Suppose you had a very long tube, maybe a 100 miles long. The diameter of the tube was fairly large say 6 ft. The tube was leak proof 100%. Say you had a pump to bring it into a vacuum that took 3 months to pull it down to its best ability.
Questions would the vacuum be as great as it would if the tube were only 1 ft long? Would the pressure read the same on both ends of the tube?
A vacuum is a vacuum no matter the vessel.
The thing about a vacuum is: there’s a maximum value (in a negative sense).
Since air pressure is around 14.7psi, no vacuum can ever exceed that negative pressure at sea level.
So, the size of the container is irrelevant. The total force may be greater, but the force per square inch (psi) can never exceed around 14.7psi.
beowulff: I don’t understand your answer. What is “negative pressure?”
Isn’t pressure an absolute thing, from zero to…very high?
Earth’s air pressure, at sea level, is around 14 pounds per square inch.
A really good vacuum pump can bring the pressure in a sealed container remarkably close to zero. Never all the way to absolute zero (very much as with temperatures) but pretty awfully close.
The Wikipedia article on the subject talks about “Extremely High Vacuum” being around 1.5 * 10 ^ -14 psi. That’s awfully close to zero!
There is absolute pressure and Gauge pressure.
Most people are familiar with Gauge Pressure, and it is generally the most useful measurement. Gauge pressure is differential, and measures vs. a reference, which is generally atmospheric pressure. So, a vacuum is negative with respect to atmosphere, going from 0 (no vacuum) to -14.7 psi (or 760 mm of Mercury).
Absolute pressure starts at zero (perfect vacuum), but isn’t very useful in most cases, because most pressure (and vacuum) effects are differential (a tire, for instance has 30psi GAUGE pressure in it, but 44.7psi ABSOLUTE).
Depends. Is your 100 mile tube curved to match the Earth’s surface? If not, then the center will be “downhill” from the ends, and your remaining air will accumulate there. You should read a slightly lower remaining pressure at the two ends of the 100 mile tube than you would at the end of the 1 ft tube, assuming the total density of remaining air was identical. There will be other interesting effects based on the variation of temperature across your 100 mile tube, but those are much more complicated.
Well if the pump did its best… then its the same… The best a pump can do is the same pressure … (unless it wears out beforehand) no matter the size of the vacuum tube.
Vacuum doesn’t suffer from dynamics, as there is nothing to move.
negative pressure is the pressure below the measurement … We routinely measure measure our tyre pressure as pressure above the local atmospheric pressure… of course we can measure the pressure in the vacuum tube as an amount less than the local atmosphere, or any other reference pressure.
Suppose you have a long syringe with a perfect seal - the outlet nozzle is attached to an ideal vacuum pump, just for good measure - you withdraw the plunger an inch and evacuate the inside to as close to perfect vacuum as possible.
You now withdraw the plunger another inch. Is the pull* force on the plunger the same? I don’t see how it could be different - there’s ‘more’ vacuum inside, but it’s more of zero.
So the syringe doesn’t act like a spring (a spring requires increasing load to stretch it further).
*(of course it’s not an actual ‘pull’, it’s caused by a push, but it can be measured by a spring balance or other tension method)
If you Mangetout’s method above, the longer tube will have a better vacuum. What little air there was between plunger and tube wall at the beginning will be spread over a larger volume.
If you start with a air filled tube and use a pump to evacuate it, you need to define “down to its best ability”. At some point the vacuum will be so great the remaining atoms are rarely interacting and increasing the vacuum will require gas atoms randomly exiting through the pump. The longer the tube the longer it will take for the lonely atoms the furthest from the pump to randomly encounter it and be evacuated. And then your question becomes one of the practical behaviour of gas atoms in near vacuum and extremely efficient pumps.
For what it’s worth, we don’t have a vacuum tube 100 miles long, but we do have one 4 km long (four of them, in fact) at the two LIGO facilities. They’re extremely good vacuums, but that’s mostly just because, for that application, they need to be, so we spent the extra time, money, and effort to engineer them really well.
But even if it was 0 psi, that limits the pressure differential between the vacuum and the surrounding atmosphere to around 14.7 psi.
This is why you can’t use a vacuum to raise water more than about 30 feet.
Not only does it need to be 100% leak-proof, but it also needs to be 100% non-porous and 100% clean. Porous surfaces can trap gases and release them very slowly. Contamination (grease, oil, sweat, fingerprints, dead bugs, etc) will evaporate. Both of these act like leaks, especially at high vacuum and/or when you have a very large surface area.
In a real-life vacuum system, there is always a pressure gradient when the pump is running - i.e. the vacuum is better closer to the pump. If we’re talking about a hypothetical 100% leak proof, 100% clean vacuum system which is only limited by the pump’s ability - I guess it depends on how the pump behaves near the limit. A real-life pump usually gets less and less efficient as it nears its capability, and will reach the limit exponentially, so there will be a pressure gradient.
We have a 100-meter vacuum tube used for X-ray and optical testing. It has cryogenic pumps every few meters along the length, capable of pumping down the whole tube to high vacuum (probably 10^-6 torr range). But it costs a lot of money to run these pumps. I’m told most of the time, they just hook up a small pump at one end, and eventually (days or weeks) the whole tube gets down to 10^-3 torr level.
Except when we’re talking about achieving good vacuum in a vacuum chamber, then it’s the absolute pressure that matters. Vacuum gauges measure absolute pressure, and vacuum pumps are limited in how low an absolute pressure they can create.
Is that you Elon ?
My main experience with vacuum tubes are, well, vacuum tubes as you would find in old time electronics.
There are some odd things that happen in vacuum tubes that electronic tube makers had to take into account in making them.
E.g., not all gases are of equal harm in this situation. Oxygen is especially bad, inert gases not so much. Usually.
One way that was discovered early on to add extra oomph to a vacuum was to add a getter substance. A material inside the tube that “gets” gases out of the near vacuum. You might see a silvery blotch on the side of an old tube. That’s getter.
Anyway, the OP might be interested in reading more about getters. In addition to helping the quality of a vacuum, they also absorb gases that come out of the material in the tube. Even glass will off-gas a bit over time due to impurities. The getter will help with this. (One reason a tube will burn out is that the getter stops being good at removing the off-gas, the vacuum quality goes down and the filament burns out.)
So, if you scale up a vacuum tube what are the ratios: The volume would go up as the cube of the length, but the OP seems to restrict the width quite a bit.
With the OP’s narrow (relatively) tube, it’s all pretty much linear so maybe no problem. Double the length, double the volume, double the surface area that will off-gas, double the area available to apply getter.
[del]But if it was a standard cubic scaling, the off-gassing in a larger tube would significantly degrade the vacuum compared to a smaller tube.[/del]
No, strike that. The cubic volume wouldn’t be heavily affected by the quadratic off-gassing. OTOH, the existing remnants of air would be harder to scrub out via getter.
Another fun thing about near vacuums: the gases tend to easily get ionized. And ionized molecules tend to cause more problems than their neutral friends, as usual. I wonder how volume & surface area affects this.