X-Message-Number: 1988
Date: 19 Mar 93 06:13:26 EST
From: "Steven B. Harris" <>
Subject: CRYONICS Thermodynamics heat transport
Tim Freeman says:
>>>Also, Mike said that the mean free path of the gas molecules
in the near vacuum has to be comparable to the distance between
the walls of the dewar for the near vacuum to act as an in-
sulator. This doesn't make sense: suppose our gas molecules have
a mean free path of 1 inch. If Mike is right, a one-inch wide
void filled with this low pressure gas will insulate better than
a ten-inch wide void filled with the same gas. I would expect a
thick insulator to be better than a thin one. The observation
Mike [actually Brian Wowk] mentioned to support this is that the
quality of insulation of the dewar goes up dramatically as a high
vacuum is reached. ..... Surely this is dealt with in thermodyn-
amics textbooks. Does anyone here remember their thermodynamics?
(This isn't sarcasm; I don't remember my thermodynamics.) Gasses
are fairly simple, and I would expect the thermal conductivity to
simply be proportional to pressure.<<
Comment: This is true only at intermediate pressures,
exactly as Brian said. At very low pressures, as you EXCEED the
mean free path distance, you get NO increase in insulating power
with increasing distance.
Okay, folks, since Tim asked, here's the thermodynamics
without the math (and anyone who complains about THIS kind of
boring discussion will be consigned back to the Net Flame Wars
where we talk about personality rather than physics):
If you'll pardon the homely analogy, think of a gas molecule
conducting heat between surfaces (as between walls of a Dewar) as
a postman carrying a package of energy. As Brian Wowk says,
where the pressures are low enough that the distances between
conductive surfaces are large compared with the mean free path of
molecules in the gas (the distance each can statistically be
expected to travel without running into another gas molecule),
then thermal conductivity IS proportional to pressure, simply
because more gas pressure means more energy carriers (more
postmen!). At low pressures, every molecule leaves one conduc-
tive surface with the characteristic velocity (or distribution of
velocities) characteristic of that temperature, and flies
straight to the other conductive surface with no interference,
where it deposits heat energy there proportional to the tempera-
ture difference in conductors plus some fractional factor which
accounts for all the subtleties of surface interaction. Double
the pressure and double this rate of energy (heat) transfer.
Note that all this (and again we speak only of very low pres-
sures) is *independent* of the distance between conductors, since
the process is sort of like a conveyor belt or post office-- once
the system gets working letters or packages are delivered at the
same rate they are sent at each end, no matter how far apart the
stations are (we don't care how long the trip takes for any
individual package, in heat transfer we only care about the
volume of mail). So at very, very low pressures (below 1/100th
mm Hg or so) one inch of near vacuum conducts heat by gas
convection at about the same rate as 10 inches of it. This has
been verified experimentally, and the theory was developed by
Knudsen quite a long time ago.
The change in gas conductive behavior comes when pressures
(and thus gas particle numbers per volume) rise to the point that
molecules can be expected to hit other molecules and be thwarted
in their delivery of energy *before* they hit the other conduc-
tive surface. Again, this effect starts to show up at pressures
above 1/100th Torr or so for dewar wall separation distances in
the range that interest us, and this is the critical break
pressure below which big gains in insulation are made ny harden-
ing vacuum. For pressures much above this break point, gas
pressure begins to act AGAINST conductivity because of this
molecule-molecule impact interference with wall-to-wall heat
transfer (i.e., as pressure rises each molecule becomes less
efficent as a heat transfer agent, because it gets to transfer
its energy over a shorter and shorter distance at high velocity
before it collides with another and has to give the energy up),
and this effect (as it happens) pretty much exactly cancels out
the conductivity-increasing "more-postmen" effect of pressure
(the one we already discussed, and which operates unopposed at
lower pressures). I can't tell you why the two effects *exactly*
cancel without posting the math (it's not intuitive), so you'll
have to trust me, unless you really want the equations. In any
case, over a wide range of intermediate pressures (mean free path
much less than conductive distance), gas thermal conductivity
becomes pretty much independent of pressure. And of course, at
these higher pressures, since heat is now being transferred
between layers of gas as it goes from one conductor to another,
heat transfer *is* inversely dependent on distance between
conductors (i.e., on the number of "layers" of gas), just as
Tim's intuition suggests. It's as though a lot of postal systems
are now working back-to-back, with a delay in each. Gas mole-
cules move very fast (practically instantaneously) over Dewar
wall distances, but that's no help when they're crowded to the
point that they can't go even a tiny fraction of that distance
without bumping into something. I suspect that Professor
Ettinger's "soft vacuum" systems opperate in this pressure range,
and that is why he wants to run the maximum distance between con-
ductors that he can (with perlite in between not for insulation,
but rather for a mechanical support which has as little heat
conduction as possible). With really HARD vacuums, however,
distance between conductors is not important.
[By the way, just to complete things, we should note that at
really *high* pressures (10 or 100s of atmospheres) where the
mean free path becomes so small it's on the order of molecular
size, and gas densities approach liquid densities, the molecules
start to act like water in a hose, or cars on a freight train,
(push here and you get movement over there much faster than the
speed of the conductors themselves), and efficiency of heat
transport begins to go up again-- so now we have a pressure
dependence once more, albeit a complex one. Of course, this has
nothing to do with cryonics.]
Hope that all helps clear up this confusion.
Steve
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