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thank you

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- Thread starter mafra
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thank you

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Drakkith

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Have a look at relativity on wikipedia or do a search for google. Also, I read an interesting book called "The Anime Guide To Relativity" I believe. It explains the basics pretty well. It's a good read if you enjoy anime or you don't like very technical books.

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Root mean square speed is the measure of the speed of particles in a gas that is most convenient for problem solving within the kinetic theory of gases. It is defined as the square root of the average velocity-squared of the molecules in a gas. It is given by the formula

it is saying that, higher the speed of the particles, higher the temperature (or in the other way, idk)

so if it is impossible to particles to reach the speed of light, it is impossible to temperatures get beyond some another value (c².Mm/3.R), or you can't apply this relation to higher speeds?

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Drakkith

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Edit: Just FYI, I don't know the correct formula to use in this situation. I just know that at very high speeds you must use relativistic formulas instead of classical ones.

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That formula is based on the assumption that the kinetic energy of a gas molecule is [itex]\frac{1}{2} m v^2[/itex], which is a nonrelativistic approximation. That approximation does not hold at relativistic speeds, and hence the expression [itex]v_{rms} = \sqrt{3RT / M_m}[/itex] is not valid.

Root mean square speed is the measure of the speed of particles in a gas that is most convenient for problem solving within the kinetic theory of gases. It is defined as the square root of the average velocity-squared of the molecules in a gas. It is given by the formula

it is saying that, higher the speed of the particles, higher the temperature (or in the other way, idk)

so if it is impossible to particles to reach the speed of light, it is impossible to temperatures get beyond some another value (c².Mm/3.R), or you can't apply this relation to higher speeds?

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thank you, people

that answered my question

that answered my question

- #7

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In addition there is certain limit to the temperature. I've heard there is some "highest temperature that could be reached". But I couldn't remember

And at that enormous velocity it would be no gas any more. Have you seen any gas in stars?

That formula is based on the assumption that the kinetic energy of a gas molecule is [itex]\frac{1}{2} m v^2[/itex], which is a nonrelativistic approximation. That approximation does not hold at relativistic speeds, and hence the expression [itex]v_{rms} = \sqrt{3RT / M_m}[/itex] is not valid.

What about using relativistic mass? I think that Tayloring γ factor would give terms like that

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Drakkith

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Which star is made of gas? It must have extremely low temperature comparing to normal stars.

I think taylor the (γ-1)mc^2, there would be a term like that. And if you plug in some moderately high speed, you can still find it a good approximation.

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However, relativistic effects typically are of no concern with regard to thermodynamics. The temperature has to be incredibly high, and the particles incredibly small, for relativistic effects to come into play. For a cloud of electrons, you need to worry about relativistic effects if the temperature is on the order of 10

- #11

Drakkith

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Which star is made of gas? It must have extremely low temperature comparing to normal stars.

Quote from wikipedia:

The coolest layer of the Sun is a temperature minimum region about 500 km above the photosphere, with a temperature of about 4,100 K.[50] This part of the Sun is cool enough to support simple molecules such as carbon monoxide and water, which can be detected by their absorption spectra.[55]

- #12

cjl

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Which star is made of gas? It must have extremely low temperature comparing to normal stars.

I think taylor the (γ-1)mc^2, there would be a term like that. And if you plug in some moderately high speed, you can still find it a good approximation.

Most stars have surface temperatures of below 10,000 K, which is the temperature required for nearly complete ionization of hydrogen (approximately), so most stars have surfaces that are mostly gas (below around 7000K, there isn't very much ionization at all, and they are nearly 100% gas). Only the very hot stars are close to completely ionized.

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