid is evolving from the volume Vmin to   
   Vmax,
-    4->1 : Isochoric cooling at the volume Vmax, with a decreasing of the pressure of the fluid.

    The stages 2->3 and 4->1 are isochoric and don't take or supply any work to the gaz : 2->3 makes the gas pass from Tf to Tc and 4->1 from Tc to Tf.

    On the contrary, the exchanges of mechanical work are taking place during the stages 1->2 and 3->4 :
-    During the stage 1->2, the isothermal character of the compression gives a thermal transfer from the fluid to the cold source and   
    imposes the supply of a mechanical work to the fluid.
-   During the stage 3->4, the isothermal character of the relaxation imposes a thermal transfer from the hot source to the fluid : thus the
    fluid leaves a mechanical work bigger than the one it has received during the compression 1->2, that's why the cycle is motor.

Robert Stirling quickly chose to improve its engine by equipping it with a regenerator.

    This regenerator allows the fluid to recover during its isochoric heating 2->3 the heat it has leaved thère during its isochoric cooling 4->1. Thanks to this interal heat recycling, the thermodynamic output of Stirling's cycle with regenerator attemps the one of Carnot's motor cycle :

   
   

    For a receptor cycle, as illustrated on the figures 1C and 1D, the course of the cycle is inverted :
-    1->4 : Isochoric heating at the volume Vmax, with an increasing of the pression of the fluid,
-    4->3 : Isothermal compression to the contact of the hot source at a temperature Tc, the fluid is evolving from a volume maximum
     Vmax to a volume minimum Vmin,
-    3->2 : Isochoric cooling at the volume Vmin, with decreasing of the pressure of the fluid,
-    2->1 : Isothermal relaxation to the contact of the cold source at a température Tf, the fluid is evolving from a volume Vmin to Vmax.

    The stages 1->4 et 3->2 are isochoric and don't take or supply any work to the fluid. They are only thermal transfer stages : 1->4 makes the fluid pass from Tf to Tc and 3->2 from Tc à Tf.
    During the stage 4->3, the isothermal character of the compression gives a thermal transfer from the fluid to the hot source and imposes the supply of a mechanical work to the fluid.
    During stage 2->1, the isothermal character of the relaxation imposes a thermal transfer from the cold source to the fluid and forces the fluid to leave a mechanical work smaller than the one it has received during the compression 4->3, that's why the cycle is receptor.

    Thus the engine can be used as a coolling machine or a heat pump under the condition to communicate it some mechanical work. When the engine is equipped with a regenerator, allowing the fluid to recover during its isochoric heating 4->1 the heat that it has leaved during it isochoric cooling 3->2, the thermodynamic efficiencies of the cycle attempts those of Carnot's receptor cycle, more precisely :
   





 

These some fundamental recalls of thermodynamics are going to permit to better understand the limits of the present art of the Stirling's machines and the multiple advantages of the present invention (1).