# Temperature below 0 K?

1. Jul 23, 2006

### whoelsebutme

Can we obtain temperatures below absolute zero i.e. 0 Kelvin?

2. Jul 23, 2006

### jbusc

no, because absolute zero is the lowest possible temperature.

In simple, rough terms, temperature is some measure of the motion of atoms and molecules at the small scale. Therefore, asking "can we go to temperatures below absolute zero" is like asking "can we go slower than 0 miles per hour".

3. Jul 23, 2006

### HallsofIvy

In fact, because of quantum uncertainty, if we know a molecule is in the laboratory, we can't be certain that it's speed is 0 so can't even get 0 degrees K.

4. Jul 23, 2006

### jbusc

I think absolute zero is also impossible to achieve in classical thermodynamics too, by 2nd and 3rd laws. So it's "double" prohibited. :)

5. Jul 23, 2006

### deepakalways

It is practically impossible to obtain even 0 K , so there is no question of reaching something below it.

6. Jul 23, 2006

### ZapperZ

Staff Emeritus
I suppose it's time to step in here and point out something.

If you look at how "temperature" is defined within statistical mechanics, you'll see that, using the partition function methodology, there CAN be situations where you can get a negative absolute temperature. While this is not a system under equilibrium, you can still get such temperature based on an inverse population of states.

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/neg_temperature.html

If you have taken a class in Thermodynamics, and have used texts such as the one by Reif, you would have seen a similar discussion (maybe even a homework problem).

Zz.

7. Jul 23, 2006

### Gelsamel Epsilon

I think there is a difference between 0K and Absolute Zero, 0K describes absolute zero in terms we can understand, temperature. Which is defined as the average kinetic energy of the substance. Since kinetic energy isn't a vector it can't be logically negative. I say no - you can't get below 0K or rather into negative values of K. But maybe you can get below Absolute Zero. (But can that logically be denoted in terms of K and temperature?)

8. Jul 23, 2006

First Question. This negative temperature concept appears to be limited to "spin" degree of freedom systems--is this correct ? Second Question. Since a spin system with negative absolue temperature should be hotter than a positive temperature system, would you predict that the outcome of linking two quantum spin engines ( one with negative absolute temperature, and the second with positive) would be an engine with efficiency > 1 ?

Last edited by a moderator: Jul 23, 2006
9. Jul 23, 2006

### Danger

If you mean 'more energy out than in, then the answer is a definite 'no'. That would be a perpetual motion machine. :yuck:

10. Jul 23, 2006

### -Job-

Is the maximum temperature then when the particles are moving at 99.(9)% of the speed of light? How many Ks is that?

11. Jul 24, 2006

### lalbatros

-Job-,

There is no upper bound in energy and therefore no upper bound on temperature.

If you get 100 times closer to the speed of light, you get 10 times more energy.
So v = 0.9999 c means 10 times more energy than for v = 0.99 c .
There is an upper bound on velocity but not on energy. Infinite room for high energy physicists!
Look at the relation for energy of a particle as a function of velocity in relativity.

In particle physics, the usual unit of energy is the electron-volt.

1 eV = 1.6022 E-19 J​

Temperature can be converted to energies via the Bolzmann constant.

kB = 1.38 E-23 J/K​

Therefore, the link between energies and temperature is:

1 eV = 11605 K​

Such units are used where high temperature prevail, like in plasma physics or solar physics. From this point of view, the chromosphere of the sun is rather cold: about half an eV ! In tokamaks, like Jet, the temperatures are typically in the range of 10 keV = 10000 eV, like in deeper layers of the sun.

The rest mass of an electron is mcÂ˛ = 511 keV. This number is used very often as it plays a frequent role in nuclear and particle physics. When an electron reaches a velocity of 0.99 the speed of light, its total energy is 5110 keV and its kinetic energy is 5110-511 = 4599 keV.

A typical tokamak plasma temperatures reach 10 keV equivalent to 116 050 000 K.
The electrons have -in the average- a kinetic energy of 3/2 10 = 15 keV (see kinetic theory of gases).
You can calculate that they reach an average velocity of 16.9% of the speed of light.

Michel

Last edited: Jul 24, 2006
12. Jul 24, 2006

### ZapperZ

Staff Emeritus
It doesn't have to be exclusively only for spin systems. It just happens that this would be the easiest system to illustrate.

Sure! Under certain non-equilibrium situation, you can violate the 2nd law. There's nothing here that contradicts thermodynamics since this all came out of thermodynamics predictions. However, such a system doesn't last very long, and if you calculate the Helmholtz free energy out of such a system, you'll be hard pressed to use it to do any work (a fact that most quacks tend to overlook).

Zz.

Last edited: Jul 24, 2006
13. Jul 24, 2006

### J77

Last edited by a moderator: Apr 22, 2017
14. Jul 24, 2006

### Danger

There's only so much energy in the universe, though. Doesn't that also imply that there's a limit to how much you can channel into heating something?

15. Jul 24, 2006

### lalbatros

Well, we should then talk about when, just near the big-bang, or maybe before? And about energy conservation in the early universe, and maybe the Noether theorem, and what else?

I would prefer not to go so far and stay practical.

Personally I have no experience with the universe, and I find it already difficult to talk about how mopeds work. Lets keep whoelsebutme on tracks!

Michel

16. Jul 24, 2006

### Danger

Works for me.

17. Jul 29, 2006

### Clausius2

Talking in response about the efficiency of an engine greater than one, in my opinion even if this may be allowed by the physics law, from an engineering point of view seems there is no practical application. I heard that those substances able to reach negative temperatures by means of an inversion of population are not common substances, from Zemanski's books I scarcely remember that it was done with crystal of something, but not with air or water or fuel, and by means of application of magnetic fields. I'm not an expert on that stuff, but clearly seems very difficult to me to apply a negative temperature business in a heat engine, and I'm pretty sure that the original aim of classical thermodynamics was to overcome the difficulties that in middle of the 19th century engineers had when designing those noisy steam engines and how could they increase the efficiency of the machines. Those machines, and current machines too, work with classical substances, which by the way behave very well for transporting fluid-thermal energy.

18. Jul 30, 2006

### lalbatros

Have a look at wiki:

Michel

19. Jul 30, 2006

### vanesch

Staff Emeritus
I don't know if they only occur with spin systems, but these are of course obvious examples. You only need a system where the number of microstates diminishes when the total energy increases. Usually, this is the opposite: the more energy you give to a system, the more different microstates can correspond to it. And the (inverse) of the derivative of the (logarithm of) the number of states wrt the energy is the temperature. So if the number of allowed microstates diminishes with energy, then this derivative is negative, hence the negative temperature.

Difficult to say at first sight. First of all, I'm not sure that there really exist systems with negative temperature once one takes into account all their degrees of freedom. Maybe an expert can answer this (I'm not an expert). But I don't expect anything spectacular when there's interaction between such a system and a "normal, positive-temp" system. After all, that's what happens when one includes, say, the translational degrees of freedom (normal system) to a spin-system (negative-temp): you will just get almost total decay of the "excited spin states" and a corresponding increase in temperature of the normal system.

The difficulty with the normal application of "efficiency" is that we get a strange relationship between heat and temperature in the case of negative temperatures: while we still have dQn x Tn = dSn,
dSn increases upon contact by GIVING OFF heat (dQn < 0) because Tn is negative, and it is maybe possible to extract even some heat from the normal system dQp x Tp = dSp, which can now decrease its entropy with dSn (so that, in an adiabatic process, dS = dSp + dSn), so that dQp can be negative too.
The total work done is then dW = -Qp - dQn.
So it seems (I'm finding this out while I type it), that a negative-temperature system can help you extract heat from a normal system and do work with it.
This is probably the "over-unity" efficiency of the heat engine in contact with a negative-temperature heat reservoir, while respecting the overall second law.

20. Aug 2, 2006

### lalbatros

heat from cold to warm ?

Let's put two systems in thermal contact.
One (A) with a positive temperature.
A second (B) with a negative temperature.

How can we predict the heat flux?

I could imagine heat going from B to A simply because the number of microstates of A+B could be higher so. Indeed, less energy in B would mean more microstates for B and eventually also for A+B.

Is it possible that heat goes from cold (B) to hot (A) ?
Is it compatible with the second law ?

Michel

Last edited: Aug 2, 2006