Does maximum temperature exist?

[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.