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

[John Mallinckrodt <ajm@CSUPOMONA.EDU>]

John Denker wrote:

> 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.

JD is, of course, correct. I had in my mind a fuzzy (i.e.,
nonquantitative) version of the idea that the volume might be
described by something like

   V(P) = Vo + delta_V (1 - exp(-P /P_char))

where P_char is a characteristic pressure near which the container
would reach its optimum volume to surface area ratio with delta_V
being the attendant increase in volume.

I was attracted to the negative second derivative of THIS function,
but the weight of the gas involves another factor of P, relegating
the first negative term to the third derivative.  So I should have
expected to see positive curvature in a plot of weight versus
pressure that gets less positive at larger pressures.

--------

My mistake reminds me of current attempts to define the Social
Security crunch in terms of when the annual surplus (the first time
derivative of the trust fund balance) vanishes rather than when the
trust fund itself is depleted.  At least one person argues that the
crunch comes when the SECOND time derivative of the trust fund
balance becomes negative--that is, when the annual surplus stops
getting bigger each year as it is doing now and HAS been doing for a
LONG time.  That is expected to happen in just a few years.