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[Phys-L] Re: Weighing air - revisited.



"... its greater stiffness (NOT greater compliance, as one contributor thought)"

yes,

Actually I couldn't know as you hadn't reported (initially) the expansion of the first (2 l) bottle, but did for the second. ["At the higher pressure (47 psi) that I used here, it was obvious from the air in the neck that the bottle appreciably swelled under pressure, when initially full of water."] So I thought it more compliant. Intuitively, I think a larger bottle, with the same dimensional ratios will expand a greater %age. So, if true, the small (1 l) is indeed less compliant.

45/ 2000 = ~ 2.3%

rigid 2 l bottle at ~ 3 Atm. gauge 300% 2 / 300 = ~ 0.7 % (7 / 1000)

v.~ delta = 4.x gm (3 At.) resolution 0.1 / 4 = 2.5% So as BW wrote, barely possibly detectable.

Another matter:

I plotted BW's below w/ a counter intuitive result. I recommend BW
(please) do also.

bc, as I wrote, this is quite a project, I'm only kibitzing, laudate Deum.

p.s. because of BW's main point, I thought (wrote) the result
nonintuitive, he has explained why. I thought the bottom would bulge.
I've frozen water in soft drink bottles and found they are no longer
bottom stable. The bottoms are ribbed?, so under <~50 psig the bottom
is sufficiently rigid.

Brian Whatcott wrote:

I finally worked out the problem with the square law component of
volume versus pressure.

This is it: Physics educators bring many experiences with compliant
containers to the party. If your tool is a balloon, everything looks like
an inflatable.

It turns out that at the modest pressure used with the 2 liter soda bottle,
the square law component does not contribute more than one least significant
digit to the weighing at the highest pressure used.
With the higher pressure used in the one liter soda bottle, its greater
stiffness (NOT greater compliance, as one contributor thought)
counteracted the greater square law contribution.

Here are some rough n ready values for the head space growth with
pressure in a 2 liter bottle:
15 psi 12 cc
26 psi 19 cc
45 psi 45 cc
50 psi 59 cc

Brian Whatcott Altus OK Eureka!