Analysing a thermodynamic cycle can seem complicated, but it becomes mechanical if a systematic method in four steps is followed. The underlying idea is to separate two levels: first the states (the vertices of the cycle) are fixed, then the processes (the segments connecting the vertices) are studied.
- Identify the processes. Recognise the type of each transformation (isothermal, isochoric, isobaric, adiabatic, …): establish which are reversible and which constraints hold on each segment (for example constant , or ).
- Table of states. For each vertex of the cycle compute the triplet , , using the ideal gas law and the specific relations of the process leading to that vertex.
- Table of processes. For each segment compute the four exchange quantities: heat , work done by the gas , change in internal energy and change in entropy .
- Checks. Verify the consistency of the calculations by closing the cycle.
Cycle-closure checks
Over a complete cycle the state functions return to their initial value, so: If one of these three relations does not hold, there is an error in a row of the table: they are a powerful automatic check on the calculations.
The first law guarantees that over every closed cycle, because internal energy is a state function; for the same reason the entropy of the gas also returns to its starting value. The net work, on the other hand, is not zero: it is the difference between the heat absorbed and that released, and in the - plane it coincides with the area enclosed by the cycle.
Links
Topics: Macchine termiche Concepts: Primo principio della termodinamica Skills: Risoluzione di un ciclo termodinamico Methods: Diagramma P-V e ln P - ln V
Related exercises: Problema — Frigo con la porta aperta · Problema — Rendimento di una macchina reale (4000-3000 J) · Problema — Bilanci di un ciclo