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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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