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

[Bob Sciamanda <trebor@VELOCITY.NET>]

Hi David,
I think that there is a different approach which is both historical and
useful for elementary courses:

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).
R is a constant number, for a fixed quantity of gas.  (I collapse much
about Boyle et al and subsequent data reduction.)

2)  Enlisting Newtonian mechanics and atomism one proposes a conceptual
model of the ideal gas as a collection of non-interacting point particles.
The reading of the manometer is naturally correlated to the Newtonian
force/area concept, but T remains merely an instrument reading.  Applying
Isaac's laws (as Joule actually did) one can show that the model predicts
that PV  is proportional to the average particle kinetic energy.  This can
be done algebraically and quite rigorously, with appropriate assumptions
(eg., all possible system microstates are equally probable, etc).

3) The valid conclusion can be drawn that T as defined by the ideal gas
equation is proportional to the average ideal gas particle kinetic energy.
(Other appreciations of T come later, both historically and
pedagogically.)

I always use this as an historical illustration of the interaction between
experimental and theoretical physics, for introductory courses.  (There is
much more to be learned along the way - the historical development of the
IG equation is a pedagogical gold mine.)

Bob

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor


----- Original Message -----
From: David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Tuesday, October 26, 1999 12:43 AM
Subject: Re: KE & temperature (was: Newton's 3rd law? ...)


> Regarding Rick's disagreement:
> > I have to strongly disagree with David here.  The derivation of
absolute
> > temperature (as a measure of the average translational kinetic energy
per
> > molecule due to random motion) IS, IMO, very accessible to AP level
students
> > and IS a very good example of how a concept such as temperature that
seems
> > far afield from their basic kinematic and dynamic studies can be shown
to
> > arise from just such studies.
>
> The concept of temperature does not arise from either "kinematic" nor
> "dynamic studies".  The concept of thermodynamic temperature is defined
> as the rate of change of a system's internal thermal energy w.r.t. the
> change in its entropy where the change is taken both as a quasistatic
> perturbation which preserves equilibrium, *and* under conditions such
> that no work is done by (or on) the system during the change.  This
> concept has little, if anything, to do with both dynamics and
kinematics.
> It is a (quasi)static equilibrium statistical concept.  . . .
> David Bowman