# Maximum Tempurature

1. Nov 20, 2004

### Jake

What is the maximum tempurature? That is, if there is one. But since heat is just kinetic motion and kinetic motion has a limit in c, I would expect there must be a limit to how 'hot' things can become. Correct me if I'm wrong

Thanks!

2. Nov 20, 2004

### zefram_c

No current theory predicts a maximum temperature. Heat is kinetic motion, but relativistically that can increase without limit, and hence so can temperature (E=1/2mv^2 is only valid non-relativistically).

It is possible to speculate a maximum temperature using the Planck scale. Supposedly, energies greater than the Planck energy cannot be achieved, so this can be used to set an upper limit. This energy is:

$$E_p = h\sqrt{\frac{Gh}{c^5}} = 1.4*10^9J$$

So a Planck temperature can be

$$T_p = E_p / k_B = 3.55*10^{32}K$$

3. Nov 20, 2004

### marcus

in some situations, perhaps all, the temperature of
1.4 x 1032 kelvin
known as the Planck temperature can serve as
a top of the scale.

It is basically the hottest temp around time of Big Bang

above this temperature ordinary laws of physics dont seem to apply

You can find the official recommended value of the Planck temp
listed at the US gov. site for the NIST (natl inst. of standards and technology)

or google "fundamental constants" and when you get to the NIST site select "universal constants"

you find it along with the speed of light and planck's constant and G, the universal gravitational constant, and other really basic quantities

here is the NIST fundamental constants site

http://physics.nist.gov/cuu/Constants/

when you select "universal" there, you get
http://physics.nist.gov/cgi-bin/cuu/Category?view=html&Universal.x=74&Universal.y=9

and you see "Planck temperature"
I just went there to see what they actually said and it was
1.41679 x 1032 Kelvin

I see while i was typing, Zefram said something different which is, i guess, different by a factor of the square root of 2 pi.
what I am telling you is probably more widely accepted as planck temp.
It uses the h-bar constant instead of the h constant which is bigger by a factor of 2 pi. Most people when they talk planck units, in my experience, base them on h-bar. there is no one right way but being consistent leads to less confusion

Last edited: Nov 20, 2004
4. Nov 20, 2004

### Jake

How can relativistically motion can increase without limit? From whatever frame of refrence you are in, nothing can be moving faster than C, so how can there be no limit.

Just curious, thanks for the info

5. Nov 20, 2004

### Jake

Thanks, I suppose that answers my question, but I'm just not clear as to why C cant be used.

6. Nov 20, 2004

### marcus

temperature scale is a kind of alternative scale to energy (the boltzmann constant k relates the two-----E = kT)

temperature is not directly related to the speed of molecules moving in the air but to their kinetic energy (which involves their masses as well as their speeds)

as a massive object goes faster and faster, and approaches the speed c,
then its kinetic energy increases without bound

so the speed of light does not, by itself, provide us with an upper limit on temperature or on the kinetic energies of particles.

but h-bar steps in and says that as any kind of particle's total energy goes up its quantum wavelength shrinks, so intuitively highly energetic particles become more compact

then G (gravity) steps in and says that if something is very massive and concentrated very compactly it can collapse to a black hole under its own gravity.

So everything goes to hell at a certain level of energy.
Planck temperature is the temperature where that happens.

It is based not only on c, but also on h-bar and G. you have to use all three fundamental constants to calculate what it is.

Planck temperature is the temperature where even photons of light, in a space that hot, would be so energetic and have such short wavelength that even they would form black holes.

this may sound ridiculous but it is more or less right, and gives a notion of why there is an upper temperature limit that you have to calculate using c, hbar, G.

7. Nov 20, 2004

### Jake

Ok thanks, it's all clear now

8. Nov 20, 2004

### zefram_c

To wrap things up, kinetic energy in relativity is:

$$T = (\gamma-1)m_0c^2$$, where m0 is the rest mass, c is the speed of light, and $\gamma$ is the usual. Since $\gamma$ can increase without bounds as the speed v approaches c, so can kinetic energy, which is what temperature is based on.