Again... amazing detail here Bruce... thanks...
altitude and even stratify. So your intuition is not wrong in
quality... just in quantity. Here's to your intuition! (Raising a
imagined planets. Put in the presumed (or known) mix of gasses, the
idealized profile of the atmosphere by altitude. I don't remember the
characteristics.... I don't remember any worth mentioning... I mostly
The ozone layer and damage to it by CFCs and NO (not N2O?) and ... are
all storied evidence of such things. Or something...
> I realize that I didn't address one of the questions (or one of the
> possible questions): "Why don't all the air molecules just fall to the
> ground and stay there"? In case anyone was wondering about that
> question, the answer is that the air molecules DO fall toward the
> ground, but they continually run into other air molecules (or
> molecules in the ground if they get that far down), all of which share
> a nonzero absolute temperature and therefore are in random motion, and
> in collisions sometimes a molecule will be knocked upward. When you
> work out the statistical mechanics of all this, you get an exponential
> falloff of density (in the approximation of a constant-temperature
> non-convective atmosphere). This falloff is a bit faster for the
> lower-mass nitrogen molecules than for the oxygen molecules, but as I
> explained in a previous note, both of these molecular species have
> mean heights of around 8000 meters, so you shouldn't expect much
> difference in oxygen vs nitrogen between your cellar and your attic.
>
> A picturesque way of looking at this is the following. Imagine there
> is no atmosphere, and you're sitting at a table out in the open (in
> your spacesuit). Place a cup on the table. The atoms in the bottom of
> the cup are in contact with atoms in the top of the table, and all of
> these atoms are moving with random thermal motion related to the
> absolute temperature. At any given moment, there is a finite (but
> exquisitely small) probability that all of the atoms in the table
> underneath the cup happen to all be heading upward. In that case the
> cup will leap up off the table, knocked upward by the upward-moving
> atoms in the table. This would not violate conservation of energy or
> conservation of momentum (the Earth would recoil), but it would
> violate the Second Law of Thermodynamics, because given the gigantic
> number of atoms lying underneath the cup, the probability of all those
> atoms simultaneously heading upward is vanishingly small. You might
> have to wait for billions of billions of billions of years to observe
> the leap.
>
> Suppose instead of placing a cup on the table you place a single
> molecule of oxygen. Now it's not so improbable that an atom in the
> table might impart a significant upward speed to this single molecule
> of oxygen. Statistical mechanics provides the tools for calculating
> quantitatively the probabilities of various upward speeds. What you
> find is that the average speed imparted to an oxygen molecule by an
> atom in a table at room temperature is a speed sufficient for the
> oxygen molecule to go up 7920 meters before falling back down!
>
> In other words, statistical mechanics gives the answer (the same
> answer) to two different questions:
>
> 1) What is the average height attained by one oxygen molecule in
> contact with a table at room temperature? (Ans. 7920 m)
>
> 2) What is the average height of all the oxygen molecules in a
> constant-temperature atmosphere? (Ans. 7920 m)
>
> (I'm deliberately playing rather loose with the word "average" here,
> but the basic idea is correct.)
>
> There's yet another source of amusement in this statistical picture.
> Suppose you have a box whose sides have an accurately known mass.
> Suppose you weigh the box in an airless room (to avoid buoyancy
> effects) with and without the box being filled with
> atmospheric-density air. You're not astonished that the extra mass
> with the air is equal to the mass of the air added to the box. But
> maybe you should be astonished, because at any given instant almost
> none of the air molecules are touching the inside of the box! The
> reason why the scale measures an increase is because of the e to the
> (-mgy/kT) density gradient. The air density and pressure are just a
> tiny bit higher at the bottom of the air (in contact with the bottom
> of the box) than at the top of the air (in contact with the top of the
> box). Momentum transfer per second from the bottom of the air to the
> bottom of the box is very slightly greater than the momentum transfer
> per second from the top of the air to the top of the box. When you
> work out the details, you find that this difference provides the
> conspiracy that let's you think you're measuring the mass of the air.
> The difference is small, but so is the mass of the air.
>
> Sometimes one describes air pressure at sea level as "the weight per
> area of the column of air above that area". But almost none of those
> air molecules are in contact with your measuring device! However, the
> number of molecules per cubic meter, and their average y component of
> velocity, is such (conspiratorially) as to hit your area with the same
> force as though an object with the mass of the total column of air sat
> on this area.
>
> Related amusement: Consider a steel ball bearing dropped from a height
> h onto a scale, and rebounding to nearly the same height every time.
> If the scale can respond very quickly, you will see sudden sharp
> spikes when the ball bearing hits, and zero at other times. Now
> suppose that the scale is sluggish, and/or h is small enough that the
> ball bearing hits the scale at a high rate (though small speed). What
> you can calculate is that the average reading of the scale is exactly
> the same as if you simply place the ball bearing at rest on the scale!
>
> Bruce
>
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