1) Over the years, lots of people have noticed that you
can always separate the kinetic energy of a complex
object into the KE of the center-of-mass motion plus
the KE of the relative motion (i.e. the motion of the
components relative to the center of mass).
2a) Also a lot of people have noticed that you can
sometimes separate the energy of an object into a
thermal piece and a non-thermal piece.
2b) Or you can sometimes sorta kinda separate energy
_transfers_ into a thermal piece and a nonthermal
piece.
3) It is an all-too-common mistake to think that
split #1 is the same as split #2. But they're not
the same. Let me give several easy ways of seeing
that they're not the same, and then suggest a better
way of thinking about the issue.
A) First of all, thermal energy is not restricted to
being kinetic energy. You can have thermal potential
energy just as easily as thermal kinetic energy.
(Except in an ideal gas, where all the energy -- thermal
or otherwise -- is kinetic.) So trying to understand
the thermal/non-thermal split in terms of kinetic
energy is guaranteed to fail.
B) A standard counterexample is flywheels. As I've
mentioned on previous occasions, suppose you have a
cart with flywheels on board. You can impart KE to
the flywheels without imparting either center-of-mass
KE _or_ thermal energy _or_ potential energy to the
system.
C) Notice the "always" in split #1 and the "sometimes"
in split #2. It's unlikely that something that is
always true is equivalent to something that is only
sometimes true.
So let's address the pedagogical issues. If this is
such a common mistake, why do people keep making it?
Is there something positive we can say? A correct
idea that can displace and supplant the wrong idea?
Supplanting an idea generally works better than trying
to uproot an idea without offering a replacement.
The correct idea is entropy.
Center-of-mass motion is an example BUT NOT THE ONLY
EXAMPLE of low-entropy energy.
A complex object has something like 10^23 vibrational
modes. The center-of-mass motion is one of these
modes. It is technologically fairly easy to couple
to this one mode while not coupling to the other modes.
The motion of the flywheels is another example of low-
entropy energy. It is techologically easy to couple
to the flywheel modes, again without significantly
coupling to the 10^23 other modes.
The aforementioned coupling can be accomplished by
pushing with a thermally-insulating stick.
Note that if I push on a hot object with a thermally-
conducting stick, even though I am imparting energy
to one or two of the object's modes by pushing, the
object could be losing energy overall, by thermal
conduction.
Entropy has to do (roughly speaking) with the number of
modes involved. Entropy absolutely does not count the
center-of-mass mode differently from any other mode.
If you want to do thermodynamics, you are going to
need a clear understanding of what entropy is, and
why it is one of the central indispensible ideas of
thermodynamics.