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I have a doubt related to the behaviour of gases in a vacuum. In the following figure:

The grey part is the vacuum and the green part is the gas, let the gas be Carbon Monoxide. The following are my questions:

  1. Now when we open valve A will the gas move in one direcion towards valve B ?
  2. If valve B is opened when the gas is about to reach it, will the gas be moving towards valve B when it used to be closed at a constant speed?
  3. Will there be any decrease in its speed if there are some obstacles through which it can pass?

Lastly if the gas molecules distribute in the grey and green region and there is no quick movement of gas molecules then, how can we make the gas molecules travel at the speed they used to when we first opened valve A?

Thanks in advance!

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When you deal with vacuums like this, you may be dealing with rarefied gasses. Normally with gasses we assume there are so many random collisions that we can treat velocities as random distributions. This is true in most environments. However, as you decrease the pressure, they start to change. We start having to pay more attention to the specific collisions and we start having to treat the gasses as ping pong balls. When you get to this state, you only get to assume random distributions if you can demonstrate that it's a reasonable assumption.

Thus, the answers to these questions depend a lot on the size of the apparatus and the pressures. The "mean free path length" is a measure of how far a gas molecule goes before colliding. The longer it is, the longer it takes for the gas to reach a nice easy statistical ensemble where you can treat things as random.

  1. Now when we open valve A will the gas move in one direcion towards valve B ?

The instant you open the valve, the system is no longer in equilibrium. All molecules will generally start moving counterclockwise. At some point, the path lengths may get long enough that we can no longer treat it as a normal gas, but instead must treat it as a rarefied gas, which will matter for your next question.

  1. If valve B is opened when the gas is about to reach it, will the gas be moving towards valve B when it used to be closed at a constant speed?

At this point, you should treat the air like a bunch of ping pong balls. They have no idea that valve B exists because there hasn't been a bunch of random collisions ahead of the gas to pass that information clockwise. As such, you should expect it to work just like a bunch of ping pong balls. They'll keep moving, unaffected by value B, because they're just particles.

  1. Will there be any decrease in its speed if there are some obstacles through which it can pass?

Use the ping pong model again. If you put a bunch of obstacles in the way of ping pong balls, would they slow down? The answer, of course, is yes.

Interestingly, we also see putting obstacles in front of normal gases can slow them down too. The effect is very noticeable at high flow speeds. We call it "drag."

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For the first part,there will be a diffusion of the gas into the vacuum when valve A is opened.The gas will try to distribute uniformly all over the system.In this process it will travel towards B.

For the third part if there is an obstacle ,suppose it to be immovable.Now applying Equation of continuity we can see that the speed increases at the cross section where the obstacle is present.

Once the gas is uniformly distributed there will not be any observable movement of the gas stream but the particles of gases will move.The driving process of the movement of the gas stream is due to the non uniform distribution of the matter.

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  • $\begingroup$ So when the gas particles get distributed in the grey and green region there will be no quick movement of gas molecules? $\endgroup$ – Deepam Sarmah Dec 9 '15 at 13:41
  • $\begingroup$ Well the molecules will move on their own at the molecular level but the gas stream as a whole will not show any movement once the gas is uniformly distributed.It can be treated as a fluid,the bulk of the fluid will not show movement but the individual particles shall move at the atomic scale $\endgroup$ – Ananyo Bhattacharya Dec 9 '15 at 13:56
  • $\begingroup$ Your second paragraph is not correct when the mean free path of the gas molecule is much longer than the dimensions of the container (or constriction in this case). Under those conditions, the gas does not behave as a 'fluid'. $\endgroup$ – Jon Custer Dec 9 '15 at 15:02

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