In response to Larry's comment about the operational definition
of temperature, I have a couple of comments. First, this particular
science education professor is incompetent because he wanted the
*wrong* operational definition. A correct operational definition
of temperature would specify an unambiguous procedure for determining
the temperature of an object numerically. (Of course any such
definition is limited in scope since real thermometers tend to
freeze up or vaporize or whatever at extreme temperatures.) But
just because this particular operational definition is stupid doesn't
mean that all operational definitions are bad.
My second comment is that the PhD physicist is wrong too; temperature
is *not* defined as something that's proportional to the average kinetic
energy of molecules (or whatever). This statement (when made
precisely) is a correct statement *about* temperature, but it is
not a correct *definition* because it is much too limited--even more
limited than an operational definition. For instance, in a diamond
at room temperature most of the vibrational modes are frozen out,
so the average kinetic energy of an atom is far less than what
the equipartition theorem would predict. And in a paramagnetic
salt in an external magnetic field, there is a temperature associated
with the spin orientations that has absolutely nothing to do with
kinetic energy and that can even be negative. The correct definition
of temperature, if you want to know what it really *is* and not just
how to measure it, is that temperature is the thing that's the same
for two objects that are in thermal equilibrium. More precisely,
temperature is the reciprocal of the slope of the graph of an
object's entropy vs. its energy. Thus an object at low temperature
tends to suck in energy (in order to increase its entropy in accord
with the second law) while an object at high temperature doesn't
so much mind losing some energy (since it doesn't lose much entropy).
If you don't want to talk about entropy, it's hard to be precise,
but temperature is still the relative willingness of an object to
spontaneously give up energy. (Feynman's analogy with the towels
is good here: temperature is like wetness, with energy analogous
to water.)
Sorry to rant on for so long, but I'm kinda tired of having to teach
students to unlearn the incorrect definition of temperature as being
proportional to average kinetic energy.