Work Done On or By System?

theintarnets

1. The problem statement, all variables and given/known data
I am supposed to determine whether work is being done on or by a closed thermodynamic system from a diagram that's sort of like this, and provide justification for my answer:


My problem is I have no idea how to tell if that system is doing work or if work is being done on it based on the graph. I heard that if it's going in the clockwise direction, that means the work is being done by the system, but that isn't a proper justification. Can someone help me understand this better?

TSny

Work done by a force is positive if the force is in the same direction as the displacement. So, if you have a gas, say, in a cylinder with a piston and the piston moves outward (increase volume) then you can see that the force of the gas on the piston is in the same direction that the piston moves. So, you see that this implies that if the volume increases, the system does positive work on the environment (which is equivalent to saying that the environment does negative work on the system). The greater the pressure, the greater the magnitude of the work.

So, if you look at your diagram, which leg of the "triangle" corresponds to positive work done by the system?

Which part corresponds to negative work done by the system? Which part to zero work?

Which is greater in absolute value, the positive work or the negative work?

theintarnets

Thank you for the explanation. If I'm understanding this correctly, the segment from 2 to 3 represents positive work being done by the system, and the segment from 3 to 1 represents work being done on the system, which I guess is negative. I'm not sure about 1 to 2 though...

TSny

Yes, that's right. Now, from 1 to 2 there is no change in volume. Since forces do work only when there is a displacement, there is no work done from 1 to 2.

Hopefully, you can see that if you have a closed loop ("cycle") on the diagram, then the net work done by the system will be positive for a clockwise cycle and negative for counterclockwise.

theintarnets

But how do I explain why the positive work done here is greater than the negative work? I mean, aside from the fact that the hypotenuse is always the longest side of a triangle...

TSny

The pressure during the positive work is higher than the pressure for the negative work and the magnitude of the volume change is the same. Greater pressure (force) for the same displacement means greater work.

It is possible to show that the magnitude of the work for a section of the pV diagram is just the area underneath the section. So, the area underneath the line from 2 to 3 is greater than the area underneath the line from 3 to 1. "Area underneath" means area down to the V axis, as shown below.

Attached Thumbnails

 

theintarnets

Wow, thank you so much! I understand it a lot better now.