Geography 140
Introduction to Physical Geography
Lecture: Vertical Pressure Structure of the Atmosphere
III. The vertical pressure structure of the atmosphere
A. Although we're not constantly aware of it, air is a tangible, material
substance, and, therefore, it has mass. Anything with mass is subject
to gravity. So, air, responding to gravity, exerts pressure on any
surface exposed to it.
B. The reason we're not conscious of it is that our bodies exert as much
pressure outward as the air exerts down and in on us: The two
pressures balance each other out.
C. At sea level, this pressure amounts to about 1 kg/cm2 and
it declines quite rapidly the higher we go (that would be a tad under
15 lb./sq. in.)
1. If we were to examine any given square centimeter at sea level and
imagine all the air lying above it in an imaginary cylinder clear
out to the edge of the atmosphere, 10,000 km up, that column of air
would weigh 1 kg. Picture this column 10,000 km tall, with a
square cross-section 1 cm on a side at sea level and tapering out
to about 2.5 cm at the other end.
2. The higher you go in that column, the less air is sitting on top of
you, so it weighs less and less.
a. Air is very compressible, unlike liquids and solids.
b. So, air is densest toward the bottom of our imaginary column of
air, because more of it is compressed down there by the weight
of all the air molecules above it.
c. Compression, then, falls off with elevation in that column.
There is, then, an inverse relationship between air pressure and
altitude above ground. The higher you go, the less air is
pressing down on you, so density and weight dwindle.
3. The rate of this fall off in air pressure is about 1/30th of itself
for every 275 m gain in altitude (~900 ft.). That is, if air
pressure were 1 kg/cm2 at sea level, it would be 0.97 at
275 m, 0.93 at 550 m, 0.90 at 825 m, and so on.
a. Actually, it's a little more complicated than that, because air
pressure is a function not just of altitude, but also of
temperature and proportion of water vapor in it.
b. All things being equal (which, of course, they rarely are), the
greater the temperature, the greater the pressure (Gay-Lussac
Law): Hotter air means more energetically moving air molecules,
which means more pressure from all those higher-speed
collisions.
c. Humid air is less dense than dry air (water molecules with a
molecular weight of 18 displace nitrogen and oxygen molecules
with molecular weights of 30 and 32, respectively) and, so,
exerts less pressure.
d. All these caveats out of the way, the exponential rate of
falloff in air pressure with increasing altitude can be graphed:
![[ graph of air pressure with altitude ]](https://home.csulb.edu/~rodrigue/geog140/pressuregrams.gif)
4. A cool experiment established that air is a material substance with
mass that exerts pressure on anything exposed to it: It was
devised by Evangelista Torricelli (one of Galileo's students) back
in 1643!!!
a. He closed off one end of a glass tube about 1.2 m long (~4 ft.)
and then filled it with mercury, a liquid metal (and a very
toxic one at that), and flipped it over into a dish. A bunch of
the "quicksilver" ran out of the tube and into the dish but not
all of it (and a good thing, too, or Torricelli would have had
himself an early toxic waste spill in his lab!). Only about 45
cm or so ran down and out of the tube, leaving a column about 76
cm tall (760 mm or 29.92 in.). And a clean lab table.
b. He reasoned that something was pressing down on the open surface
of mercury in the dish, enough to support the weight of a column
of mercury in the tube about 760 mm tall. That something, he
figured, was air pressure.
c. He used mercury because, if he used water, the water, being
lighter than mercury, would need a tube a lot longer. When he
was looking around for a suitable liquid for his famous
experiment, Galileo suggested mercury to him.
d. Torricelli correctly deduced that mercury, rising only about
1/14 as high as water, must be about 14 times denser than water.
e. He also figured out that there must be a vacuum between the top
of the column of mercury and the end of the glass tube.
f. This must have annoyed him: The level of the mercury column
varied somewhat from one day to another. He commented on it and
deduced that air pressure itself must vary to produce this
change.
g. This experiment, which rocked the science of the 17th century,
became the parent of the mercury barometer, which is still used
today as one way of measuring ("-meter") barometric pressure
("baro-").
h. This gizmo is what the TV weather reporters are referring to
when they talk about air pressure being "28.3 inches and rising"
or when weathercasters elsewhere talk about "785 mm and
falling."
5. The importance of air pressure (getting personal).
a. Our lungs can extract oxygen from the air at the air pressures
(and, implicitly, the molecular densities) that our species has
normally encountered.
i. This mechanism breaks down on us if we wander off into
elevations our ancestors did not hang out in and survive to
leave us their genes. This is mountain sickness. Your
body is pressing out harder than the atmosphere is pressing
in, so bits of you start leaking out (nosebleeds) and your
blood vessels expand (giving you headaches), and you get
weak because your red blood cells aren't carrying the load
of oxygen to which they're accustomed. Within limit, we
can adapt a bit: If you go camping at high elevations, say
above 3,000 meters, you'll be pretty wretched for a day or
two and then your body adapts. Go much higher and you
begin to get out of the range of our genetic adaptability,
and you can die.
ii. This is why jets are pressurized when they fly at their
favored 10,000-15,000 meters and why, when a plane's
external structure is seriously ruptured, there is an
explosive outrush of its contents near the rupture
(remember those nine people that got sucked out the back of
their 747 when a 40 foot hole blew open in its fuselage
over the Pacific just south of Hawai'i back in 1989 and the
guy in Brazil who got pulled out of a plane in 1997?).
Even if the plane doesn't explosively discharge its
contents, sudden depressurization causes people to lose
consciousness almost instantly and die a few minutes later
-- remember Payne Stewart, and his
companions in 1999?
b. Another homely example is cooking (not that I know anything
about it!<G>)
i. Water boils at 100° C at sea level (that would be
212° F). The boiling point drops about 1° C for
every 165 meters of elevation (1° F for every 889
feet).
ii. This means that the higher you are, the cooler the water is
when it boils, so that is why you have to take longer to
cook food at higher elevations (and a pressure cooker helps
you cook faster).
iii. I have a terrible anecdote about the ramifications of
forgetting this important bit of geographical information!
A friend of mine at Jet Propulsion Lab told me about a
group of guys there that like to go off camping now and
again. One of the guys fancies himself a gourmet cook. On
one of their trips, they went into the High Sierra, and Mr.
Gourmet had brought ... lentils to make a custom stew.
They set up camp and le gourmet put the lentils on
to boil mid-day. They boiled. And boiled. And boiled.
And were not getting cooked, remaining adamantly chewy
despite hours of boiling. Pretty soon, it was starting to
get dark, and everyone else was getting hungry. An
executive decision was made to just put in the other
ingredients and finish making the stew. As darkness
descended, they supped on the still very chewy lentil stew,
which was hideous. Then, they all turned in for the night.
And faced the consequences of forgetting about Boyle's Gas
Law.
a. Time out for an important announcement about Boyle's
Law, named after Robert Boyle who figured it out in the
18th century.
b. Boyle figured out that there is a relationship between
gas pressure and the volume gas occupies. Reduce the
volume into which you cram X molecules of gas, and you
thereby raise the gas pressure. If you reduce the gas
pressure, the gas will expand into a larger volume.
c. Back to our regularly scheduled anecdote...
iv. Being at high elevation, the JPL rocket scientists were in
an area of significantly reduced air pressure. Lentils
are, er, how to put this delicately? gas-producing,
particularly when they haven't been cooked enough. Which
these hadn't, because of the unanticipated drop in the
boiling point of water with elevation. In the middle of
the night, Boyle's Law hit them, first in the stomach and
then in the intestines, as the gas expanded in the reduced
pressure of the Sierra, producing extreme human
wretchedness, both of the stomach-cramping and bloating
variety and of the aromatic variety. None of them got much
sleep. Which meant they were murderously disposed toward
the author of their discomfort and embarrassment and, I
understand, the man is under vigilante sentence of death if
he ever even fantasizes about gourmet lentils in the piney
woods again!
v. I had my rocket scientist pal check out this anecdote. He
affirmed it was accurate as to the facts, but he thought
that the Boyle's Law dimension would not apply unless the
lentils were eaten at lower elevation and then they climbed
to higher elevation. I didn't buy that, because, no matter
where you ate them, they might be expected to generate a
certain number of CH4 gas molecules in digestion, which
should be invariant whether you were at low or high
elevations. With the same number of gas molecules and the
lower air pressure at high elevation, I should think you'd
be in for an unusually bad bout of bloat. The rocket
scientist has come to endorse this conclusion! ;-)
Come away from this lecture knowing that pressure is inversely related to
altitude, that Torricelli's experiment is the basis of the modern barometer,
and the core idea of Boyle's Law (given the same number of gas molecules,
pressure is inversely related to volume) and Gay-Lussac's Law (temperature and
pressure are directly related to one another, if all else is equal).
In the next lecture, I'll discuss the vertical thermal structure.
Document and © maintained by Dr.
Rodrigue
First placed on web: 10/08/00
Last revised: 02/17/01