I have been preparing to teach thermo for the first time this spring and
have learned a lot mostly lurking on this list. However, I have come to a
bit of a paradox having to do with the definitions of heat (Q) and
adiabatic. Let me see if I can state this well.
Background ....
I like Jim Green's web page, ( http://users.sisna.com/jmgreen/FirstLaw.htm
) which basically says that anything that increases entropy is "heat". By
this definition, "energy transferred because of a temperature difference"
is a subset of "heat", but "heat" also includes a paddle wheel turning. In
each of these cases, the work done microscopically from outside the system
translates into a greater kinetic energy in the gas molecules inside the
system.
Now my sticking point. "Adiabatic" is generally defined roughly as "no
energy transfer because of a temperature difference between the system and
the surroundings", but heat is defined, in Sears and Salinger anyway, as
Q = W - W(adiabatic)
i.e. heat is any work that isn't abiabatic. (There is also a problem with
a circular definition of adiabatic, but that's not my point here.)
Now the paradox....
Consider a "perfectly insulated" container with a paddle wheel sticking
through (the shaft is also perfectly insulated). Viola! "Heat" (using the
definitions expounded on in Jim's page) gets through an "adiabatic" wall
(using the standard definition above)!
I have three possible resolutions for this paradox
1) The term "adiabatic" needs to be expanded to include a boundary though
which no "heat" in any form can travel. (i.e. insulation is a necessary
but not sufficient condition to be adiabatic.)
2) The definition Q = W - W(adiabatic) is scrapped for a more precise
statement, and adiabatic still means "insulated"
3) If the paddle at rest and the gas are originally the same temperature
then they have the same average KE/particle and collisions between gas and
blade produce no average change. When the paddle is rotating, the average
KE/particle in the blades increases, hence the "temperature" of the paddle
is higher than the gas. So an average collision will increase the speed of
the gas molecules.
Ack! I'm getting in deeper than I thought! I kind of like (3). Perhaps
temperature needs to also be considered frame dependent (just as was argued
recently for KE). So the moving piston can also be considered "heat"
since its motion raises its "temperature" (average KE)- this "heat" just
happens to have the neat propertiy that the decrease in volume leads to no
net change in the entropy.
Jim had argued that all heat is really work and now I seem to have argued
that all work is really heat. In any case heat and work seem to be the
same thing. All processes do heat/work, but the piston is singled out by
the coincidence that increase in entropy due to the heat/work done on the
gas is exactly offset by the decrease due to the smaller volume.
Sorry, but I have to leave town for two days so I won't get to see what
becomes of this idea until Saturday ;-)