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

[Brian Whatcott <betwys1@SBCGLOBAL.NET>]

Casting around for instrumental errors, I notice one that may be
what you [bc] are pointing to:

When I filled the bottle with water, I could turn it upside down
with no air bubble. but as I already mentioned, a proof pressure
gave a visible collar of air in the neck.
But when I removed the air chuck, the visible air disappeared.

Why would that be? A schrader valve is meant to be a one way
valve, after all.
An air chuck, and a tire pressure gage, opens the valve - and this
air loss would be proportional to pressure, one would suppose.

So as the protocol involved  a proof test, empty water,
repressurize with air, wait, weigh, let air out with a pressure gage
to a convenient lower pressure, weigh again:    a plausible error
would be the air loss due to pressure testing.
I used both a piston style gage, and a push-on bourdon style gage.
Both involve an air loss with each measurement.
An obvious refinement would be a plumbed in pressure gage.

Now a remark on John M.'s plausible non-linear mechanism.
It is quite possible for dv/dp to be positive while the curve is
concave down over some low pressure region. I feel he backed
off too fast.

A remark on bc's query as to which is the independent variable.
The variable that I was varying independently was the pressure.
  The variable that depended on this change was the weight.
Accordingly, I plotted pressure as the [horizontal] abscissa,
and weight as the [vertical] ordinate, in the usual manner.

Brian W

At 12:56 PM 2/6/2005, you wrote:
> But it's not found; why?
>
> We already know it did expand -- too little and something else over
> compensated?
>
> I ask BW to take data up to (near) the limit; w/ appropriate
> precautions, of course.
>
> BTW, what is the convention?  X vs Y of Y vs. X?  If Y vs. X, I'd expect
> an upward curve.
>
> bc, still confused.
>
> 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
> > bottom, in particular, will easily expand.  At higher pressures it
> > becomes more like the cylindrical walls; further expansion will
> > require the plastic itself to stretch.
> >
> > Another way of saying it is that the unpressurized container does not
> > start in its maximum volume to surface area configuration.
> >
> > John Mallinckrodt
> > Cal Poly Pomona
> >
> >
> >
> > > To further analyze I (one?) need(s) to know the measurement error.
> > > Because this second set of data w/ a supposedly more compliant container
> > > still better fits * linearly, and the power fit's exponent is sl. < one!
> > >  Either I'm confused, or the lack of precision masks the expansion, or
> > > the gas is not ideal.
> > >
> > > * furthermore, the new data's fit is noticeably better.
> > >
> > > I assume the weight is linearly proportional to the pressure plus the
> > > increase in volume, which is proportional to the pressure hence a power
> > > law with the exponent > one.
> > >
> > > bc, puzzled.


Brian Whatcott    Altus OK    Eureka!