1.3 Cycles

Take-home message: If a process returns a system to its starting point, all functions of state are unchanged, but net heat may be added to the system, and work done by it.

By definition, functions of state return to their starting value at the end of a cycle. However heat and work are not functions of state, so

$$\oint {\rm d}E = 0 = \oint{}\raise0.44ex\hbox{\bf\symbol{'040}}\llap{d}Q+\oint{}\raise0.44ex\hbox{\bf\symbol{'040}}\llap{d}W$$

and

$$\oint{}\raise0.44ex\hbox{\bf\symbol{'040}}\llap{d}Q=-\oint{}\raise0.44ex\hbox{\bf\symbol{'040}}\llap{d}W$$

but in general

$$\oint{}\raise0.44ex\hbox{\bf\symbol{'040}}\llap{d}Q\ne 0\qq... ...\qquad\oint{}\raise0.44ex\hbox{\bf\symbol{'040}}\llap{d}W\ne 0$$

(Note that $\oint$ is used for the integral round a cycle.)

References

• Mandl 1.3