# What is the smallest possible packing of earth air inside a box?

It is often stated that all the air in a room could suddenly rush into one corner but that there is simply a very low probability that it would do so. One possible way this could in fact happen is via the phase change of gas into a solid via really low temperatures.

What is the smallest possible way of packing a 1 by 1 by 1 meter box of Nitrogen gas that starts at standard temperature and pressure that is still Nitrogen and not some other kind of matter such as Neutronium or Lead?

• "at standard temperature and pressure" would be impossible. One cannot reduce volume while maintaining the same pressure in a near-ideal gas like nitrogen. Packing into a small volume means accepting high pressure.
– Gert
Oct 8, 2015 at 1:46
• Why is the fact that the air could randomly flow into a corner relevant to the rest of the question? I don't see how that's connected to the part about low temperatures. Oct 8, 2015 at 3:40
• Hi Steve, by using the word packing, do you mean the same general idea as packing spherical larger objects, like oranges, for example? I think you may need to clarify what you mean by packing molecules, as opposed to macro objects.
– user81619
Oct 8, 2015 at 7:59
• @Gert Initially at a STP. Obviously, that would change later on. Oct 9, 2015 at 18:34

The relevant properties of nitrogen at 20°C and 1 atm are:

13.8 standard cubic feet per pound of nitrogen gas.

0.808 specific gravity of liquid nitrogen.

1/13,8 = 0.07246 pounds of gaseous nitrogen per cubic foot. Converting to metric units we get 1.1607 kg/m³ for the density of gaseous nitrogen

1000 kg/m³ equals the density of liquid water. Therefore 808 kg/m³ is the density of liquid nitrogen.

1.1607/808 = 0.001437

1 m³ of gaseous margin will condense to all 0.14% of a cubic meter.

• Is liquid nitrogen the smallest possible packing of Nitrogen? I would think so but I don't know for sure or how one would prove that. And just to be sure, this does mean that if Nitrogen gas collapses into a corner of a room it could only collapse to about 0.14% of its size? Oct 9, 2015 at 18:36
• Well I'm sure the volume occupied by even liquid nitrogen would be affected to some extent by the pressure. And of course if it got involved with the Black Hole, all bets are off! But yes, your interpretation of my answer is correct. Oct 10, 2015 at 4:33

Partial answer in the case of auto-gravity: the Chandrasekhar limit gives the threshold where electron degeneracy pressure exactly counterbalance gravity pressure (after that electrons fall on the nucleus, white dwarf collapse into neutron star). This should provide ingredients to answer your question.