Re: hot air rising

[Robert A Cohen <bbq@ESU.EDU>]

On Wed, 21 Jul 1999, John Denker wrote:

> At 12:14 PM 7/21/99 -0400, Robert A Cohen wrote:
> > As for point (b), this is what I was referring to in regard to the
> > "mixing" theory.  I apologize for not being more specific.  As you say,
> > there are many ways to force an air parcel upwards/downwards.  The key is
> > that the air is moving up and down, which leads to a well-mixed atmosphere
> > and a temperature profile that is adiabatic.
>
> Mixing does occur, but IMHO it is not the main point and tends to distract
> attention from the main point.  Suppose you had air parcels in floppy
> plastic bags (to prevent mixing), going up and down on a Ferris wheel.  Any
> given parcel would be cooler when on top and warmer when on the bottom.

Hmmm...perhaps the difference is just one of terminology.  I would say
that the floppy plastic bags prevent molecular mixing.  I was using mixing
to describe the larger-scale exchange of air parcels, since the effect of
molecular mixing is so small (i.e., occurs on a much smaller spatial
scale). I apologize for not mentioning that, as students will typically
not recognize that and will end up interpreting "adiabatic cooling" as
cooling that occurs because the air parcels mix with the surrounding,
cooler air.

> > Point (b) by itself doesn't
> > explain why the top floors of a house are the warmest, does it?
>
> No, but it is part of the explanation.  The profile you described (warm on
> top, cool on bottom) corresponds to what is called a temperature inversion
> on those rare occasions where it occurs in the atmosphere.

Good.  We agree here, which leads me to believe that once we get beyond
the symantics, we don't disagree.

> We should not assume that all the heat sources are upstairs, nor all the
> cool sources downstairs, so it would be better to assume that the hot air
> upstairs typically came from somewhere else.  According to our newfound
> understanding, such air parcels must have been EVEN HOTTER before they went
> upstairs.  This is easy to believe.  Just think how hot the air is coming
> out of the heating-system vents.  That air will cool a tiny bit on its way
> upstairs (which is not after all a very great distance) but it will still
> be warm enough to stay up there;  if it were not still warm it would be
> cooler than the air already there, and would sink.

I guess I am still confused.  If the hot air was "even hotter" before it
went upstairs, then wouldn't it be "even hotter" on the lower floors?  As
long as you allow for interchange (mixing) between the top and bottom
floors, the air on the top floors should be cooler than the air on the
bottom floors no matter where the source of heat, correct?  I believe it
is the lack of parcel interchange (vertical mixing) that produces the
temperature inversion (as in the atmosphere on clear, calm nights, or in a
house on a warm day).  Am I wrong?
   I think being able to explain this situation is important since this
(incorrectly) reinforces to the students that rising warm air does not
cool as it rises.  Perhaps someone can set me straight.

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| Robert Cohen               Department of Physics       |
|                            East Stroudsburg University |
| bbq@esu.edu                East Stroudsburg, PA  18301 |
| http://www.esu.edu/~bbq/   (570) 422-3428              |
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