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

[David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>]

Regarding Joel's request:

> I would like to hear a little more about why you find the usual derivation
> mentioned below to be not what it is cracked up to be; i.e. the "holes" in
> the derivation.

I thought I had mostly already indicated my concerns regarding this, but
maybe I was less than clear.  Let me try again. I have three essential
problems with the derivation.  1) The derivation can only apply, at most,
to the special case of ideal gases, even though the result of the
proportionality of translational KE to absolute temperature has a much
more general validity than this special case.  The gratuitous restriction
to Ideal gases is a red herring as far as the actual result is concerned.
2) *Even* for that special case the derivation pulls the ideal gas law
out of the air as somehow given without any prior proof. If such a
derivation is to actually constitute a proof of the KE/T proportionality,
we must be sure to only use results (in that derivation) that are
themselves either demonstrated results or are just definitions.  Thus the
Ideal gas equation of state itself needs to then be shown as a
consequence that obtains for the system of independent noninteracting
particles that characterizes the nature of what it conceptually means to
be an ideal gas.  Unfortunately, such proof of the Ideal gas equation of
state itself *also* tends to be beyond the level of introductory
students.  3) Related to 2) above is the problem that by appealing to the
Ideal gas equation of state there is no understanding of the real meaning
of temperature.  At most, any understanding of temperature is forced (by
the assumed ad hoc equation) to relate to the product of the pressure and
the per-particle volume of the gas.  This does not make for a very
comprehensible understanding of the concept of temperature (IMO).

I hope this more clearly spells out my problems with the "usual
derivation".

David Bowman
David_Bowman@georgetowncollege.edu