[allybalder (OP)]

quote from cosmos2 BBC2 tues
A 10 metre cubed doughnut of plasma with a staggering temperature of tens of million degrees centigrade! It might not be as big as, but it is hotter than, the sun – our nearest star.
newbielink:http://www.open2.net/sciencetechnologynature/planetsbeyond/makingstars.html [nonactive]

Especially after the prog Absolute Zero I was wondering is there a theoretical maximum temp?
Presumably as temp is related to speed of atoms then the speed of light is a limitation - but pressure is not limited so maybe there is no max?
What is the highest we have ever achieved on earth?
Dr Karl struggled answering this Q on radio5 live 'up all night' a few weeks ago!
alan

[Bored chemist]

"is there a theoretical maximum temp?"
No, except that there's only so much energy in the universe to heat something with.

[another_someone]

Temperature is a measure of energy density.  There is a finite (although massive) amount of energy in the universe, and there is a maximum density an object can attain before becoming a black hole, and these two factors should provide a limit to temperature.

The hottest anything could become should be the temperature of the Big Bang at the birth of the universe; since that contained the entire energy of the universe in its most compact form.

[syhprum]

The Planck energy limit is 1.2*10^31 eV, converting this into temperature we get approximately 1.3*10^35°K the highest temperature commonly encountered is that of the fastest cosmic ray particles of 10^20eV

[lightarrow]

The Planck energy limit is 1.2*10^31 eV, converting this into temperature we get approximately 1.3*10^35°K the highest temperature commonly encountered is that of the fastest cosmic ray particles of 10^20eV

Planck energy should be ~ 1.22*10²⁸ eV, according wikipedia:
http://en.wikipedia.org/wiki/Planck_energy
so the max temperature should be ~ 1.4*10³²K (using, as you did, the relation E = kT with k = Boltzmann's constant = 1.38*10²³ J/K).

Yes, the more energetic particle we have detected (the famous "Oh My God! particle") is that one. However, it's impossible to attribute a temperature to a unique particle: we need many of them with a Planck distribution of energies, to do it.

Example: you know that a blackbody at room temperature emits EM radiations of many frequencies = energies, even very high ones (but with very low intensity, of course); if you analyzed only those very high frequencies, for example with a filter, would you conclude that the body's temperature is very high?

Actually, kT can be associated to the average energy of a particle, so, if Planck energy is the max energy, then the average one is much smaller (which means that limit for T is too much optimistic!)

[syhprum]

lightarrow

Apologies for defective arithmetic, as you say to get a concept of temperature you must intergrate over the whole range of emissions from a hypothetical blackbody and not consider only the highest frequencies.
That is the beauty of this board sometimes you get your muddled ideas sorted out.

[lightarrow]

lightarrow

Apologies for defective arithmetic, as you say to get a concept of temperature you must intergrate over the whole range of emissions from a hypothetical blackbody and not consider only the highest frequencies.
That is the beauty of this board sometimes you get your muddled ideas sorted out.

No need of apologies! We all make mistakes, and we are here to learn from those who know more about a specific problem!