What is the Highest Temperature Possible?

[unipidity]

Well, yes, im using a purely classical definition of temperature. But then temperature is a statistical concept as far as I am concerned.

As to what a high temperature would 'do' to a solar system- what exactly is at this temperature? The whole thing? A thousand particles? etc

As for temperature of Big Bang... errr.... well I dont see how a singularity can have a real temperature. Myabe a Hawking temperature? But thats a black hole, not a 'big bang'. Plus methinks there are no particles to have a temperature for a while, so youd just have to look at radiation concentration, which would be... infinite. Eeek.

 

[MisterChief]

I believe the highest possible temperature that can be attained is...1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
00,000,000 degrees Kelvin. Of course, that's just an estimate based on speculation and sheer ignorance...

 

[zugzoog]

Originally posted by: f95toli

Originally posted by: zugzoog
So the particle does not have to exceed the speed of light to acheive infinte temperature.

So? Again, what definition of temperature are you using?
If you just do a direct "translation" between energy and temperature (by dividing by kb) then this is true, however in many other cases (statistics) temperature is more related to the speed of the particles and then there is a maximum temperature set by c.

Please note the fundamental definition of temperature.
Temperature is that property which governs the transfer of thermal energy, or heat, between one system and another. When two systems are at the same temperature, they are in thermal equilibrium and no heat transfer will occur. When a temperature difference does exist, heat will tend to move from the higher temperature system to the lower temperature system, until thermal equilibrium is established.


The speed of the particles by itself is not an indication of temperature. For example, which has the higher temperature?
1) Hydrogen atoms with an average speed of 10m/s or,
2) Uranium atoms with an average speed of 5m/s?
(yes, I am aware that the speeds will have a bell curve distribution).

Since the Uranium atoms have a greater average energy (even though they have a lower average speed), then energy will flow from the Uranium atoms to the Hydrogen attoms if they were placed side by side (second law of thermodynamics).

Therefore Mass is an integral part of the definition of temperature.

As the average speed of the particles approaches c the average mass of the particles will approach infinity causing a (thoeretical) infinite temperature. Therefore, while there is a limit to the speed of the particles, this does not limit the temperature to a finite size.

Do you have any links to definitions of temperature that are based more on the speed of particles, I would be interested.

 

[f95toli]

No, I think you just summarized what I meant. My point was that when you talk about the temperature of a classical gas you can calcultate the average kinetic energy of the particles (3/2kbT) and hence the average speed (note that this does not work anymore in the Knudsen limit which is still classical) if you know the temperature.

In "modern" physics the concept of temperature is often "generalized" so that ANY energy divided by kb is considered to be a "temperature", this is often very usefull but has little to do with classical thermodynamics. This is btw also true in laser-cooling etc since the number of particles involved is sometimes too small for the classical (statistical) "definition" of the temperature to be strictly correct.

In my field we tend to think of everything, including temperature, in terms of frequeny instead; we divide the energy by h and that gives us a frequency. This makes sense because frequency is what I can "see" in an experiment.


I would like to point out that there IS no fundamental definition of temperature, your definition is just one. I have colleagues who work on temperature standards (low-temperatures) and a fundamental problem in that field is to agree on what you consider to be the "temperature" of the system (as far as I remember temperature is actually "undefinied" below a certain temperature (1K?) because there is no international standard, in part because of this problem).
At low temperatures you can also have situations where the statistical temperature (the escape temperature from a well for example) is actually higher than the bath temperature (which is what you are refering to) because of quantum mechanical effect (tunneling out of the well); hence there are actually two temperatures.

 

[TitanDiddly]

Originally posted by: cquark

Originally posted by: WoodenPupa
I know there is absolute zero for the coldest temperature. What physical laws govern the upper limits of temperature? Or is there a limit at all? The fate of the moon might depend on an accurate answer so I need info fast!

There's no upper limit. For practical high temperatures, the Sun's core is about 15 million K and a supernova starts at around 5 billion K.

Sure there is. Heat energy is about the speed that the particles are travelling. There's a limit to speed(lightspeed), therefore there exists a limit to temperature.

 

[Epimetreus]

Notwithstanding the upper limit imposed by c, what temperature would be required for an atom to vibrate so rapidly its constituent sub-particles were no longer able to remain bonded?

 

[MetalStorm]

As the particles approach the speed of light and special relitivity kicks in and the particles gain mass, I think the maximum temperature would be at the point where the particle turns in to a black hole.

In terms of molecules or atoms, their maximum temperature would be much lower as they heat up and approach very high speeds they would break down. As someone mentioned the amount of energy an atom has is dependant on mass, I would have thought beyond a certain threashold the atom it's self would destabilise and break in to it's constituent parts, or posibly emit radiation in the process. Then the above would follow.

Particles actually leak energy in the form of gamma radiation when accelerated to very high velocites - that is the reason why super colliders can only attain a certain velocity - the energy put in to accelerating the particles is ballanced with the energy being emmitted by the particles in the form of gamma radiation.

 

[Gibsons]

Originally posted by: Epimetreus
Notwithstanding the upper limit imposed by c, what temperature would be required for an atom to vibrate so rapidly its constituent sub-particles were no longer able to remain bonded?

If you're talking about electrons and nuclei, that can be done at fairly low temperatures link. If you're talking about breaking the nucleus apart, that takes Ridiculously High Temperatures.

 

[ZeroNine8]

In theory, wouldn't the maximum temperature possible be a result of concentrating all of the energy in the universe into a point-particle? This kind of goes back to the predicted temperature of the instant after the Big Bang, I would imagine.

 

[MetalStorm]

Do you people just ignore my posts for fun?

 

[bobsmith1492]

I didn't, but it seems everyone else thinks they know everything...

 

[f95toli]

The problem with the "black hole" solution is that then you can not use the statistical definition of temperature, simply because a single (pointlike) particle does have a temperature.
I think the same is true for a system of particles that disintegrate; the statistical temperature would vary wildly but the total energy would increase.

If you on the other hand use the more "general" definition of temperature (energy/kb) you might be right.

So, for the nth time; you need to specify what definition you are using; they do NOT give the same answer.

 

[MetalStorm]

Exactly, the maximum temperature (speed) will be when the particle collapses in to a black hole, the maximum temperature can't be beyond that as far as I can see.

 

[fogus]

Originally posted by: WoodenPupa
The Sun doesn't have enough mass to attain temperatures above the 100 million K required for helium fusion, so there won't be a supernova. However, during helium fusion, it will become a red giant with a radius near that of the Earth's orbit, so the Earth/Moon system may be consumed in that event.

Actualy if the sun didn't have enough energy for helium fusion then there would be no sun, as the power of the sun comes from fusion.

There are several possibilities for the destruction of a star, the biggest ones colapse into blackholes.

Nothing can go as fast as the speed of light, and thus while the amount of energy at a piont may not be limited, the temperature will be limited. Temperature is s measure of the average kinetic energy of the particles in a sample of matter, and this kenetic energy is limited by the speed limit of the particles.

 

[fogus]

Sorry guys, I'm rather new here; I didn't see the "Pages: 1 2 Next" thing.

 

[Chaotic42]

I've only glanced through the thread, but I would say about (10^32)K. This is, to the best of my knowledge, the temperature of the big bang.

The ideas is that in order for something in our universe to be this temperature, the universe must be a singularity, and vice-versa.

I suppose in a more massive universe, the temperature at Time 0 (Just before the big bang), might be higher.

Just some "up for 29-hours" thoughts.

 

[silverpig]

It's probably whatever temperature corresponds to 10^19 GeV (Planck mass). At that point your particle would turn into a black hole and then instantly evaporate. Of course this is if we are in a 4 dimensional universe only

 

[compusaguy]

This is a very interesting question that I have wondered about as well. There does not seem to be any limitations on the temperature that objects can attain. Temperature is usually explained using gas in a container. The pressure of a gas is directly proportional to its temperature. A scientist named Boltzmann showed that the average kinetic energy of the gas molecules was directly proportional to the pressure. Therefore, the average kinetic energy of the molecules is directly related to temperature.

Average kinetic energy = 3kT/2 = (mv2)/2

k = Boltzmann's constant = 1.38x10-23J/K

T = Temperature in Kelvin

m =Mass

v = velocity (random mean velocity)

As the temperature increases, so does the average kinetic energy of the molecules increases. Since the kinetic energy increases, so does the velocity of the molecules. As molecules go faster their mass also increases. In the equations below, something to the .5 power is the square root.

m = (m0)/(1-(v2/c2)).5

(m0) = mass at rest

m = mass in motion

v = object velocity

c = velocity of light

As the molecule approaches the speed of light, its mass approaches infinity. This may not be the best wording to a mathematician. You could put all of the energy in the universe in the molecule and it would never reach the speed of light. I suppose that to find the highest possible temperature, you could calculate all of the energy in the universe and then cram it into the lightest particle possible.

[because the limit of the mass of the particle approaches infinity as its speed approaches the speed of light, its energy also approaches the limit of infinity. The maximum possible temperature therefore approaches the limit of infinity!]

 

[cquark]

Originally posted by: fogus

Originally posted by: WoodenPupa
The Sun doesn't have enough mass to attain temperatures above the 100 million K required for helium fusion, so there won't be a supernova. However, during helium fusion, it will become a red giant with a radius near that of the Earth's orbit, so the Earth/Moon system may be consumed in that event.

Actualy if the sun didn't have enough energy for helium fusion then there would be no sun, as the power of the sun comes from fusion.

The power of the Sun comes from hydrogen fusion, not helium fusion. You might be confusing the names because hydrogen fusion produces helium.

Nothing can go as fast as the speed of light, and thus while the amount of energy at a piont may not be limited, the temperature will be limited. Temperature is s measure of the average kinetic energy of the particles in a sample of matter, and this kenetic energy is limited by the speed limit of the particles.

Kinetic energy isn't limited by velocity. It approaches infinity as the velocity approaches c. You're forgetting about the factor of sqrt(1-v^2/c^2) in the denominator of the relativistic kinetic energy definition.

 

[MetalStorm]

Originally posted by: silverpig
It's probably whatever temperature corresponds to 10^19 GeV (Planck mass). At that point your particle would turn into a black hole and then instantly evaporate. Of course this is if we are in a 4 dimensional universe only

Thank you for backing up my statement.

 

[MetalStorm]

Also of note is that the sun uses the CNO cycle for fusion as well.

 

[shortylickens]

This may be a little late in the game, and I am definately not an astronomer.

Would a Quasar have a measurable temp?

 

[MetalStorm]

Originally posted by: shortylickens
Would a Quasar have a measurable temp?

Are you refering to the gamma radiation stream or the actual singularity? The temperature of the material falling in to the blackhole will be very high - as it approaches the speed of light. But I don't know what you are actually asking.

 

[DrPizza]

Originally posted by: MetalStorm
Also of note is that the sun uses the CNO cycle for fusion as well.

And, I thought that was more important...
or at least, wasn't a Nobel prize awarded for its explanation?

 

[Googer]

Originally posted by: cquark

Originally posted by: WoodenPupa
I know there is absolute zero for the coldest temperature. What physical laws govern the upper limits of temperature? Or is there a limit at all? The fate of the moon might depend on an accurate answer so I need info fast!

There's no upper limit. For practical high temperatures, the Sun's core is about 15 million K and a supernova starts at around 5 billion K.

If a supernova is 15,000,000° K then if the big bang happend could you Imagine the amount of heat that Golf Ball Sized Piece of matter may have contained? WOW!