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Re: KE & temperature (was: Newton's 3rd law? ...)

Regarding Ed's latest comments on this thread:

David Bowman writes responding to Rick's defense of a previous post of my
own:

Actually, I thought I was the one who was defending your post. Your post
recognized that the usual pressure on the walls calculation for an assumed
ideal gas was not the proof it was cracked up to be, and even your AP
student saw this themselves. I merely disagreed with your claim that the
real physics was in the Kantian leaps between the microscopic and
macroscopic realms that you seemed to think was not bridged by
appropriate equations. It was Rick who appeared to think that this
derivation actually constituted a real derivation or proof of some kind.

>What *is* relevant to the concept of temperature is how
> fast the relative number of allowed accessible microscopic
>states increases as the system's internal energy increases. I
>contend that the proof of how this concept relates (i.e.
> proportionally) to the mean per particle translational kinetic
>energy is beyond the ken of typical HS AP students.

Of course this approach to temperature is beyond AP students.

Then we agree.

My point
is that teaching the concept of the temperature does not have to begin at
this point for the teaching to be useful, nor do I think it would be
possible at any level to introduce temperature at David's level of
sophistication without a student having grasped the less sophisticated
approaches.

Again, I agree 100%. I never claimed that we should actually tell the
students the truth (as best we know it). I'm all for such pseudo-
derivations when appropriate. I only ask that when they are given that
we level with the students about what we are doing and admit the problems
with the pseudo-derivations, and that the real truth of the situation
will have to wait for a later (sometimes, much later) course.

We are never going to give our students a complete grasp of
physics on a first exposure covering every subtlety - nor could we.

Again, 100% agreement.

But aside from teaching, I have always been suspicious of attempts to
make physics too axiomatic. Yes we can begin by defining temperature in
terms of "how fast the relatibve number of allowed accessible microscopic
states increases as the system's internal energy increases" and avoid the
details of relating temperature to macroscopic perceptions.

Such an approach does not avoid those details. It shows why those
details are the way they are. (It just that that approach is not very
suitable for low level courses.)

But the definition is abstract to the point of meaninglessness if if we
don't have the messy details to indicate what inspired us to make that
definition in the first place. Attempts to axiomatize thermo don't make the
subject more elegant, they just hide the inelegancies and refuse to look at
them.

I disagree. The axiomatic developments of the theories of physics *do*
make it quite elegant, and they *do* consider the messy details, but they
consider them as theorems and conclusions in the logical structure rather
than as postulates.

David Bowman continues:

>This "derivation" was already *admitted* by Ed to not really
>prove the desired result, and his (2 yr) previous AP class
>was even sharp enough to call him on it. In discussing this
>swindle with his class Ed appealed to some sort of principle
>that real physics involved making plausibly interpreted
> jumps of logic between a microscopic and maroscopic
>description

I hardly think of my derivation as a swindle.

OK, maybe the word "swindle" might be a little too strong here. How
about "invalid as an actual proof"?

This is where the
connection between macroscopic and microscopic interpretations of
temperature began and without this level of insight David's conceptions of
temperature would never have evolved.

Certainly in the historical development of any field of physics the
various partial clues can aid the proposal of certain theoretical
hypotheses (atomic theory matter, quark theory of hadrons, etc.) before
there is any direct experimental support for such proposals. But once
the theories have been axiomatically worked out, their predictions
have been found, and the experimental support is there, and those
theoretical proposals have been confirmed in multiple ways beyond a
reasonable doubt, we then tend to understand the phenomena in question
*via* the theory that has stood the test of experiment. Then we no
longer imagine that those original theoretical proposals were so bold,
but rather merely accurately describe the way nature really is. (At
least that's the way it is until a Kuhnian-type revolution/paradigm
shift comes along and turns everything on its head again.)

And yes, the macroscopic and
microscopic realms have a completely different vocabulary and cannot "speak"
to each other without interpretation

The "interpretation" is provided by statistical mechanics (first
worked out by Boltzmann and Gibbs) and it makes both realms conceptually
unified in ways analogous to how other unifications in physics have
happened, such as Newton's unification of celestial and terrestrial
mechanics via his universal law of gravitation, and Maxwell's unification
of electricity and magnetism, and Weinberg/Salam/Glashow's unification
of Electromagnetism and Weak interactions, etc.

David certainly has not persuaded me to skip this derivation.

Good. I never advocated skipping it. I said that it is probably the
best that one could do at that level. I only wanted to point out that
we do not always have to appeal to some Kantian leaps of faith/physics
interpretations connecting the different realms where the holes in the
simple arguments happen to be. These holes *are* often filled at a more
advanced level, and correct logical proofs do exist. We just can't use
them at the lower levels of instruction. And, sometimes, we may have to
ask the students to just "trust us" until they have developed the
wherewithal to understand those advanced proofs. But we shouldn't claim
to the students the gaps are not logically bridgable, when in fact they
are bridged.

I think
that it is very exciting for students just a few months into physics to be
able to begin seeing a connection between temperature and molecular KE that
is not at all obvious.

Me too.

David Bowman
David_Bowman@georgetowncollege.edu