Submitted by Cedar- t3_y1w01p in askscience
Weird question, but I was reading that the water pressure that deep down is over 1000 times that at the surface level. So a bubble of air would be compressed to 100x the density, correct? Air is roughly 1.29g/L, while seawater is 1.04 kg/L. At that depth the density should make the air heavier than the water, and sink, correct?
I made a mistake. Pressure being about 1,000x means density would be about 1,000x, not 100. That's where I got the math of 1000*1.29 [g/L]=1,290 [g/L]=1.29 [kg/L]
Pressure and density are only proportional for ideal gases. At sea level pressure that's a good approximation, at 1000 times that pressure it is not. It's in a supercritical state, which is a state between a gas and a liquid. This page says nitrogen has a density of 0.3 g/cm^3 at the critical point. I don't find data for 1000 times the atmospheric pressure, but it's likely the density doesn't exceed the density of liquid nitrogen (~0.8 g/cm^(3)), so it would still rise. The 20% oxygen content shouldn't change that, even though liquid oxygen has a higher density than water.
But the water around the air would also be compressed by the water on top of it.
Only very slightly, it's not even 1% denser at that pressure.
Air is much more compressible than water is.
2000bar is 200Mpa, the units are different on those charts, but by 10,000 bar air will be more dense than water at around 20C.
E: I extrapolated poorly, read the response to /u/Origin_of_Mind
looks like these are the wrong charts and below 1Gpa water will always be more dense.
Water is basically incompressible, or at least substantially less compressible than air, even though it’s at the same high pressure.
NIST has tables of thermodynamic properties of gasses over a wide range of parameters. (Here is a large pdf for nitrogen up to 900 MPa.) The data proves that you are 100% correct -- even at circa 9000 times the atmospheric pressure, the density of nitrogen is still only 1.07 g/cm^(3) (at room temperature).
Nice plots!
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>by 10,000 bar air will be more dense than water at around 20C
Why do you think so?
At 10,000 bar and close to the room temperature, the plot for the density of air gives 1.16 g/cm3.
But if we extrapolate the plot for water beyond the shown 200 MPa, it hints at the densities around 1.2-1.4 g/cm^(3) (the correct value from NIST tables (pdf) is 1.23 g/cm^(3)).
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As far as compressibility of stuff goes, water is fairly compressible -- its bulk modulus (2 GPa) is similar to the compressibility of wood along the grain. It is a hundred times more compressible than steel, but even steel is compressed several-fold at megabar pressures in explosions.
you are right that I am extrapolating off of the water density chart I posted, and even so poorly.
Goes from 1000 to 1080 kg/m³ over 200 Mpa, by the time you get to 1000Mpa it would be 1400 kg/m³ and the nearly equivalent air temperature goes to around 1150 kg/m³
The log plot threw me off. This would be even worse for salt water since it is more dense than pure water which is the chart I have.
True_me4 t1_is0zpek wrote
100*1.29 [g/L]=129 [g/L]=0.129[kg/L]. Air would still be less dense than water there. The required pressure to make air the same density of water is 827 atm. However, air will probably dissolve into the water before reaching that pressure.