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But if the volume was infinite for gases not enclosed in a container, then how would the ideal gas law even function?

Thanks to anyone who can point out the piece of this puzzle I am not considering!

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    $\begingroup$ An absence of container does not mean an absence of external pressure. If gravity is involved, it ends with limited volume of unconstrained gas in the Earth atmosphere. As very minor fraction of molecules crosses the escape velocity. $\endgroup$ – Poutnik Oct 12 '19 at 6:24
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    $\begingroup$ Yes a gas that isn't enclosed will have infinite volume. What's the problem with that? $\endgroup$ – Ivan Neretin Oct 12 '19 at 7:13
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    $\begingroup$ @Ivan Neretin Finally the gas own gravity become equal the repulsion pressure, as the gravity decreases with r^2, but the pressure with r^3. So no infinite volume. It is seen in astronomical scales. $\endgroup$ – Poutnik Oct 12 '19 at 8:52
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    $\begingroup$ @Poutnik In effect, you are talking about the Jeans instability. Yes, that's a thing; I ignored it. $\endgroup$ – Ivan Neretin Oct 12 '19 at 9:02
  • $\begingroup$ @Ivan Neretin Yes, it is closely related by the critical density for given volume. $\endgroup$ – Poutnik Oct 12 '19 at 9:07
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I give you a case. Suppose you opened an airtight jar containing an ideal gas. Suppose by some mysterious power, you are able to observe the molecules of the gas. What do you think you'll see on opening the jar? Obviously you'll see the molecules dissipating in space(the correct word would be diffusing). Initially they suppose on opening occupied 100ml, then they occupied 200, then 300... Thus at every point of time the molecules have a finite volume, the value may be very large, but still its finite. Thus we say a gas "will occupy infinite volume" but only after "infinite time".

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  • $\begingroup$ When radioactive gases are released, you can trace them around the world. During the Fukushima Daiichi nuclear disaster, iodine-131 was released between 12 and 15 March 2011. Elevated levels of the isotope were recorded on the east coast on March 27, 2011 (i.e. about two weeks later). With such large volumes of gas as in the atmosphere, transport mechanisms like wind will play a larger role. See pubs.usgs.gov/of/2011/1277/report/OF11-1277.pdf $\endgroup$ – Karsten Theis Oct 17 '19 at 14:59
  • $\begingroup$ Yes you're right. Iodine-131 was also detected in the air at the time of Chernobyl. $\endgroup$ – Priyanshu Das Oct 20 '19 at 2:10
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Yes. But with several complications you don't normally use the gas laws to deal with

The ideal gas law is useful in laboratory situations where you can control the various components in the law (volume, pressure, amount of gas, temperature). And it usually describes the equilibrium reached when those factors are held constant. In the situation you describe, while the laws still work, you may never be able to observe the equilibrium state of the gas.

Consider practical experiments such as releasing a container of hydrogen held while you were spacewalking in the vacuum of space. The lack of a container means the hydrogen molecules will spread out eventually occupying an infinite volume. But you can never see this state as the individual molecules travel at a finite (and not very fast) speed. Even at the end of the lifetime of the finite universe, they may not have spread far enough to reach the equilibrium predicted by the gas law when the volume is infinite.

The more constrained case of opening a container of hydrogen to the atmosphere in a laboratory has a similar constraint. The gas sees a nearly infinite volume (the entirety of the earth's atmosphere is pretty large compared to one cylinder of hydrogen). But there are more constraints than in space. The hydrogen will diffuse into the atmosphere (more slowly than it would expand into space) and perhaps constrained even more by the walls of the lab. The expansion is also limited slightly by gravity which might contain the ultimate volume occupied to be the same as the volume of the atmosphere (but we normally ignore the complication in the ideal gas law). But, again, you would never really see the final equilibrium predicted by the gas law as it would take a long time to reach and other factors would prevent it being reached (some molecules in the upper atmosphere would be swept into space rather than being constrained by the atmosphere).

In both these cases the final equilibrium state predicted by the gas law is still the same. But you can never observe it as it takes too long to happen and other complicating factors will become more important and will dominate the outcome.

The gas law is not wrong but it is sometimes irrelevant.

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