Does heating matter generate relativistic effects?

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John Burnap

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John Burnap  asked the Naked Scientists:
Hi Chris!
Love the show of course! I have an hour drive on the LA freeways, and thanks to you it goes much faster.

I have a question that has been bugging me for years.

Does heating matter generate any relativistic effects? That is, do the individual atoms in a hot gas have significant velocity to give the system more mass, etc.? I suppose it would have to be pretty hot!
Thanks again,

What do you think?
« Last Edit: 05/04/2011 04:30:03 by _system »


Offline JMLCarter

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Does heating matter generate relativistic effects?
« Reply #1 on: 06/04/2011 00:21:27 »
Yes apparently it does.

As the gas gets hotter the Boltzman velocity distribution changes to become a Maxwell-Juttner distribution due to the relativistic effects.

The transition occurs as kT approaches mc².

So for water,
T = (18*1.660 538 782(83)E−27[Kg])*(299,792,458 [m/s^2])^2 / 1.380 6504(24)E-23 [J/K]

T = 30E-27*9E+16/1.5E-23 which is about 10.8E+12 degrees K.
This is much hotter than I had expected intuitively,
a lot hotter than the sun at 10E+7 K
and even than a fusion reactor core at around 1E+9 K

(I'm fairly sure the water wouldn't actually survive that intact, it would become a plasma, actually it's high enough to think about quark/gluon plasma.)

Relativistic effects might be measurable at temperatures as low as 5E+10 Kelvin, which v. aprox corresponds to a molecular speed of 0.1c (using T = mv²/2K )

« Last Edit: 06/04/2011 00:38:40 by JMLCarter »


Offline John Burnap

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Does heating matter generate relativistic effects?
« Reply #2 on: 21/04/2011 17:16:01 »
Thank you!!

This is wonderful! I had long suspected this to be true.

So, now I have a couple of new questions: If this matter were heated in an unbreakable vessel, would it reach such a temperature to fuse? If so, would the new atomic mass change the relativistic factor?

I guess what I am asking is: Would the matter fuse at a lower temperature than the temperature of observable relativistic effects?

Thanks again,



Offline Bored chemist

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Does heating matter generate relativistic effects?
« Reply #3 on: 22/04/2011 09:58:10 »
Relativistic effects occur when I walk across the room, it's just that they are rather small.
They will become significant at some arbitrary temperature depending on how hard you look for them.

Relativistic effects also occur in the chemistry of heavy elements like lead and gold at room temperature. (The electrons near the nuclei have classical velocities near C)
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