Compression / Momentum in a cylinder

[Raptor01601]

Ok...this is a thought model to help me understand some things

you have a cylinder with a gas in it. You also have moveable piston. I move the piston into the cylinder, compressing the gas by 25% of the original volume.

I know the pressure of the gas will increase for two reasons:

Decreased volume (increased density)

I have done work on the gas, transfering energy to the gas, which appears as an increase in gas temperature , which also increases the pressure along with the increased density (decreased volume)

I know because of the random motion of the molecules (Vx, Vy, and Vz) the pressure will increase equally in all directions

THE QUESTION:
When I moved the piston into the cylinder, I know that I did work on the gas, increasing the temperature, but the "molecules" that were in contact with the piston when I moved the piston, don't they have a "momentum" imparted to them also in the down "-Y" direction. Wouldn't this momentum eventually reach the bottom of the cylinder (through transfers), and cause some type of small pressure fluctuation. Doesn't gas pressure have some kind of statistical element to it? Would this "flow of momentum" sway the statistical average for a very short (extremely short) period of time?

 

[Clausius2]

THE QUESTION:
When I moved the piston into the cylinder, I know that I did work on the gas, increasing the temperature, but the "molecules" that were in contact with the piston when I moved the piston, don't they have a "momentum" imparted to them also in the down "-Y" direction. Wouldn't this momentum eventually reach the bottom of the cylinder (through transfers), and cause some type of small pressure fluctuation. Doesn't gas pressure have some kind of statistical element to it? Would this "flow of momentum" sway the statistical average for a very short (extremely short) period of time?

Of course it has. You know, it depends on what kind of calculation do you want to do. If you look at times of order $$L/a$$ where L is the cylinder length and $$a$$ is the speed of sound in the gas, then you will see a non linear acoustic wave traveling towards de bottom, and leaving the gas behind it with a new increased pressure caused by the piston. That wave is reflected in a difficult way at the bottom and still runs up to the piston, causing reflecting effects which collaborate to reestablish a new cuasi equilibrium as the piston movement is started. If the piston velocity is slow enough, the characteristic time of piston movement is negligible compared with the characteristic time of the acoustic wave, hence you can assume statiscal equilibrium in the gas. Here Nonequilibrium is understood as the existence of macroscopic gradients of thermodynamic intensive variables.

 

[Danger]

This brings something to mind that I haven't thought of in decades. When I was a little kid someone did a demonstration of some type (might just have been some guy on the farm, for all I can remember). It involved a steel tube welded vertically to a plate, so that the bottom was sealed. A piston was then set in the top and belted full-smack with a sledgehammer. The piston came flying out, of course, but I think it also formed ice around the mouth of the tube. I would have thought that the heat loss through expansion would be slightly less than the heat of compression from bashing the thing (given some absorbion by the steel), so why the ice? Am I remembering it wrongly? Any old coots like me out there ever see or do that?

 

[Q_Goest]

Any old coots like me out there ever see or do that?

Ok, I may be old (- er) … <sigh> but not coot like whatsoever. I fail to see any resemblence.

But hey, what you describe is possible though I seriously doubt there's much ice. I suspect you saw some snow or ice crystals forming in the air, more likely in the ejected stuff and only for a split second, but what you're describing is possible.

Assuming (and I think this is a safe assumption) there is little or no heat being transferred from the air to the metal pipe, then when the air's compressed and re-expanded in the pipe, you can assume the process is isentropic (ie: no change in entropy). More likely, there's some small amount of heat transfer out of the air and into the pipe at first. During the compression phase you have hot, dense air which may shed a small amount of heat to the pipe and cool off. But let's neglect that for a moment, and also neglect any air loss from the pipe. We'll assume there's a seal on it or at least the amount of leakage is small.

What happens is the metal rod compresses the air from roughly ambient conditions (14.7 psia, 70 F) to some high pressure and temperature. As it does this, the rod slows down and comes to a stop. Then the air re-expands and throws the rod upward. As the rod comes back to the original position, the conditions of the air come back to their original condition of 14.7 psia and 70 F. Note that if we assume there's a small amount of heat transfer out of the air, the air will be slightly colder than 70 F when it gets back to 14.7 psia.

Now the rod continues to fly upward, but if its still in the pipe the pressure must drop. As the inside pressure drops the rod slows down, but the air is actually doing work on the rod as it is forced to expand. Again, this is an isentropic expansion.

If the pressure drops to 11.3 psia, and if we maintain our assumption of no heat loss (adiabatic), then the temperature of the air will reach the freezing point, 32 F.

If the rod still hasn't left the tube, it must expand yet some more, further cooling the air.
At 10 psia, the temperature is 15 F.
At 7.5 psia, the temperature is -23 F
At 5 psia, the temperature is -71 F
At 2.5 psia, the temperature is -141 F
At 0.1 psia, the temperature is -333 F

That's just a quicky thermal analysis, but yea the air can get very cold. The thing is, as the pressure goes down, you have less air so you have less thermal mass, which means you can't refrigerate too much with it, and the steel pipe represents considerable thermal mass, so I doubt the pipe can get that cold. I could see water in the air getting cold and freezing though, so I suspect that's what you saw.

Edit: Correction - the mass of air doesn't decrease as it gets cold because the air is all trapped inside the pipe. <argh> Mass stays constant.

 

[Raptor01601]

Thanks...so if I had a really sensitive pressure gauge at the top and bottom of the cylinder, would I see a periodic pressure fluctuation?

Even after the piston has stopped moving, as the "momentum flow" travels back and forth to the top and bottom of the cylinder?

 

[Q_Goest]

Yes, a pressure pulse can travel up and down after its been initiated. Reminds me of a job I had where we ignited small amounts of explosives in a test cell. The pressure pulses rapidly traveled from one end and back many times before dissipating. Same thing can happen to a smaller degree at the lower pressure.