Re: Density of gas mixture

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

On Tue, 20 Jul 1999, Doug Craigen wrote:

> Robert A Cohen wrote:
> > On Tue, 20 Jul 1999, Doug Craigen wrote:
> >
> > > One of my  examples to show how people learn particular situations as
> > > absolute rules - I ask how it is that hot air rises but the air is
> > > colder the higher up you go in the atmosphere (where all the hot air
> > > went)....  most people are at a loss, having never even realized a
> > > contradiction between two of their absolute rules.
> >
> > Hmmm...because the source of heat is at the ground (either because the
> > ground absorbs radiation from the sun or because the ground is closer to
> > the magma which we know is very hot) and the air cools as it rises because
> > it gets further away from the heat source?  This is the explanation most
> > often given to me by students.
>
> And how do you then respond to this?  Perhaps you ask about temperatures
> on mountain sides where you are both close to the ground and at a high
> altitude.

I used to ask this question because I too thought that it showed a
contradiction between two assumed "rules".  When I learned of the "source
of heat" theory, I realized that the question itself wasn't enough to
demonstrate a conflict.

Now that I know about the "source of heat" theory, I must say that I don't
have a good answer to this.  The "close to magma" theory can be somewhat
addressed by measuring the temperature below ground (not in mines, mind
you).  The "close to ground" theory can be somewhat addressed by measuring
the temperature on mountain tops, as you say.  Neither totally convinces
the students of the fallacy of their theory (is Denver always colder than
New York City?) but they do get the students to question.  I then
introduce another "theory", based upon mixing, and ask the students how
they might determine the "better" theory.

I'd like to hear what others have to say about this.

P.S. When I introduce my "theory", I first ask what the vertical
temperature profile of the atmosphere would look like if the air was
well-mixed vs. static.  Most students would incorrectly predict that the
well-mixed air would be the same temp at all levels.  Such conflict makes
them more willing to consider my theory of adiabatic warming/cooling.  I'm
not totally comfortable with this approach, though.  If anyone has a
better approach, I'd like to hear it.

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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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