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Joe Dees
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virus: A High Temperature Head-Scratcher
« on: 2003-02-21 14:46:44 »
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Walter Watts
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Re: virus: A High Temperature Head-Scratcher
« Reply #1 on: 2003-02-21 16:52:38 »
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Yes, I have comments.

However, I've been in bed for 3 days coughing myself a new asshole, so I'll defer til
later.

Walter

joedees@bellsouth.net wrote:

> It has long been accepted that there is a lowest possible temperature,
> known as absolute zero, at which the constituent atoms do not vibrate
> at all.  It is less frequently stated, but seems to be assumed, that there
> is, however, no highest possible temperature; in other words, that,
> unlike the low-temperature absolute-zero closure, that high temperature
> is open-ended.  But there is indeed a limit to the possible vibratory
> speed of atoms, and that is, of course, c, or the speed of light.  It seems
> to me that one should be able to correlate vibratory speed with
> temperature and arrive at a maximum possible temperature, beyond
> which the constituent atoms could not vibrate faster due to c
> restrictions.  Any comments?
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Joe Dees
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Re: virus: A High Temperature Head-Scratcher
« Reply #2 on: 2003-02-21 17:02:53 »
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David Lucifer
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Re: virus: A High Temperature Head-Scratcher
« Reply #3 on: 2003-02-24 13:11:10 »
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----- Original Message -----
From: <joedees@bellsouth.net>
Sent: Friday, February 21, 2003 2:46 PM


> is open-ended.  But there is indeed a limit to the possible vibratory
> speed of atoms, and that is, of course, c, or the speed of light.  It
seems
> to me that one should be able to correlate vibratory speed with
> temperature and arrive at a maximum possible temperature, beyond
> which the constituent atoms could not vibrate faster due to c
> restrictions.  Any comments?

If you plug c into the molecular speed formula from [1] (using the root mean
square from the distribution, since there is no max velocity formula), you
get 3.6e+15 K.

However this page [2] about the early universe says that the earliest
temperature was 1e+32 K and by the time there were particles to vibrate it
had dropped to 1e+15 K (remarkably close to my calc above).

[1] http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html
[2] http://casswww.ucsd.edu/public/tutorial/BB.html

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Joe Dees
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Re: virus: A High Temperature Head-Scratcher
« Reply #4 on: 2003-02-24 13:21:39 »
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rhinoceros
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Re:virus: A High Temperature Head-Scratcher
« Reply #5 on: 2003-03-15 12:16:12 »
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[David Lucifer]
If you plug c into the molecular speed formula from [1] (using the root mean
square from the distribution, since there is no max velocity formula), you
get 3.6e+15 K.

However this page [2] about the early universe says that the earliest
temperature was 1e+32 K and by the time there were particles to vibrate it
had dropped to 1e+15 K (remarkably close to my calc above).

[1] http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html
[2] http://casswww.ucsd.edu/public/tutorial/BB.html



[rhinoceros]
Hmm... The relativistic increase of the mass is missing.

1/2 mv^2 = 3/2 kT

When the speed of the particles v approaches c, the mass m approaches infinity, and T approaches infinity as well. No upper limit for T using this model.

We could look into the actual properties of matter and space-time to find out whether there is an absolute maximum temperature. An answer is the Planck Temperature T = 10^32K. This temperature corresponds to the maximum enegy density possible before a gravitation collapse happens -- that is, before the particles become black holes.

Here is a simple explanation:
http://www.straightdope.com/classics/a3_347.html

And here is another one, a little bit more quantitative:
http://www.lns.cornell.edu/spr/2001-09/msg0035678.html


I am afraid this is not the end of the story. There have been given more generalised definitions of temperature in thermodynamics and in laser physics (phase inversions), covering more than the kinetic model. There is even a concept of negative temperature (below absolute zero). You can take a look here:

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/neg_temperature.html

« Last Edit: 2003-03-15 13:58:14 by rhinoceros » Report to moderator   Logged
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