Re: KE & temperature

[John Denker <jsd@MONMOUTH.COM>]

At 02:00 AM 10/26/99 -0400, Bob Sciamanda wrote:
> I think that there is a different approach which is both historical and
> useful for elementary courses:

Those are two different statements.  Historical and useful are not always
equivalent.

> 1) The ideal gas law PV=RT is accepted (and I believe, historically first
> appeared) as an empirical statement concerning the readings of
> instruments.  At this point, T has no meaning other than the reading of a
> thermometer (labeled in Kelvins), just as P is only the reading of a
> manometer (measuring absolute pressure).

1) Indeed, the ideal gas law was known *before* there existed thermometers
labelled in kelvins or anything nearly so useful.  The key thing was to
notice that PV/R for one ideal gas was the same as PV/R for another gas
under certain experimental conditions (i.e. conditions that we would
nowadays call thermal equilibrium between the two samples of gas).  In
effect one gas was being used as a thermometer for the other.

Such "gas thermometers" existed for hundreds of years before the concept of
energy appeared in the physics literature.

2) The remaining question is whether this is useful.  Mentioning the gas
law and not mentioning energy runs the risk of giving students the idea
that temperature is *defined* by the gas law and perhaps that it doesn't
fully apply to things other than ideal gasses.

The modern notion is that temperature is *defined* by energy.

See below for a possibly helpful pedagogic way to deal with this.

> 2)  Enlisting Newtonian mechanics and atomism ....

Again, you can do that.  You can even do that correctly.  But it misses the
point.  Thermodynamics is independent of mechanism.  Sure, Newtonian
mechanics is consistent with the rules of thermodynamics.  But it cannot be
used to *prove* the rules of thermodynamics, because the latter apply
equally well to non-Newtonian mechanics and non-atomistic non-ideal-gas
situations.

> 3) The valid conclusion can be drawn that T as defined by the ideal gas
> equation

For hundreds of years it was defined that way but not recently.

> (Other appreciations of T come later, both historically and
> pedagogically.)

Historically true, pedagogically questionable.

=============

At this point I would like to thank David for his note (Tue, 26 Oct 1999
00:43:41 -0400) that got the physics right.  But being an optimist I would
like to question the idea that getting the physics right

> is beyond the ken of typical HS AP students.

Consider telling students the following story:  Suppose I live in a
well-insulated house which has certain internal heat sources including
computers, light-bulbs, and people.  Suppose I know exactly how much heat
those sources produce.  I want to pump that heat out of the building using
an air conditioner.  The question arises, how much power does it take to
run the air conditioner?  What's the most efficient possible air
conditioner permitted by the laws of physics?  Can I get one that runs for
days on a size-AA battery?

It turns out that there is a minimum amount of air-conditioning energy
required to pump a certain amount of house-energy.  This minimum amount
depends on something we call Temperature.  In winter I could perhaps run
the air conditioner for free but not in summer.  This energy relationship
is independent of what working fluid is used in the air conditioner.  The
working fluid could be R12 or R134a or whatever, even the electrons in a
Peltier cooler... but in every case there is an efficiency limit set by
thermodynamics.  This energy relationship can be (and is) used to *define*
temperature.

If we lived in a world where ideal gasses never existed, temperature would
still exist.

Thermodynamcis is independent of mechanism.  Thermodynamics is independent
of mechanism!

______________________________________________________________
copyright (C) 1999 John S. Denker             jsd@monmouth.com