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Let there be a hollow container made of glass or some other transparent material, roughly the size and shape of an apple. Let the walls be of sufficient thickness for the container to be safely evacuated to some reasonable degree, perhaps around $10^{-8}$ mbar, and then hermetically and evenly sealed.

  1. How could one prove that the container is evacuated, and with what accuracy? Would x-ray crystallography, laser scattering, light absorption or emission or ultrasound be possible ways?

  2. Is there a simple way of demonstrating that the container is evacuated, perhaps by placing something inside it before sealing which behaves in a very specific and obvious way in a vacuum, without actually removing said vacuum? Aside from the obvious feather, which would fall without air resistance. I was thinking of something along the lines of a small quantity of cesium, but that wouldn't be distinguishable from an inert gas atmosphere.

Thanks!

Edit: There is no reference container to compare with and the container itself isn't standardized, so density/weight considerations are out, if I am right. Actually, so is light refraction, probably, as the container walls aren't really level enough, considering the small refraction delta mentioned in Andrew S.'s reply.

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  • $\begingroup$ Do we know what the gas would be if it was there? $\endgroup$ – Floris Feb 26 '15 at 1:40
  • $\begingroup$ Strictly put, no, but if it makes things a lot simpler, normal air. $\endgroup$ – Zubo Feb 26 '15 at 1:46
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Freeze it in liquid helium. Any gas inside will condense out.

Spin it quickly then stop it. The internal turbulence of the spinning gas will be visible with a sensitive detector.

Apply a short sharp impact to one side. If there is gas inside, the sound energy peak from the sound transiting the gas will be temporally distinct from the spectrum of the sound transiting through the glass.

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  • $\begingroup$ Great, very simple and elegant. $\endgroup$ – Zubo Feb 26 '15 at 15:30
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For 1. In principle, the refractive index of a true vacuum is identically 1. For air at atmospheric pressure, the index is 1.000293 for visible light. Therefore, you should be able to determine the deviations between in refractive angles for a jar filled with air and one under vacuum. Since we're talking deviations on the order of one in ten thousandth, it's be quite difficult to measure this as a demo, but it could be done in the lab. The buoyancy/weight of the container could also be used to differentiate it from one filled with air.

For 2. A lot of metals have solid room temperature vapor pressures in the ultra-high vacuum region. For instance, if you had a chunk of Cadnium of Zinc (down scroll for the charts) in your container, all you'd need to do is shine a heat lamp on the container heating the metal by a few dozen degrees Celsius and they'd begin to evaporate away. These materials have vapor pressures around 10^-8 mBar somewhere between 300 to 400 K.

One more fun way to determine the success of your vacuum process would be to watch a Crookes radiometer as you lower the pressure. As you reach below 10^-6 mBar, the rotation should stop.

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  • $\begingroup$ The radiometer works in a range of pressures - as you say it doesn't include very good vacuum, but it also doesn't include atmospheric pressure. As such it is probably not a good candidate for the problem (but a fun clip!) $\endgroup$ – Floris Feb 26 '15 at 1:38
  • $\begingroup$ Thanks for the detailed info! I naively thought Crookes radiometer spins because of light pressure. $\endgroup$ – Zubo Feb 26 '15 at 1:42
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    $\begingroup$ @AndrewS. At the risk of demonstrating my ignorance, I have to voice my curiosity: Wikipedia mentions "Crookes incorrectly suggested that the force was due to the pressure of light." and provides a lot of explanation relating to thermal difference. Don't know if it's correct, of course. $\endgroup$ – Zubo Feb 26 '15 at 1:59
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    $\begingroup$ @Zubo Err... When I said "light" pressure. I meant, light as in not much! Oops! I didn't even consider "light" being confused with light-light. My apologies for the homonyms. I can't seem to edit the comment, so I will delete it and repeat it here: "It does spin because of low pressure, I was pointing out that if the pressure becomes too low, the force due to molecular motion is no longer able to overcome the friction of the bearing." $\endgroup$ – Andrew S. Feb 26 '15 at 2:04
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You can use electric discharge of appropriate frequency, as its threshold in gas depends on pressure (and frequency).

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  • $\begingroup$ This would require, blatantly put, putting two wires through the glass into the container, right? $\endgroup$ – Zubo Feb 26 '15 at 1:44
  • $\begingroup$ @Zubo: Not necessarily - en.wikipedia.org/wiki/Electrodeless_lamp . You can also use much higher frequencies, e.g., microwave beams. $\endgroup$ – akhmeteli Feb 26 '15 at 4:15
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It all depends on what kind of sensitivity you want in pressure measurement. If you just want to distinguished a vaccum state from atmospheric pressure, then there are many non-destructuve ways:

  1. index of refraction of air at atmospheric pressure (and a few orders of magnitude down) is different from 1 - optical interferometry.
  2. if you apply a temperature difference, you should be able to see turbulence with Schlieren photography. Measuring thermal conductivity is a worse idea because the container walls will conduct the majority of the heat.
  3. light absorption measurement in gasses - spectrometry - is also a very sensitive method.
  4. listening for the echo off the opposing wall could measure the speed of sound.

All four methods eventually reach the limit of sensitivity when the pressure is sufficiently low - below some threshold, you will just see no signal. The method #2 is qualitative (gas or vacuum, true or false). The other 3 are quantitative, they can actually measure the pressure. The first one could be problematic without calibration. #3 and #4 seem very reasonable, although I don't know how small pressures can be detected. It depends on the width of the container. #3 is probably the only one that could possibly still detect the gas content at $10^{-8}\rm mbar$. High-end gas sensors can detect trace gas concentrations in parts-per-billion (american billion: $10^{-9}$).

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  • $\begingroup$ Schlieren photography sounds very cool - is that the German word for convection? And I agree that #3 is probably the lab way to go for measurement. Trace gas detection only makes sense if the putative gas inside differs from normal air, otherwise that would probably be ideal. $\endgroup$ – Zubo Feb 26 '15 at 15:35
  • $\begingroup$ Sure, but if it can detect a small trace of a gas in air, it can also detect the change in spectrum in vacuum for the same partial pressure - maybe not the same device, but a modified setup of the same principle. $\endgroup$ – orion Feb 26 '15 at 15:54
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Why don't you just put a balloon inside? It will enlarge because the proportion of the pressure inside and outside the balloon will change.

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  • $\begingroup$ I guess that's not really a proof, though - once the container is sealed, there is no way of telling how the balloon was before it was put in. Or am I misunderstanding your idea? $\endgroup$ – Zubo Feb 26 '15 at 15:32
  • $\begingroup$ In my opinion there's a visual proof. While reducing the pressure in the container you can see the balloon enlarge. But yeah, once the minimal pressure is reached, there is no proof that the balloon was smaller before. $\endgroup$ – SoBiT Feb 27 '15 at 9:19

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