Re: Definitions of Temperature

[DSCHROEDER@cc.weber.edu]

Rick says:

> Well the well worn 'definition' of temperature to which you object is good
> _only_ for ideal gasses but is usually stated as:

> "Absolute (Kelvin) temperature is proportional to the AVERAGE,
> TRANSLATIONAL, KINETIC ENERGY PER  MOLECULE, due to RANDOM MOTION."

> Here all the capitalized words are essential (the translational part takes
> care of your vibrational states problem).  What I like about this
> description is that it can be derived from first principles (well you do
> have to assume the ideal gas law, but all my students are Chem & Bio majors
> so they accept the IGL without much question).  At the next level, this
> description easily explains the differences between heat capacities of
> various gasses based on the number of open channels (translational,
> rotational, and vibrational) and the equipartition of energy.  The majority
> of  students who receive such instruction in introductory courses never get
> to a junior level thermo course where your entropy description can be
> effectively taught, but those who do should not have a problem with the
> more complete and sophisticated description.

I object to any "definition" of temperature that applies only to ideal
gases; most students, not just upper-division students, need to apply
the concept to solids and liquids as well.  It does no good to say that
T is proportional to translational kinetic energy *by definition*, and
then to show them a graph of the heat capacity of a solid which shows
how the linear relation utterly breaks down at low temperature (and 
for diamonds and many other materials room temperature is low).

But you've already given yourself away:  You say you can *derive* this
relation between energy and temperature, starting from the ideal 
gas law.  I absolutely agree.  Which proves that the relation is not
a definition.  You can't derive a definition.  So you need some *other*
definition of temperature to determine what the T in the ideal gas
law stands for.  Even in an upper-division course, I think this other
definition should be an operational one (how to make a thermometer).
Then, when students ask what temperature really *is*, even in an
introductory course, you need to tell the truth:  it's a measure of
the willingness of an object to spontaneously give up energy.  In many,
but not all cases, this "willingness" happens to be proportional to
how much energy the object already has.

I've encountered many many students who think that the direct
proportionality between energy and temperature is fundamental and
applies to all objects.  I even audited a physical chemistry course
where the professor defined temperature in this way (and not just
for ideal gases).  I think this misconception is one of the many
reasons why students find thermal physics to be extremely confusing.

As an aside, I happen to believe that the precise theoretical 
definition of temperature in terms of entropy *can* be taught very
effectively in a calculus-based introductory course.  But even
if we choose not to, we shouldn't perpetuate serious misconceptions
about temperature.

Dan