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Absolute Zero and Molecular Motion
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Question:
I understood that at absolute zero all molecular motion.
Does gravity influence them if they stop moving?
Replies:
If it were possible to attain a temperature absolute zero
for a material then all the vibrations/random motions will
stop. It is not possible to reach absolute zero - it is
not possible in theory or in practice according to our
present understanding.
Gravity is an ever present influence so it will effect them.
If you are worried about the material being crushed by self
gravity then the answer is that quantum effects like Pauli
exclusion principle will prevent this collapse up to masses
several times that of the Sun ( 2-3 times ). Here I am talking
about the Chandrasekhar limit for Neutron stars.
Jasjeet
Temperature is defined statistically and not mechanically, so the
statement "T=0" is actually not exactly equivalent to the statement "all
motion ceases." The latter is a pretty good approximation, but there are
important exceptions. For example, quantum mechanical "zero-point motion,"
which allows systems in their "ground" (lowest possible energy) state to
have nonzero probability of being found over extended areas of space. Thus
at T=0 the two atoms of a diatomic molecule (e.g. nitrogen) are not rigidly
separated at some distance from each other, but can be thought of as
undergoing rapid vibration with respect to one another. The entire molecule
also "rotates," even at T=0. In the context of spin systems the mechanical
interpretation of temperature as motion is even more misleading, because
you can get T < 0.
There is no strict theoretical barrier to T=0 like there is to attaining
the speed of light for massive objects, but practically your insulation
could never be good enough, and some energy would always leak in from the
surroundings, so that T = 0 K could only be achieved for an ordinary system
like a gas in an entirely empty universe. In this universe you are limited
in approaching T=0 mainly by your patience and money.
That gravity would influence a system you were trying to cool to T=0 is
another way of saying energy would leak in unless your insulation was good
enough. In the case of gravity the only insulation is sufficient distance
from the massive object, so it is fortunate the energy represented by
gravitational forces is undetectably minute in the near-zero temperature
experiments about which you may have been thinking.
christopher grayce
1.Classicaly speaking ALL MOTION CEASES AT ABSOLUTE ZERO.
2.Zero point Quantum motion is always there.
and that is what prevents collapse in the hypothetical scenario
at absolute zero. For very massive objects, this has to be
supplemented with Pauli repulsion.
3.The third law of thermodynamics, also known as the Nernst
theorem, can be written as BY NO FINITE SERIES OF PROCESSES
IS THE ABSOLUTE ZERO ATTAINABLE. No matter how much patience
and money you have, you can not execute an infinite series of
steps.
Jasjeet
For those interested, "negative" temperatures in spin systems are
discussed by F. C. Andrews in "Equilibrium Statistical Mechanics,"
2nd ed. (Wiley-Interscience, N.Y., 1975), p. 175, and in an article
by Norman F. Ramsey in "Physical Review" (vol. 103, 1956) on p. 20.
A careful statement on the "unattainability" of absolute zero can
be found in Herbert B. Callen's book, "Thermodynamics and An Intro-
duction to Thermostatistics," 2nd ed. (Wiley, N.Y., 1985) on p. 281.
How temperature is understood quantum-mechanically is explained
by J. J. Sakurai in his (wonderful) book "Modern Quantum Mechanics,"
(Benjamin/Cummings, Menlo Park, 1985) beginning on p. 182. It might
be worth mentioning that T=0 in the context of quantum mechanics is
equivalent to the statement that there is a 100% chance of finding a
system in its ground state.
christopher grayce
Let me just add my $0.02...
Jasjeet is absolutely correct...if the system is bounded,
there will be zero-point motion. Moreover, it is indeed
impossible to reach absolute zero by a finite number of steps..
this is a fundamental principle that cannot be completely
overcome by mere experimental technique + $. If you
find a way, though...PUBLISH!!!
I forgot to mention that Chris' slyly implied comment that
one should also think about the possibility of negative
temperatures is also worth considering carefully in this
context....and that another place worth looking for information
on this point is Atkins' Physical Chemistry textbook.
topper
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Update: June 2012
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