Ed Schweber (edschweb@ix.netcom.com)
Physics Teacher at The Solomon Schechter Day School, West Orange, NJ
David Bowman writes responding to Rick's defense of a previous post of my
own:
>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. 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. We are never going to give our students a complete grasp of
physics on a first exposure covering every subtlety - nor could we.
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.
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.
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. 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. And yes, the macroscopic and
microscopic realms have a completely different vocabulary and cannot "speak"
to each other without interpretation
David certainly has not persuaded me to skip this derivation. 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.