# Thread: temperature and speed of matter

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## temperature and speed of matter

If something is 6 trillion degrees centigrade, is this equivalent to a fraction of the speed of light. If so, what would the equation for calculating this speed?

2. In what way are you imagining equivalence? The mean speed of the particles?

Grant Hutchison

3. The Kinetic Energy of a gas particle is directly proportional to the Temperature of the gas or plasma made of those particles.
Oxygen atoms at 273K (0C) travel about 460 meters per second on average. Hydrogen nuclei would be going 16 times as fast.

4. Originally Posted by antoniseb
The Kinetic Energy of a gas particle is directly proportional to the Temperature of the gas or plasma made of those particles.
Oxygen atoms at 273K (0C) travel about 460 meters per second on average. Hydrogen nuclei would be going 16 times as fast.
Isn't that closer to 4 times as fast? Kinetic energy is proportional to velocity squared.

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Thanks all. That was enough info.

6. Originally Posted by Hornblower
Isn't that closer to 4 times as fast? Kinetic energy is proportional to velocity squared.
Yes. In my quick response I saw it was linear with mass, but then I used the word fast instead of talking about energy.. Good catch, thanks.

7. So, using antoniseb's figures, that means that yes, if you had hydrogen plasma a six trillion K, a naive calculation would have the protons moving at about 91% of the speed of light, and the electrons moving much faster than the speed of light. Obviously, under these conditions, you'd have to use the relativistic expression for kinetic energy to work out the actual mean velocity. We call this a relativistic plasma.

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Originally Posted by Grey
So, using antoniseb's figures, that means that yes, if you had hydrogen plasma a six trillion K, a naive calculation would have the protons moving at about 91% of the speed of light, and the electrons moving much faster than the speed of light. Obviously, under these conditions, you'd have to use the relativistic expression for kinetic energy to work out the actual mean velocity. We call this a relativistic plasma.
When a proton is moving at .9999999996 of the speed of light is this equivalent to a certain temperature or is a traveling object not the same as temperature? The hottest measured temperature is some number around 4 trillion degrees centigrade, but it seems to be that something moving at 0.9999999996 times the speed of light would be equivalent to something much hotter than the 4 trillion degrees. What am I missing?

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Originally Posted by Copernicus
When a proton is moving at .9999999996 of the speed of light is this equivalent to a certain temperature or is a traveling object not the same as temperature?
Strictly the equivalence of average KE per particle and temperature is only true for systems in thermal equilibrium. It get hard to make it a meaningful concept for an isolated particle in motion. Plus it is usually measured in the COM frame of the system, since relativistic notions of temperature get complicated fast (see: https://www.nature.com/articles/s41598-017-17526-4, for example)

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Originally Posted by Shaula
Strictly the equivalence of average KE per particle and temperature is only true for systems in thermal equilibrium. It get hard to make it a meaningful concept for an isolated particle in motion. Plus it is usually measured in the COM frame of the system, since relativistic notions of temperature get complicated fast (see: https://www.nature.com/articles/s41598-017-17526-4, for example)

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Originally Posted by Shaula
Strictly the equivalence of average KE per particle and temperature is only true for systems in thermal equilibrium. It get hard to make it a meaningful concept for an isolated particle in motion. Plus it is usually measured in the COM frame of the system, since relativistic notions of temperature get complicated fast (see: https://www.nature.com/articles/s41598-017-17526-4, for example)
So is it not known whether something appears hotter, colder, or the same at rest or at relativistic speeds.

12. Originally Posted by Copernicus
So is it not known whether something appears hotter, colder, or the same at rest or at relativistic speeds.
It is known. If that something is a body consisting of a vast number of particles which are jiggling with collective kinetic energy, it will be hotter with the jiggling at relativistic speeds than with them jiggling at very low speeds. If that something is a single particle in motion through space, once again temperature is not a meaningful concept.

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Originally Posted by Hornblower
It is known. If that something is a body consisting of a vast number of particles which are jiggling with collective kinetic energy, it will be hotter with the jiggling at relativistic speeds than with them jiggling at very low speeds. If that something is a single particle in motion through space, once again temperature is not a meaningful concept.
The article in nature seemed to imply that we really don't know this, but I am not sure that I am understanding this correctly. https://www.nature.com/articles/s41598-017-17526-4

14. Okay, now I see your point, which involves a body for which temperature is a meaningful concept, and the question of whether or not extremely fast motion relative to that body changes an observer's perception of that temperature.

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