# Work done on the system through a piston?

I am stuck on like the first page of thermal physics. It seems like the signs of the work done on the system are opposite when the volume is expanded and compressed. But when I imagine myself pushing or pulling the piston, I get confused from $$W = \textbf{F}\cdot \textbf{d}$$
This work will be positive as the direction of the force and the direction of the displacement of the piston will be the same regardless of the change in volume.

What am I missing?

(I got the image from http://www.splung.com/content/sid/6/page/work)

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BvU
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What am I missing?
In the one case it's the fluid that's doing the positive work and in the other it's you, the pusher. So then the fluid does negative work: it exerts a force outwards but the displacement is inward.

In the one case it's the fluid that's doing the positive work and in the other it's you, the pusher. So then the fluid does negative work: it exerts a force outwards but the displacement is inward.
If I consider a piston in equilibrium with atmosphere such that it won't move unless I push it or pull it. This case, whichever way I do, won't I be doing positive work? From above formula for work.

BvU
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Correct.

If I consider a piston in equilibrium with atmosphere such that it won't move unless I push it or pull it. This case, whichever way I do, won't I be doing positive work? From above formula for work.
Correct.
Then either case I am doing positive work. But the above and other text says when volume expands, external work done on the system is negative and vice versa (so the signs of work I do for compression and expansion of gas are opposite). How does this work?

CWatters
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I am stuck on like the first page of thermal physics. It seems like the signs of the work done on the system are opposite when the volume is expanded and compressed. But when I imagine myself pushing or pulling the piston, I get confused from $$W = \textbf{F}\cdot \textbf{d}$$
This work will be positive as the direction of the force and the direction of the displacement of the piston will be the same regardless of the change in volume.
I think you are confused about the direction of the forces....bear with me...

Consider a car jack/lift and define up as positive...

When you raise the car the force applied by the jack is in the same direction as the motion eg both upwards. No problem with that. The work done by the jack s positive.

When you lower the car slowly at constant velocity the jack still applies an upward force on the car but the direction of motion is downwards. The work done by the jack is negative.

Its similar with a piston in a syringe.....

If you let the gas push the piston out slowly at constant velocity you will still be applying a push force on the plunger eg opposite to the direction of motion. So the work you do will be negative.

You could pull the piston really fast. But there will be a net force on the piston that causes it to accelerate. You would have to take into account the work done accelerating the piston. Both you and the gas would do positive work.

BvU
I think you are confused about the direction of the forces....bear with me...

Consider a car jack/lift and define up as positive...

When you raise the car the force applied by the jack is in the same direction as the motion eg both upwards. No problem with that. The work done by the jack s positive.

When you lower the car slowly at constant velocity the jack still applies an upward force on the car but the direction of motion is downwards. The work done by the jack is negative.

Its similar with a piston in a syringe.....

If you let the gas push the piston out slowly at constant velocity you will still be applying a push force on the plunger eg opposite to the direction of motion. So the work you do will be negative.

You could pull the piston really fast. But there will be a net force on the piston that causes it to accelerate. You would have to take into account the work done accelerating the piston. Both you and the gas would do positive work.
This solved the mystery for me... Thank you so much.