# Can a single atom have a temperature?

1. Aug 20, 2013

### Nathew

I know temperature is the measure of how much atoms are moving, so can a single atom even have a temperature?
The quarks inside the protons and neutrons are moving around, so?

2. Aug 20, 2013

Staff Emeritus
Temperature is a property of a statistical ensemble of particles. It is poorly defined for a single atom.

3. Aug 20, 2013

### Baluncore

Temperature is proportional to the average kinetic energy of a population of molecules. If a single atom has velocity then it has a particular kinetic energy and therefore a non-zero absolute temperature. As a member of a population of one atom, if you know it's mass and instantaneous velocity you can calculate a theoretical temperature.

If you know why you calculated that instantaneous theoretical temperature then maybe you will know how to interpret and use the result.

4. Aug 21, 2013

### Crazymechanic

Yes but I think it's important to notice tat atoms themselves don't have temperature , it's not like you can "overheat" an atom it's just that they have velocities which translates into kinetic energy and as vanadium said kinetic energy is only useful for temperature if you have some material in which those atoms are many and upon their interactions you get a average temperature.

Just like people are categorized in groups , races , social groups because they are more than one if you would have one single guy in the whole world and noone else it would be hard to say something about him as there is nothing to compare to.

5. Aug 21, 2013

### Electric Red

Well.. the definition of temperature is:

$(\frac{\partial S}{\partial E})^{-1}=T$

Which means, the partial derivative of the entropy to the Energy, of which you should take the inverse, and that IS the temperature - per definition.
So.. Since the molecule has a certain energy because it is moving, you only need to think about what the entropy of this one molecule is.
Then you will be able to calculate the temperature, I assume.

Last edited: Aug 21, 2013
6. Aug 21, 2013

### Staff: Mentor

I don't think this is correct. Accelerating a baseball to 0.99c doesn't increase its temperature. The kinetic energy of the object is not something temperature takes into account.

7. Aug 21, 2013

### lightarrow

In an inertial frame of reference which is co-moving with the atom, the atom has velocity zero (for example the atom is in a box and the box follows its motion). So the atom's temperature would depend on the inertial frame I choose? The temperature of a gas in a box doesn't depend on the inertial frame I choose...

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lightarrow

8. Aug 21, 2013

### lightarrow

No.

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lightarrow

9. Aug 21, 2013

### Baluncore

Laser cooling of individual ions has been in the news. There has even been talk of negative absolute temperatures. That suggests a single atom can have a theoretical temperature. The problem then becomes one of interpreting what that concept of temperature actually means.

10. Aug 21, 2013

### ZapperZ

Staff Emeritus
The OP. has not explained to what extent he/she understands the concept of temperature. So lets wait until there is a response to such inquiry before we delve in to exotic aspect of this phenomenon.

Zz.

11. Aug 21, 2013

### Crazymechanic

the problem then also becomes measuring that single atoms temperature without distorting the result and now were into quantum mechanics , oh dear.

the only way to say it's temperature I assume would be to get to know it's kinetic energy at the moment and then translate that into a possible temperature via maths.

12. Aug 21, 2013

### Electric Red

But.. if the entropy is a function of the energy, you actually can calculate the temperature with that formula. Imagine the baseball you were talking about, if you'd give that an enormous velocity, ofcourse the temperature of the environment will change.

13. Aug 21, 2013

### Staff: Mentor

But not of the baseball...

A subtlety here is the distinction between the atom/object ITSELF, and the atom/object itself + the environment.

14. Aug 21, 2013

### Crazymechanic

if the environment is in the same reference frame as the baseball than there is no temperature difference.

15. Aug 21, 2013

### Electric Red

My point exactly, but... let's not go to much into detail about the fraction of the speed of light. A lot of other concepts come in place, and those are not relevant to his question.

I have to say, that my last formula isn't valid, because we are not talking about a equilibrium. And I'm getting more and more convinced about the fact that it is almost impossible to talk about the temperature of a single atom.. but think about this:

the theory of the big bang states that in the beginning of the universe, the universe was made of vibrating quarks, and they were vibrating at such speed, it wasn't possible to create nucleons, because it was too hot.

So, what now?

16. Aug 21, 2013

### ZapperZ

Staff Emeritus
If this thread is going to be derailed into the physics of the Big Bang and nucleosynthesis, it will be locked.

Zz.

17. Aug 21, 2013

### Baluncore

The answer to the OP cannot be an unconditional definitive “NO” because there are peer reviewed Physicists reporting the theoretical temperature of individual atoms.

But then if the answer is “YES” there must be more precise definitions of the particular concept of temperature that is being considered in each case.

If we restrict our definition of the term “temperature” to a subset of those used by others, then our answer could be “NO”, “MAYBE” or “YES”. It is all a question of definition.

18. Aug 21, 2013

### Staff: Mentor

Please provide a reference for this.

19. Aug 21, 2013

### jfizzix

If the entropy of a single atom is well defined (and it is),
and the energy of a single atom is well defined (and it is),
then its temperature is well defined.

The entropy of an atom is just a measure of the number of possible states it could have for constant energy. A single particle in a 3D box can have many different states for a given total energy, and this number goes down as the energy goes down until you reach the unique ground state, a state of minimum energy and zero entropy.

The energy of an atom is well defined to the extent that it can be calculated and measured. There are limits imposed by the uncertainty principle, but this doesn't affect what the energy levels themselves are.

Knowing this, it is perfectly legitimate to speak of the temperature of a single atom as a measure of how quickly the energy changes in response to a change in entropy.

Hope this helps:)

20. Aug 21, 2013

### Staff: Mentor

Can you elaborate on this?