Physics Quiz Question

Dallas wrote:
On Tue, 07 Aug 2007 18:31:41 -0000, Jim Logajan wrote:

So when Jeppesen said "assuming all other variables remain constant"
it was basically saying "assuming the density remains constant."

Are you pretty comfortable with that statement?

Pretty comfortable. Although I admit I did better in quantum mechanics in
college than thermo and statistical phsyics. :-)

I can't imagine why
Jeppesen would bother to publish the paragraph if the assumption was
that the density would remain constant, which is basically impossible
outside the laboratory, (at least, as far as I know) and makes whole
statement of no value to a pilot in the real world.

Well, it looks like they were trying to make a point and be technically
accurate. I believe that typically requires making text-book simplifying
assumptions.

"Assuming all other variables remain constant". - I picture two
barometers a few miles apart on a consistent, flat surface. There is
no wind and the sky is overcast. A hole in the overcast opens up and
heats the area around the first barometer. If I correctly interpret
what Jeppesen appears to be saying, the pressure in the area of the
heated barometer will rise above the barometer in the shade.

Your interpretation matches exactly what they say: "On the other hand, a
warmer temperature increases atmospheric pressure, all else being equal."

But the problem is that "all else" _doesn't_ remain equal in your
scenario. That is why I think the Jeppesen paragraph is misleading, since
it will lead students to believe certain values remain constant when they
really don't.

In your scenario the air over the sunny area may try to increase in
pressure to, for example, 14.8 lb/in^2 with surrounding air at, say, 14.7
lb/in^2. The pressure difference will cause the heated air to balloon
outward till the pressures at the imaginary boundary equalize. What you
get is an outflowing "wind" as the hotter air balloons out. The hot area
should also cool a little. The details get ugly, but suffice to say that
almost immediately after the heating begins, the volume starts expanding
so the density starts dropping and the barametric pressure will appear,
in this example, to be between 14.7 and 14.8.

So in general if it is going to be a hot day, the air density will _tend_
to be either the same or less than on a cooler day. So wing lift and
oxygen content/intake is slightly reduced on the hotter day.

But dang it, nothing in physics seems to rule out weather events
conspiring so that one gets a hot day and a high pressure system such
that the air density is much higher than average. Such is the nature of a
dynamic atmosphere that experiences unequal heating.