Re: Maintaining Constant Temperature, Isolated Energy Container

Dear Richard,
This is an interesting question that taps into a lot of basic principles of
thermodynamics surrounding behavior of isolated (ideal) systems vs. that of
open (real) systems.

Briefly, the first law of thermodynamics states that "the internal energy
of a system is constant unless it is changed by doing work or by heating"
is the root of your puzzle...in principle, in a perfect (closed) system,
the temperature of the iron ball should be constant (473 K or 200 C) in the
absence of any work or heating.  

The second law of thermodynamics states that  "the entropy of an isolated
system increases in the course of a spontaneous change, dStotal > 0", that
is all processes contain some inherent irreversibility, or tendency towards
equilibrium.  With your puzzle, the question is if the system, the
surroundings, are not also at the same temperature, the natural tendency is
for the temperature of the iron ball to change until it equilibrates with
its environment...place it in a swimming pool at 29C (85F) and the iron
ball will quickly cool to the same temperature with no appreciable change
in the temperature of the large swimming pool (heat sink).

The third law of thermodynamics (worded as the Nernst heat theorem) states
that "the entropy change of a transformation approaches zero as the
temperature approaches zero", implies if we could freeze out all entropy in
the system our iron ball should hold constant temperature.  In fact this is
true but only in the approximation that we try to hold its temperature at
absolute zero in outer space.

The real root of your question is this; can we put into use some
engineering tactic that approximates a situation where the iron ball is
essentially in complete isolation.  Put another way, can we beat the laws
of thermodynamics.  The answer is "yes", but only locally.

A vacuum is a good insulator because of the intrinsic source of thermal
energy.  The ideal gas law, "pV = nRT", is not just a balance equation; it
tells us that for a given volume and pressure of a closed system (balloon
or chamber), we know how many molecules of gas are present if we can
measure the temperature, or we know the temperature if we know how many
molecules of gas are present, or if we know both the number of molecules,
the temperature, and the volume, then we know the pressure, etc., etc. 
Thermal energy is also expressed as the kinetic energy of a volume of gas
in contact with a surface; the presence of the surface defines the volume,
for a fixed number of molecules of gas, we automatically know the
temperature, and the pressure.  If we reduce the number of molecules in the
system, the pressure or temperature must drop.  However, the means through
which temperature is transmitted within this space is through collisions of
gas molecules with the surface, or with the iron ball within the volume.

If we suspend your iron ball at 200K in a pressure chamber (outside
temperature at 25C) and quickly evacuate the chamber of all gas (assume we
have a high power turbine-pump that pulls micro-torr vacuum), over a short
period of time almost every gas molecule will be evacuated; the few
molecules that remain, under high vacuum, will be quite cold and move
slowly.  The absence of gas molecules virtually eliminate encounters with
either the inner surface of the chamber or with the iron ball, thereby
eliminating thermal transfer from ball to the outside world.  This true by
nature of the fact that we have significantly reduced collisions of any gas
molecules with the ball (where they would gain heat and kinetic energy that
they would then transfer to the outside world, where they would transfer
thermal energy through collision with interior wall of the cooler chamber.

The problem is that this is not really an isolated system; we can't pull a
perfect vacuum, and the iron ball can not be completely isolated from the
inner wall of the pressure chamber if physically attached.  The
consequences are that, we will significantly slow the rate of thermal
transfer, but eventually the ball will cool and we're spending a lot of
energy from the outside of our isolated system to run the vacuum pump (so
we are definitely in debt in terms of the total entropy of the system). 
Your idea of using some magnetic containment system is a valid one in that
in certain applications this approach can stabilize our "iron ball" in the
center of the pressure chamber without physically touching the ball, but in
practice that works on plasmas in torroids in nuclear fission experiments,
but only with tremendous energy input.

In short, if we think about the iron ball in a vacuum of a pressure chamber
as an isolated system, we can maintain a stable temperature difference for
a short amount of time.  The whole/open system however shows that the laws
of thermodynamics can not be violated; it takes significant energy
expenditure to generate and maintain a high vacuum, and in time (many weeks
or months) the few gas molecules that do remain will slowly transfer heat
from the iron ball to the outside world.  Of course, we can beat the laws
of thermodynamics at absolute zero...only the laws of thermodynamics also
state we can't get to absolute zero.

Thanks for the interesting question.

Regards,
Dr. James Kranz