# Is There a max temperature? My question about it.

• EU_Raider
In summary, relativistic gases have an upper limit to their temperature. Beyond that point, particle collisions become so intense that they start to undergo fusion reactions.f

#### EU_Raider

Through school I have been told That temperature has no limit, that it is infinite.

I am also told that a particle cannot exceed the speed of light.

Yet again Temperature has an effect on the speed of a particle therefore there must be a maximum temperature otherwise we would exceed the speed of light.

Using the Equation V^2=3RT/Molar Mass taking R as 9.1x10^-7 also taking the particle proton(or Neutron) for the Molar Mass

I got an answer but I was wondering is my statement correct or is there some laws or rules which I am not aware of?

Since the temperature(of an ideal gas at least) is proportional to the mean kinetic energy of its molecules(as in, it doesn't make them go faster - the whole idea of temperature is just a way of saying how energetic they are, on average), and kinetic energy is a product of velocity and mass, then I suppose as the velocity approaches c, the mass approaches infinity, netting infinite temperature.

It's just a guess, though. Don't take my word for it.

As your temperature increase you would eventually ionize the material and turn it into a plasma. Beyond that you would get particle collision so intense that particle collisions would start to undergo fusion reactions. Beyond that and the collisions would be akin to a particle collider, and would start to produce showers of particles created from the kinetic energy of each parent particle. We don't know of an end to this so you could probably keep going on forever. Keep in mind that while the speed of light is not reachable, you CAN continue to increase your average kinetic energy forever to any value theoretically. You just don't ever reach c.

You may want to check how relativistic mass depends on the speed, that will answer your question. Google for Lorentz factor.

Through school I have been told That temperature has no limit, that it is infinite.

I am also told that a particle cannot exceed the speed of light.

Yet again Temperature has an effect on the speed of a particle therefore there must be a maximum temperature otherwise we would exceed the speed of light.

Using the Equation V^2=3RT/Molar Mass taking R as 9.1x10^-7 also taking the particle proton(or Neutron) for the Molar Mass

I got an answer but I was wondering is my statement correct or is there some laws or rules which I am not aware of?

There has been some work done on relativistic gases in statistical physics, but my knowledge of the subject is rusty. I'll read up on it and see if I can get back to you. :)

I think the highest temperature was when the big bang happened, since there is finite energy in the universe, there is a finite temperature that there ever was, but I guess theoretically there is no limit to temperature?

Very high temperature is usually mostly in radiation, not matter, to which the formula used does not apply.