[Phys-L] Re: Weighing air (Was: electricity)

[John Denker <jsd@AV8N.COM>]

John Mallinckrodt wrote:

> > It seems to me that downward curvature of a plot of
> > weight versus pressure should be expected.  At
> > relatively low pressures, the

Bernard Cleyet wrote:

> still confused.

For good reason.

If we believe N ~ PV, and as long as dV/dP is positive,
N(P) should be concave upwards.  The details JM mentioned
don't change this.

> We already know it did expand -- too little and something else over
> compensated?

Exactly.

My hypothesis:  Temperature.  When I did the expt, the
compressed gas was noticeably warm, and when I let it
out the stream of air was noticeably cold.  I suspect
it takes a good long time for the heat to leak out of
a bottle that size.

===============

Other remarks:

1) Let's not forget that for the original application
(a children's museum), 10% accuracy is more than
sufficient to convince people that air has mass.
Fifteen grams of air in a 2 liter bottle is pretty
impressive.

Fifteen grams is the mass of three US "nickel" coins.
(Mnemonic:  they're 5 cents, 5 grams, and 5 to the cm,
i.e. 2 mm thick.)

2) I get valves for free, since every time I change the
tube on a bicycle, I keep the old one.  It's a source
of rubber bands (whatever size you like) as well as a
source of valves.  For the present application, cut
away most of the tube but leave a disk of rubber the
right size to fit snugly inside the cap.  Then you can
screw it down against the top of the bottle and get a
fine plastic-to-rubber seal.

The only thing you have to buy is the little tool for
removing the valve-cores.  The usual form is threaded
on one end so it serves as a valve-stem cap, and has
the two-prong core-puller functionality on the other
end.  They sell 'em at the auto parts store for real
cheap.  You want to remove the core when doing the
hydrostatic test, so you know for sure that your
gauge is reading the same pressure that's in the
bottle.

3) If you want to know dV/dP ... when all else fails,
measure it!  Fill the bottle with water and weigh it
as a function of pressure, taking care to keep it
full of water (which is super-easy when you start at
a high pressure and work down).

If you can't keep it _full_ of water, at least fill
it to the neck, put a mark on the neck, and measure
the height as a function of pressure.  If you measure
the cross-sectional area of the neck you can use it
as a home-made graduated cylinder.

Either of these techniques should easily give you the
delta(volume) within a few parts in 10^4.