Q & A: pressure and air weight

I have a problem with the standard explantion of atmospheric pressure as beeing caused by the weight of the
overlying air. If I have a hermetic sealed bowl of glass or some other material, where forces cannot be exchanged
with the outside, how am I then to explain the pressure
of the air inside the bowl ? (I think that the weight explanation implies some transmission of forces)
- martin schmidt
denmark

That’s a really good point. If some sort of disturbance happened blowing away part of the upper atmosphere, it wouldn’t have any immediate effect on the pressure down here. So ’weight’ is not a great way of thinking about it.

You can think of the local air pressure as just coming form the force of air molecules banging against any surface they contact. They’re banging around because all objects with a temperature rattle around randomly. (For a good explanation of that, you might want to look at a beginning book on statistical physics, for example the one called ’Unit T : Some Processes Are Irreversible’ by Tom Moore.)

Now why are there any air molecules down here to begin with if they rattle around so much? They’re held near the surface of the Earth by gravity, i.e. by their weight. If you pulled a bunch of molecules out of the upper atmosphere it would end up reducing the pressure down here, because as some of the lower molecules happened to rattle their way up, they wouldn’t be replaced by higher molecules falling back down. So it’s no accident that the ’weight’ explanation works, and gives the right answer, even though it doesn’t generalize well. For example, it doesn’t explain how the densities of different types of molecules changes with height, but even beginning statistical arguments do explain that.

Mike W.

To be more specific about your bowl:  once it is sealed off, the pressure inside the bowl is not dependent on the pressure outside the bowl, as long as the bowl is rigid.  Atmospheric pressure fluctuates with the weather, dropping when a storm passes, and rising in clear weather.  It is less on mountaintops and higher in valleys.  Bring your bowl around to these places or wait for a storm to go by, and the walls of the bowl provide all the needed forces to maintain pressure; the gas molecules bang on the sides of the wall instead of on other gas molecules.  Of course the temperature of the gas inside the bowl affects its pressure too; the gas molecules strike the sides of the bowl more frequently when the temperature is higher.

Tom

(published on 10/22/2007)