I don't understand P-V work?
Hi. I'm having a lot of difficulty understanding P-V work done in a cylinder. I know that force x distance is work, and since pressure is force per area then multiplying by volume would make things come out looking like work. But, I would have thought that work would really equal NET force x distance, which would seem to mean that I'd have to look at the differences in pressure between the inside and outside of a cylinder. That thought is dead wrong (especially in a "reversible process" if that means what I think it does) but I don't really see why.
Anyway, I appreciate the help. Thanks for your time.
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Lets ignore gas for a moment. You see the exact same behavior in other systems.
Imagine an object with a weight of 100N. You get it moving slightly upward, then maintain a constant force of 100N upward. Since force and weight are equal, the object does not accelerate but is constantly rising. How much work is done on the weight? F x d. Note that the F here is the absolute force. We don't measure the net force on the object, nor do we care that the force is slightly greater or slightly less than the weight. That's all taken care of by the motion of the object.
Similarly in your cylinder, a big difference in pressure would cause the cylinder to accelerate. But the work done remains the same.
Another way to think of it. If you have an excess of pressure inside, then besides doing work on the environment, you'll also be accelerating the cylinder. So at the end, you'll not only have done thermodynamic work, you'll also have a cylinder with KE. In the reversible process, the pressures are always equal, so there is no acceleration and there is no KE in the cylinder itself.