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Say we are a person sitting in a diving bell and have saturated (acclimated) to an ambient pressure of 5 MPa = 5,000,000 $kg/m/s^2$, breathing a mixture of 99% helium, 0.8% oxygen, and 0.2% impurities with a similar molar mass to surface air. Is our actual mass now higher than it was when we were acclimated to sea level pressure?

Here's an attempt to at least calculate the density of the gas . . . am I on the right track?

Here is my math:

Molar mass = 4 $g/mol_{He}$ * 0.99 $mol_{He}/mol_{air}$ + 32 $g/mol_{O_2}$ * 0.008 $mol_{O_2}/mol_{air}$ * 29 $g/mol_{impurities} * 0.002 $mol_{impurities}/mol_{air} = 4.3 $g/mol_{air}$, approximately. Not accounting for the rounded helium. Ignoring water.

$Density = mass / Volume = mass / (n * R * T / P) = molarmass * Pressure / (R * Temperature) = (4.3g/mol) * 5,000,000kg/m/s^2 / (8,314g*m^2/K/mol/s^2 * 300 K) = (4.3) * 5,000,000kg / (8,314m^3 * 300) = 8.6kg/m^3$

Ideal gas law, still just pretending you can keep things very dry. Which it turns out, you sort of can, because vapor pressure of water at habitable temperatures is much much lower than 50 atm.

If density is higher than surface air (on the order of 1kg/m^3), and solubility of gases always increases with increased pressure, shouldn't the density of our saturated body necessarily also increase? Would we feel the density increase, or would it be balanced out by the additional buoyant force of the increased ambient air density?

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  • $\begingroup$ Hi, Coel, welcome to Worldbuilding Stack Exchange. This feels more like a physics problem than a worldbuilding question - can you elaborate a bit more on its context? $\endgroup$
    – HDE 226868 ♦
    Jun 26, 2020 at 18:17
  • $\begingroup$ Sure; I was looking for a physics stack exchange but couldn't find one. The question is a simplification of one that came up while developing a 50 atm mini-Neptune-like planet that would be liveable for humans. I was kind of worried that going into the details of my setting would make it harder to answer my question succinctly - sorry if it was too off-topic! $\endgroup$
    – Coel
    Jun 26, 2020 at 20:56

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Without diving into detailed calculation, keep in mind that gases have densities of the order of 1 $kg/m^3$, while liquid water is 1000 $kg/m^3$.

Doubling or tripling the amount of gas dissolved into a liquid/solid has no significant effect on the density of the liquid/solid. As you can see from the density given above, it touches at most the 3rd significant digit.

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    $\begingroup$ Yeah, that's a fair point. I wasn't really thinking about the scale at which you can actually feel that difference. But it is correct to say that density increases, even if only by a negligible amount? $\endgroup$
    – Coel
    Jun 26, 2020 at 18:27
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Yes, by about 30 g.

The lung account for most free gas in the body. The lungs contain about 6 liters of air.

If air at 1 atm / 1 MP is 1.25 g/L then 6 L has 7.5 g. Air at 5 MP is 1.25 * 5 = 6.25 g / L. 6.25 * 6 = 37.5 g. You would be 30 grams more massive by virtue of the more massive air in your lungs.

If this is for a contest, you might pick up another few hundred mg via excessive flatuence. I want a share of the winnings, now.

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