Re: 100ft diameter beach ball = 331lbs of air?

In sci.physics, acannell@xxxxxxx
<acannell@xxxxxxx>
wrote
on 9 Apr 2007 20:05:53 -0700
<1176174353.262452.70860@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>:
If I had a giant 100ft diameter beach ball, would there be 331lbs of
air inside it? This assumes that the air pressure inside the beach
ball is the same as outside it (1 atm). Is that also reasonable?

Well, lessee. Since SI units are the most convenient, let's set up
the problem properly:

P = 101325 Pascal.
V = 4/3 * pi * (50 * 12 * 0.0254)^3 = 14826.7 m^3
R = 8.314472 J/(mol K)
T = 293 K (on a warmish day).

Ideal gas law, of course, is:

PV = nRT

so

n = PV/(RT) = 101325 * 14826.7 / (8.314472 * 293)
= 616680 moles

A mole of air is a bit tricky but one can take the more or less
standard approximation of 29 grams per mole, and work it out to
2 decimal places:

n = 17.9 metric tonnes

Heavy, man. :-)


100ft diameter sphere is 125000 cubic feet, and using the ideal gas
law you get 331.59 lbs of air at 1atm.

Erm, a 50 ft radius sphere would have 523,600 ft^3, so you're off
to begin with. One also has to use the correct value for R;
the standard value is only good if you have joules and kelvins,
which in this case clearly you do not.

I'd work it out but the natural unit of mass in this case is the slug.
Makes life weird. :-) SI units are far easier. :-)


A 10ft diameter ball would have only 0.33 lbs of air.

A 10ft diameter ball would have 17.9 kg of air. Of course
it's easily pushed because the air inside is bouyed by the
air outside, but it does have a certain inertia.


Anyone know the smallest realistic pressure vessel that could contain
all that air compressed?

Scuba gear is routinely pressurized to 3300 psi in steel
tanks, or 22.75 megaPascal. That would reduce your 100ft
diameter ball to a round spherical steel tank of about 5
meters or 16.45 feet in diameter.

One could contemplate even higher pressures but I'd have to look.
www.scuba.com is a fairly obvious place for scuba gear, which is
where I'm getting these from.


At 480 psi, I calculate a required volume of 3828 cubic feet, or a
cube 15ft on each side. Is that correct?


More like 25.22 feet, if you want to be cubical. It would
be a spherical tank 31.29 feet in inside diameter, at
that pressure.

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