Does maximum temperature exist?

[Human]

I have been wondering about the temperature rules for some time.
Since the temperature has a zero point, (0 degrees Kelvin), I often wonder if the temperature has a maximum limit, i.e. "the Hagedorn temperature".

What do you think about it? Do you think the temperature has a maximum limit?
If so, how many degrees Kelvin do you think the limit is?

 

[The Binary Monster]

The zero point is when a particle has absolutely no energy... is that correct?

So in theory, a maximum would be when a particle had the most possible energy it could have.

I don't see why there shouldn't be a maximum - perhaps with enough energy a particle would cease to be a particle and become pure energy... which would then dissapate? Would that then mean that there would be a maximum, because the temperature would simply begin to dissapate immediately at that temperature and any energy gained with instantaeously be lost through dissapation?

:: Ben ::

(I know I have some crazy ideas, and most of them will probably never even make a shred of sense. But bare with me, I want to stay creative... even if much of my creativity is in the form of bad ideas! :P )

 

[MiGUi]

Actually after infinite temperature there are the negative ones.

 

[Gza]

My take on it would be that since temperature is a measure of average kinetic energy(KE = 1/2mv^2); and since increasing the temperature obviously increases the velocity of the particles you are heating, there will be a limit for the velocity at the speed of light, thereby showing there will be a limit for the temperature.

 

[The Binary Monster]

Good point...

To reach the speed of light, a particle of any mass needs infinite energy. Saying that a particle may not reach the speed of light therefore places an upper limit on the maximum kinectic energy a particle could have and thus an upper limit on the temperature a particle may be be at. Effectively you are saying that a particle may not have infinite energy... which establishes that there must be a maximum temperature.

Is my logic correct?

:: Ben ::

 

[Ivan Seeking]

The trouble is that the mass can increase infinitely as the velocity of any particle approaches C. This would allow for an infinite increase in energy.

 

[The Binary Monster]

The trouble is that the mass can increase infinitely as the velocity of any particle approaches C. This would allow for an infinite increase in energy.

I see what you mean, but surely even if the mass increases infinitely, infinite energy will mean that the particle will travel at the speed of light, whatever the mass... and as this isn't possible, there must be a limit?

:: Ben ::

 

[Chronos]

The shortest wavelength possible is governed by the Planck length. Try plugging that into the temperature equivalent formula and see what you get [it's pretty hot].

 

[The Binary Monster]

...so do you think that the temperature equivalent of the energy of those waves also acts as the maximum temperature for particles? Are you thinking that wave/particle duality means that all matter has a temperature maximum equal to that of a wave? Or do particles have a different maximum to that of waves? What do you think?

:: Ben ::

 

[Chronos]

...so do you think that the temperature equivalent of the energy of those waves also acts as the maximum temperature for particles?

Yes. Heat is a form of electromagnetic radiation.

 

[The Binary Monster]

But isn't it also a form of kinetic energy? Or have I completely misunderstood that, somewhere?

:: Ben ::

 

[Gonzolo]

The maximum temperature I can concieve is whatever temperature the Universe was at at age Plank time : about 10E-43 seconds old. It has cooled ever since. To reach that again, you would need a Big Crunch.

 

[Chronos]

But isn't it also a form of kinetic energy? Or have I completely misunderstood that, somewhere?

Kinetic energy is what excites the atoms causing them to emit radiation [i.e., heat].

 

[kjones000]

My intuition leads me to the following:

At a certain point the kinetic energy of a collection of particles ceases to be something that can be thought of as temperature and transitions to simply being the kinetic energy of the particles. Just as it would be improper to think of the motion of galaxies moving away from us as increasing the temperature of the universe, it is improper to think of a plasma expanding in all directions as having a temperature based on the relative velocity of the particles.

IF the above is true, then the limiting factor is not how much energy you can pack into a small mass of plasma, but rather, how are you going to keep that plasma from spreading in all directions?

 

[Ivan Seeking]

The shortest wavelength possible is governed by the Planck length. Try plugging that into the temperature equivalent formula and see what you get [it's pretty hot].

This demand is still completely theoretical, isn't it?

 

[Nereid]

This demand is still completely theoretical, isn't it?

Yes.

So, what happens if you add energy to a small volume (with particles)? If the energy is EM, you get furious pair production, and the particles exit your small region tout de suite, and your small region cools down. Thus you will get an equilibrium temperature, and there will be a max (no matter how much more EM energy you pump into your test region, it won't get any hotter).

The only hotter temp you can get is, as Chronos said, the first Planck second of the universe.

 

[Metallicbeing]

The maximum temperature I can concieve is whatever temperature the Universe was at at age Plank time : about 10E-43 seconds old. It has cooled ever since. To reach that again, you would need a Big Crunch.

Very good Gonzolo. I knew someone would say it.

Edit: Sorry Chronos, They're right. You did say it first.

 

[marcus]

The shortest wavelength possible is governed by the Planck length. Try plugging that into the temperature equivalent formula and see what you get [it's pretty hot].

that gives the Planck temperature (first published by Planck in 1899)
of about 1.4 x 10³² kelvin.

Chronos answered the threadstarter's question

then gonzolo says:
"The maximum temperature I can concieve is whatever temperature the Universe was at at age Plank time : about 10E-43 seconds old. It has cooled ever since. To reach that again, you would need a Big Crunch."

yes that is the same temperature that Chronos is talking 'bout.

then Nereid confirmed Chronos reply and gave a physical argument for temp maxing out, concluding that:
"The only hotter temp you can get is, as Chronos said, the first Planck second of the universe."

finally Metallicbeing says Ah at last someone, gonzolo, has answered the question.

-----------------
if anything is missing it is a link to the National Institute website (NIST)
where they actually give this temperature, expressed in kelvin, and where they give a formula for it in terms of fundamental constants G, hbar, c, k
which agrees with what Chronos said (the temp corresp to Planck wavelength light)

so let me get the link to NIST
http://physics.nist.gov/cgi-bin/cuu/Value?plktmp|search_for=universal_in!

if you click on the symbol T_P for Planck temp
you will get the formula
(thats how the NIST constants site generally works)
and otherwise they just give you the most accurately known value for it.

here's the main URL
http://physics.nist.gov/cuu/Constants/

 

[sol2]

Thanks all, I enjoyed the exchange as it affirms the things I have been saying all along.

 

[The Binary Monster]

Surely all the ideas here based on the Planck length and/or Planck time are heavily theoretical?

And Chronos, thanks for correcting me and helping me understand. I know it may seem basic to you but I'm only just getting into this...

:: Ben ::

 

[marcus]

Surely all the ideas here based on the Planck length and/or Planck time are heavily theoretical?

I tried to think how to answer. Probably there's an easy obvious answer, like Yes, but that didnt seem quite right.

personally I don't think I would base the argument on Planck time and Planck length----the Planck temperature is pretty basic

the Planck speed is c, the speed of light
the other quantities can also be pretty basic in their own categories.
the Planck speed c is a basic speed
the Planck temperature T_P is a basic temp

----------
I guess it is like this, Monster, when you first go to college you take a Freshman physics course and in that course you meet G, c, hbar, and k.

k is the Boltzmann constant, as in PV = nkT, or any of the other kT formulas.

and the professor's strategy will be to make you do problem after problem using these constants to get the answer. over and over.
use G, use c, use hbar, use k, use G, use c, use ...etc.

after a while it dawns on you, the Freshman, that these are fundamental proportions built into the fabric of nature. they are the keys that unlock the doors. they are the ratios in the laws of nature.


much much later, someone you meet casually on a skiing trip says hey
did you know that if you combine G, c, hbar, and k in the only way that you can which makes a temperature then you get a temperature called Planck temperature which is sort of the hottest things can get?

and you say, cool that reminds me of the speed of light which is sort of the fastest things can get.


you say this is "heavily" theoretical?
I don't know as I would say quite that, it is light and deep at the same time.
and tantalizingly ambiguous too. but the feel is not exactly heavy

 

[The Binary Monster]

Thanks for the explanation/correction... As of yet I haven't even become a freshman yet - not till next year. So you see I wouldn't have reached that yet - only through a little of my own reading.

But still, I enjoyed the post. It's interesting, and I guess it's taught me a little more about Planck quantities. :)

 

[phenylalanine]

Surely the theoretical maximum temp. is the speed of light - 0.1 reccuring?

 

[Nereid]

Surely the theoretical maximum temp. is the speed of light - 0.1 reccuring?

Why?

And (belated) Welcome to Physics Forums phenylalanine!

 

[phenylalanine]

What I meant was that the maximum temp. that could be acheived is when the mean velocity of the particles is c - 0.1 as that is as fast as the particles could move without actually acheiving c.

 

[Nereid]

What I meant was that the maximum temp. that could be acheived is when the mean velocity of the particles is c - 0.1 as that is as fast as the particles could move without actually acheiving c.

I guess I'm still a bit puzzled by the '- 0.1' ... do you mean ~30,000 km/sec?

Let's consider what a really, really hot 'gas' would be like; one comprised of ... well, what? Certainly won't be atoms, because they would have sufficient relative KE to ionise each other in almost every collision. What about protons and electrons then (i.e. ionised hydrogen)? Look at just the protons; if they have speeds - relative to each other - close to c, then every collision will be like what happens in a modern particle collider ... production of lots and lots of new particles (and gammas). In other words, collisions will be highly inelastic, and any resulting protons will have considerably less relative speed than near c (not to mention, how do you heat the gas up so hot to begin with

How would you contain such a hot proton-electron plasma? Certainly not with solid walls! Probably not with cleverly designed electrical and magnetic fields. And any gravitational confinement will very quickly result in cooling (you can't keep the gammas and neutrinos - among other collision products - in a gravity well).

Except of course if you have enough mass, in a sufficiently small volume ... then all the energy of the collision products won't escape, but will go into expanding spacetime itself ... hmm, remind you of the Big Bang?

 

[Chronos]

Very subtle, Nereid.

 

[Erienion]

What I meant was that the maximum temp. that could be acheived is when the mean velocity of the particles is c - 0.1 as that is as fast as the particles could move without actually acheiving c.

I think you mean that if you take the limit at v -> c you get the maximun kinetic energy of the particle and therefore the maximum temperature.

 

[marlon]

The maximum temperature in Kelivin is infinity. Above infinity the Kelvin-temperatures become NEGATIVE !

These negative temperatures, really have to be seen as an extension of the positive infinity temperature. They are no science fiction and already proven many times in experiments.

Suppose we have a system of N dipoles with spin 1/2 , placed into some extern magnetic field. The energy of this isolated system can be calculated via 1/T = (dS/dE) with S the entropy. The energy will be E = -NmBtanh(mB/kT) , where B is the magnetic field and m is the dipole-moment.

A necessary condition is that the system needs to be in an intern state of thermodynamic equilibrium for temperature to have a significance.

Secondly : there has to be a maximum allowed value for the energy of the system. This is the case of N dipoles where the max energy is E=NmB.

Now, an infinite amount of energy can make this energy maximal. More specifically this energy is maximal when the entropy is maximal or when the chaos in the system is maximal. Suppose that we have 3 dipoles and 3 possible spinvalues. The entropy is maximal when the 3 dipoles are spread out over the 3 levels, so that dipole 1 is on the bottom spin level, dipole 2 in the middle level, and dipole 3 on the top-level.

A further increase in energy makes the 3 dipoles move towards the top spin-levels. For example : 2 dipoles at the top level and one in the middle, or all three dipoles at the top level. In this situation, the entropy decreases (less chaos) and the temperature gets negative.

Practically , in order to acquire such a system : it is fundamental that the spin-system is ISOLATED, so it may not couple to "temperature"-degrees of freedom. The reasom for this is that you need to have a maximum value for the system at finite temperature. if there is such a coupling then all the energy from the heating will be absorbed by the lattice-atoms or so that will acquire an increased kinetic energy.

One has to make sure that the spin-lattice-relaxation-time is of order 1 to 10 minutes, so that the spin system seems isolated from the surrounding lattice. An example is Lithium in a LiF-lattice

regards
marlon

 

[Erienion]

The maximum temperature in Kelivin is infinity. Above infinity the Kelvin-temperatures become NEGATIVE !

These negative temperatures, really have to be seen as an extension of the positive infinity temperature. They are no science fiction and already proven many times in experiments.


regards
marlon

Can you give an example of an experiment where a temperature above infinity has been achieved !?

 

[xepma]

Can you give an example of an experiment where a temperature above infinity has been achieved !?

He did: a system of a two-state paramagnet placed in an external magnetic field.

The confusion arises because tempature is often associated with the (average) kinetic energy of the molecules/atoms. But that's not always necessarily true. In the example given, the energy of the system is due to the magnetic field which forces the dipoles into one of two quantized energy states (aligned with the magnetic field, or aligned opposite to the field).

Because the maximum energy of the system is limited (which is in theory, I think, not the case with a gas) the maximum entropy of the system doesn't correspond with the maximum energy. The maximum energy of this particular system is when all the dipoles are aligned opposite to the magnetic field. The maximum entropy however is the point where the distribution is 50/50 (50% of the dipoles are alignede opposite, 50% not).

What this means, is that when the entropy is at max and you add a little energy to the system, the entropy will decrease, i.e. \frac{dS}{dE} is smaller than zero. But since tempature is defined by \frac{1}{T}=\frac{dS}{dE}, this will mean the tempature will be negative.

Remember that you can't "add tempature" to a system. You can only add or substract energy. And doing so will usually change the tempature. But because of the way tempature is defined, it's possible to get a system with an infinite or negative tempature.

 

[Erienion]

Thanks xepma, i think i understand what was meant a bit better now. :)

 

[ArmoSkater87]

Temperature is the measure of the kinetic energy of the particles, and relativistic KE is...
KE = m_0c^2(\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}-1)
as v -> c, KE -> infinity

 

[xepma]

Thanks xepma, i think i understand what was meant a bit better now. :)

Was my first post

Temperature is the measure of the kinetic energy of the particles, and relativistic KE is...
KE = m_0c^2(\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}-1)
as v -> c, KE -> infinity

Again, that is not always the case.

 

[Tempus Fugit]

First post. Generally I'm a complete doofus at math and physics (mostly because of teachers and the educational path I chose), but it still interests me, and I've asked several people about theoretical maximum temperature, but nobody has given me a good answer, seems there are answers to be found here.

Try to bear with me, I haven't looked at a physics book since the late nineties.

Remember that you can't "add tempature" to a system. You can only add or substract energy. And doing so will usually change the tempature. But because of the way tempature is defined, it's possible to get a system with an infinite or negative tempature.

Right, but if we define maximum temperature as something absolute (that does not involve average kinetic energy of particles - but more in terms of «how much kinetic energy can this matter contain»), it would make it possible to concieve a theoretical maximum value?

 

[genneth]

All those who have written that temperature is the K.E. of particles... Stop it! It's simply wrong! Temperature is only to do with K.E. in ideal gases and related situation -- but temperature itself is much broader. Like a couple of posters have said, beyond +inf there are the negative temperatures. So the highest temperature possible is -0. The more "natural" scale for temperature is actually 1/T, so low temperatures correspond to a large, positive 1/T, and high temperatures correspond to a large, negative 1/T.

 

[Tempus Fugit]

but temperature itself is much broader.

Is it possible to elaborate with extended use of words (over formulae).

 

[genneth]

See here: http://reddit.com/info/1h96q/comments/c1ha0f

It's something I wrote a while back, in response to a similar misunderstanding. It seems to be a prevalent mistake -- I bet some oft used textbook has it.

 

[rbj]

All those who have written that temperature is the K.E. of particles... Stop it! It's simply wrong!

i would say that this statement is not entirely correct either. temperature and energy of particles are certainly related, increase temperature and the mean energy per particle increases, but because of issues like degrees of freedom and what's in the solid state, the energy per particle and Kelvin are not always proportional with the same constant of proportionality. but it's an increasing function.

Temperature is only to do with K.E. in ideal gases and related situation -- but temperature itself is much broader. Like a couple of posters have said, beyond +inf there are the negative temperatures.

there aren't negative temperatures. not relative to absolute zero. it's likely that the maximum temperature ever possible in our universe is in the order of the Planck temp, and it happened only very close to the time of the Big Bang. if there is a Big Crunch, we might see it again.

So the highest temperature possible is -0. The more "natural" scale for temperature is actually 1/T, so low temperatures correspond to a large, positive 1/T, and high temperatures correspond to a large, negative 1/T.

dunno what this 1/T is all about. temp relative to the Planck temp (or the Planck temp adjusted by a factor of \sqrt{4 \pi}) is about as natural of a scale for temperature as you can get since the Boltzmann constant is really just a manifestation of the anthropometric units that we humans sort of accidently decided to use.

after a while it dawns on you, the Freshman, that these are fundamental proportions built into the fabric of nature. they are the keys that unlock the doors. they are the ratios in the laws of nature.

actually, marcus, i agree with everything you said but am not sure that the Freshman here is correct when it dawns on him that the Boltzmann constant, k (or c or G for that matter) "are fundamental proportions built into the fabric of nature." they are proportions that relate things we see in nature to the arbitrary units we have historically been using. they are more of a human construct than a fundamental proportion of nature (unlike the dimesionless constants such as \alpha, which truly are fundamental proportions that exist in the fabric of nature).

measure everything in Planck units and c, G, \hbar, 1/(4 \pi \epsilon_0) and Boltzmann's k, just simply go away. then we can start asking "why are our tempertures so low?" or "speeds so slow?" or "sizes so big?" or "why are particle charges so not big (or small)?"

 

[genneth]

there aren't negative temperatures. not relative to absolute zero. it's likely that the maximum temperature ever possible in our universe is in the order of the Planck temp, and it happened only very close to the time of the Big Bang. if there is a Big Crunch, we might see it again.

dunno what this 1/T is all about. temp relative to the Planck temp (or the Planck temp adjusted by a factor of \sqrt{4 \pi}) is about as natural of a scale for temperature as you can get since the Boltzmann constant is really just a manifestation of the anthropometric units that we humans sort of accidently decided to use.

Except there are systems with negative temperature -- they are created all the time inside lasers and other population inverted systems. The definition is simple, direct from the laws of thermodynamics: if any positive temperature system were to equilibrate with the negative temperature one, the net flow of energy is towards the positive temperature system, raising it further. Again, I reiterate -- temperature is not energy -- it's defined as: \frac{1}{T} = \frac{\partial S}{\partial E} (with some constants of proportionality) for a microcanonical system, and extended to cover all systems via the rigours of statistical mechanics. Temperature applies to a system -- it's a macroscopic property; energy of the particles inside a system is incidental. The possibility of negative temperature is simply that the number of configurations starts decreasing due to increasing energy. 1/T is called \beta, and is far more commonly used in statistical mechanics and condensed matter circles.

Physics doesn't just end at particles and quantum mechanics.

 

[Astronuc]

A discussion of temperature

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/temper.html

A convenient operational definition of temperature is that it is a measure of the average translational kinetic energy associated with the disordered microscopic motion of atoms and molecules.

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/temper2.html

The concept of temperature is complicated by internal degrees of freedom like molecular rotation and vibration and by the existence of internal interactions in solid materials which can include collective modes.

. . . .

Temperature is expressed as the inverse of the rate of change of entropy with internal energy, with volume V and number of particles N held constant. This is certainly not as intuitive as molecular kinetic energy, but in thermodynamic applications it is more reliable and more general.

Also, see - http://en.wikipedia.org/wiki/Temperature

The temperature of a system is defined as simply the average energy of microscopic motions of a single particle in the system per degree of freedom. For a solid, these microscopic motions are principally the vibrations of the constituent atoms about their sites in the solid. For an ideal monatomic gas, the microscopic motions are the translational motions of the constituent gas particles. For multiatomic gas vibrational and rotational motion should be included too.

I suppose one can think of an equivalent temperature based on a particle's velocity or kinetic energy.

Apparently some cosmic radiation has achieved energies on the order of 10²⁰ eV.