The Theory of Society  by Wayne M. Angel, Ph.D.

Relation Thermodynamics: The Carnot Cycle



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In the last two sections, I deliberately avoided the nature of the process by which a thermodynamic engine, refrigerator, or heat pump accomplishes the transfer of heat and work.  This was done so as to emphasize that efficiency limitations are process independent.  In this section I will consider a specific process.  Continuing the analogy with physical thermodynamics, I will discuss the Carnot cycle as it applies to human systems.

                        To carry out the required process we introduce an "auxiliary system," in addition to the two reversible heat sources and the reversible work source.  The auxiliary system is, in effect, a tool, and at the end of the process it is left precisely in the same state as it was in at the beginning.  It is this cyclic nature of the process within the auxiliary system that is reflective of the name of the Carnot "cycle."

                                                                                    Callen [1960, 77]

The cycle is a four step process.  Changes in the temperature and entropy of the auxiliary system are

The Carnot Cycle

Step 1: A->B.  In this step the auxiliary system is placed in thermal contact with system H, a hot (high temperature) heat reservoir, and entity relationship contact with system W, a reversible work source.  Due to the isothermal contact with H, the auxiliary system expands its entity relationship volume exerting a pressure on the entity relationship space of W causing work to be performed on W as the entity relationships are modified.

Step 2: B->C.  The thermal contact between the auxiliary system and H is removed, but the entity relationship contact is maintained.  The auxiliary system is allowed to expand adiabatically until it temperature falls to Tc.  During this further work is done on W.

Step 3: C->D.  The auxiliary system is compressed while in thermal contact with system C, a cold (low temperature) heat reservoir.  The entity relationship contact with W is maintained.  During this step heat flows from the auxiliary system to C, and work is transferred from W to the auxiliary system.

Step 4: D->A.  The auxiliary system is thermally isolated and compressed as it continues to receive work from W until the temperature Th is reached.  The cycle is now complete.

The heat withdrawn from H in process 1 is.  The heat transferred to C in process 3 is.  The difference  is the net work transferred to the reversible work source in the complete cycle.

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