Work in a PV Curve: Is the Work Done 0?

[gabdolce]

Hey all,

In one of my textbooks, there is a passage in the thermodynamics section that states that:

For a closed cycle where the system returns to its initial state, the work done is the area enclosed by the curve (when looking at a Pressure-Volume graph).

Shouldn't the work done by this process be a total of 0 instead?

Thanks in advance.

 

[cjl]

Not necessarily. A closed cycle can do work. Suppose it cycles between two states. If the work done getting from state 1 to state 2 is much larger than the work done (with the opposite sign of course) from state 2 back to state 1, the cycle will do net work. Note that this does require the system to be under a different load during different parts of the cycle. This changing load is what allows the system to end at the same state that it started while still doing work.