Maximum heat?

[kyle8921]

The lowest possible temperature is -273 C, so is there a highest possible temperature too, or does it only depend on how much heat a specific substance can take before it vaporizes, or dissapears?

[Qfwfq]

You can always make sure it doesn't get away! There isn't an upper limit in principle on temperature, there are only practicle matters.

[nkt]

Originally Posted by Qfwfq

You can always make sure it doesn't get away! There isn't an upper limit in principle on temperature, there are only practicle matters.

I'm not so sure that is true. We can cheat, and look at the physical limit to any system of particles, the speed of light.

If we look at the definitions of temperature, (this may be rusty) we see that it is the random movements of phonons through the structure, and the bulk increase in energy.

Obviously, once a certain temperature is reached, we get a bulk effect called melting, then boiling. Eventually you get a plasma, where the electrons themselves get kicked off the orbits around the atom. Now, at this point, the "temperature" is very high, but the particles are rarifed, so have a low density, and so the specific heat tends to be very low. However, this means that the plasma particles are flying about, colliding at random. The limit to how fast they can fly is, therefore, limited only by the energy you put in. This in turn is limited by how fast the particle can actually go, which is c. (Of course, it can only reach c for an infinite energy input, and so you are limited by that)

Now, if someone wants to go look up the formula that lets you turn particle velocity into temperature, and plug in 2.998 * 10^8 m/s, that should tell us the maximum possible temperature for that particle.

I suspect it will be quite warm!

[Qfwfq]

Check your argument over again. Most of all:

Originally Posted by nkt

The limit to how fast they can fly is, therefore, limited only by the energy you put in. This in turn is limited by how fast the particle can actually go, which is c. (Of course, it can only reach c for an infinite energy input, and so you are limited by that)

A bit contradictory. SR certainly doesn't put an upper bound on kinetic energy. I also fail to see your point about density and similar things. Even with three molecules per cubic mile you can have a high temperature. A temperature can even be given to the vacuum, see radiation temperature.

Originally Posted by nkt

Now, if someone wants to go look up the formula that lets you turn particle velocity into temperature, and plug in 2.998 * 10^8 m/s, that should tell us the maximum possible temperature for that particle.

Which formula? Relativistic or not relativistic?

BTW, temperatures can be negative according to the definition of the Boltzmann formula as long as you consider a subsystem with a limited energy spectrum, such as a spin gas. Much of a lab curio though, but when the negatemerature is induced it will go toward equilibrium with the rest by the route through infinity (down to -inf and then from there down to the surrounding temperature).

[UncleAl]

The lowest achievable temperature is an epsilon above absolute zero. The highest possible temperature is an epsilon below absolute zero (population inversion). Or, if you like, the highest possible temperature is a Planck mass-equivalent of energy occupying a Planck volume of space.

[spennithorne]

Please explain the "highest possible temperature is an epsilon below absolute zero (population inversion)" phraseology. Thanks.

[nkt]

Originally Posted by Qfwfq

A bit contradictory. SR certainly doesn't put an upper bound on kinetic energy. I also fail to see your point about density and similar things. Even with three molecules per cubic mile you can have a high temperature. A temperature can even be given to the vacuum, see radiation temperature.

Isn't that my point? You have one measure for the energy density, and another for the temperature. Bulk movement of matter is kinetic energy, rather than heat. However, taken to the logical limit, a single particle could be accelerated to whatever "temperature" was wanted. However, once the particle was accelerated to an epsilon below c, it wouldn't be possible for it to go any faster, and therefore could not get any "hotter".

Originally Posted by Qfwfq

Which formula? Relativistic or not relativistic?

It would need to be modifed for relativity.

Spennithorne, epsilon is a mathmatical construct which means "a small positive infinitesimal quantity", usually denoted ε.

[Qfwfq]

You are still contradictory nkt, I think you ought to check your calculus a little bit.

Originally Posted by nkt

It would need to be modifed for relativity.

Why not?

[Qfwfq]

Originally Posted by spennithorne

Please explain the "highest possible temperature is an epsilon below absolute zero (population inversion)" phraseology.

Any negatemperature is higher that any positive temperature, at least regarding which system will absorb heat and which will release it.

The "epsilon below" is a loose way of putting it. Strictly, the zero is an upper bound and not a maximum. For any t = 0 - ε it can have a value between that and 0, but it can't be exactly 0.

[inuyashakusho]

if you think about it there must be a maximum heat because if absolute zero is when atoms are completely still then there must be a temperature at which atomic movement reaches the speed of light, which is the fastest that anything can go unless going through a wormhole