- #1

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[itex]v^2=\frac{8kT}{\pi m}[/itex]

But there are high Temperatures that would have average speeds > c.

Are there distributions that describe gases with an average speed of 0.5 relativistically?

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- Thread starter magicfountain
- Start date

- #1

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[itex]v^2=\frac{8kT}{\pi m}[/itex]

But there are high Temperatures that would have average speeds > c.

Are there distributions that describe gases with an average speed of 0.5 relativistically?

- #2

mfb

Mentor

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The average squared velocity will go towards c^2, and all particles are always slower than c for every temperature.

- #3

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Well, you have to replace the nonrelativistic formula with the relativistic one.

...which to me is not very illuminating, since it's given without any derivation and written in terms of a goofy choice of variable.

Can't you just take the partition function and put in the relativistic expression for the energy? I.e.:

[tex]e^{-\beta\sqrt{m^2+p^2}}[/tex]

This is in units with c=1, and beta is the inverse temperature.

- #4

Bill_K

Science Advisor

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- #5

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@Bill_K

that helped a lot. i guessed that i had to do lagrange multipliers with relativistic expressions, but i was too lazy to really think about it. thanks for reminding me that it actually just leads to the partition function and you have to plug in the rel. terms there.

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