Properties of a cycle

A cycle is a sequence of reversible transformations that brings the gas back to its initial state. It is the basic structure of every heat engine: the gas is compressed, heated, made to expand and cooled, and in the end returns exactly to its starting state, ready to repeat the loop.

The fact that the gas returns to its starting point has an immediate consequence for the state functions, which depend only on the state and not on the path: over a complete cycle their change is zero.

Properties of a cycle

In a complete cycle: $\begin{aligned} \Delta E_\text{int} &= 0 \quad (\text{internal energy, a state function}) \\ \Delta S_\text{gas} &= 0 \quad (\text{entropy of the gas, a state function}) \\ \sum L_\text{gas} &= \sum Q \quad (\text{first law over the whole cycle}) \end{aligned}$

This last relation follows from the first law: if the internal energy does not change over the loop, then all the net heat absorbed by the gas is returned as net work. The net work of the cycle is read geometrically as the area enclosed by the closed curve in the $P$-$V$ diagram, and its sign depends on the direction of travel:

• clockwise $\Rightarrow L_\text{netto} > 0$: the cycle is an engine (produces work);
• anticlockwise $\Rightarrow L_\text{netto} < 0$: the cycle is a refrigerator or a heat pump (absorbs work).

Linked notes

Topics: Termodinamica · Macchine termiche Concepts: Trasformazioni termodinamiche · Primo principio della termodinamica Methods: Diagramma P-V e ln P - ln V Objects: Macchina termica

Related exercises: Esercizio svolto — espansione isoterma reversibile vs irreversibile · Problema — Ciclo rettangolare nel piano p-V · Problema — Area di un ciclo p-V