Q:

Assume I have a strong metal cylinder sealed at one end, and I have a perfectly fitting piston placed inside the cylinder, close to the sealed end. I now start to create a vacuum by pulling the piston slowly away from the sealed end. Physics tells me that if the area of the piston is one square inch, the force I need to apply in order to move the piston is 14.7lbs, and that I simply have to continue to apply this force to create a vacuum of any desired volume (provided that the cylinder is sufficiently long and strong.)

My problem is that my intuition tells me that the force I would need to apply would not in fact remain constant at the original 14.7 lbs, but become greater and greater as I attempted to increase the volume of the evacuated space.

Which answer is true?

Many Thanks.

- Ed Dowling (age 74)

Perth, WA, Australia

My problem is that my intuition tells me that the force I would need to apply would not in fact remain constant at the original 14.7 lbs, but become greater and greater as I attempted to increase the volume of the evacuated space.

Which answer is true?

Many Thanks.

- Ed Dowling (age 74)

Perth, WA, Australia

A:

Nice question. Your physics is right. Your intuition is good, but it's based on a more familiar, and slightly different, situation.

Typically, when you pull back on a piston, there's a little air behind it. Initially, there's not a vacuum. Once you've pulled it back a little, that air has to fill a bigger volume, so there's a partial vacuum and more force is required. The vacuum gets closer to full the more you pull the piston back. In your hypothetical model, however, there's no air at all behind the piston so a full vacuum is present from the start.

Mike W.

Typically, when you pull back on a piston, there's a little air behind it. Initially, there's not a vacuum. Once you've pulled it back a little, that air has to fill a bigger volume, so there's a partial vacuum and more force is required. The vacuum gets closer to full the more you pull the piston back. In your hypothetical model, however, there's no air at all behind the piston so a full vacuum is present from the start.

Mike W.

*(published on 10/22/2007)*

Q:

Many thanks for your very prompt answer.

The follow-up question is:

Assuming the hypothetical model again, since the only force acting on the one-square-inch piston is 14.7 lbs (atmospheric pressure), does that mean that by applying a CONSTANT force of say 15 lbs I can pull the piston away from the sealed end indefinitely, and create a vacuum of any desired volume (provided of course that the cylinder is sufficiently long and strong)?

- Ed Dowling (age 74)

Perth, WA, Australia

The follow-up question is:

Assuming the hypothetical model again, since the only force acting on the one-square-inch piston is 14.7 lbs (atmospheric pressure), does that mean that by applying a CONSTANT force of say 15 lbs I can pull the piston away from the sealed end indefinitely, and create a vacuum of any desired volume (provided of course that the cylinder is sufficiently long and strong)?

- Ed Dowling (age 74)

Perth, WA, Australia

A:

yes.

but remember, work is force times distance, so although a fixed force is enough, you do more work the farther you pull it out.

Mike W.

Vacuum pumps work on this principle -- it’s too hard to make an arbitrarily large (and strong) vacuum vessel that also has a high-quality seal for the piston. Usually you want the vacuum vessel to have another shape for other purposes (example -- the Tevatron beampipe at Fermilab has to be a large, narrow ring). An ordinary vacuum pump has the piston and an oil seal, and some one-way valves so that the piston can repeatedly evacuate its chamber, have gas let in from the vessel to be evacuated, and then re-compress the gas to expel it from the other valve. The maximum force needed to push the piston depends on the atmospheric pressure-- hence there is a maximum amount of power a motor would need to drive it at a certain speed. You also get some of the energy back in a piston pump like this since pushing the piston back if it’s almost a vacuum in the cylinder does work of opposite sign to what was needed to evacuate it in the first place. You can balance the load on a vacuum pump constantly pumping on a nearly evacuated vessel by putting two pistons mechanically tied together -- when one pulls out, the other pushes in.

Tom

but remember, work is force times distance, so although a fixed force is enough, you do more work the farther you pull it out.

Mike W.

Vacuum pumps work on this principle -- it’s too hard to make an arbitrarily large (and strong) vacuum vessel that also has a high-quality seal for the piston. Usually you want the vacuum vessel to have another shape for other purposes (example -- the Tevatron beampipe at Fermilab has to be a large, narrow ring). An ordinary vacuum pump has the piston and an oil seal, and some one-way valves so that the piston can repeatedly evacuate its chamber, have gas let in from the vessel to be evacuated, and then re-compress the gas to expel it from the other valve. The maximum force needed to push the piston depends on the atmospheric pressure-- hence there is a maximum amount of power a motor would need to drive it at a certain speed. You also get some of the energy back in a piston pump like this since pushing the piston back if it’s almost a vacuum in the cylinder does work of opposite sign to what was needed to evacuate it in the first place. You can balance the load on a vacuum pump constantly pumping on a nearly evacuated vessel by putting two pistons mechanically tied together -- when one pulls out, the other pushes in.

Tom

*(published on 10/22/2007)*