Cyclic process

A cyclic process is a thermodynamic process in which the system undergoes a sequence of changes and finally returns to its initial thermodynamic state . In state space, the path is closed.

Physical interpretation

Cycles model devices designed for repeated operation—heat engines, refrigerators, and heat pumps—where the working substance returns to its starting state each run while exchanging energy with reservoirs and delivering (or consuming) net work. The logical constraints of the second law on such devices are often phrased as the Kelvin–Planck statement and the Clausius statement .

Key properties and relations

Because the initial and final states coincide, every state function has zero net change over a cycle:

In particular, for the internal energy $U$,

Combining this with the differential form of the first law yields the net balance between heat and work over a cycle:

with the sign of $\delta W$ determined by the work sign convention .

Since heat and work are path functions , their cyclic integrals need not vanish even though the system returns to its original state.

If the cycle is quasistatic and the only mechanical work is boundary work, the net work can be written in terms of the pressure $P$ and volume $V$ as

interpreted with the $P\,dV$ sign convention ; geometrically, this equals the signed area enclosed by the loop in the $P$–$V$ plane.

Second-law constraint on cycles

For any cyclic process, the Clausius inequality implies

with equality if and only if the cycle is reversible . Strict inequality signals an irreversible cycle with positive net entropy production in the combined system and environment.