# Temperature as a measure of the kinetic energy of molecules

1. Nov 18, 2014

### Karol

1. The problem statement, all variables and given/known data
I know that temperature is a measure of the kinetic energy of gas molecules. at a given temperature different gases have the same average kinetic energy.
But in solids and liquids there is also potential energy between the close atoms/molecules. how do i know that temperature is here also a measure only of the kinetic energy? maybe it is a measure of part of the potential energy also?

2. Relevant equations
Kinetic energy of different gases at 00C in Jouls:
Hydrogen: 5.6E-21
helium: 5.6E-21
nitrogen: 5.6E-21
...

3. The attempt at a solution
Because potential energy is static, it doesn't affect the movement, so we can assume that what happens in gases is the same in metals and liquids

2. Nov 18, 2014

### Bystander

Is this the question you are being asked, or that you are asking?

3. Nov 18, 2014

### Karol

I ask if in solids and liquids also the temperature is a measure only of the kinetic energy and not of the potential energy as well.
In gases there is almost no potential energy because of the large distances between the molecules.
I tried to explain my opinion in The attempt at a solution

4. Nov 18, 2014

### haruspex

Yes, but can you fill in a bit more of the argument? Why is it movement that determines temperature? Think about how heat conducts.

5. Nov 18, 2014

### Karol

I don't know why movement determines temperature, although i (think i) know that molecules from a warm area move faster and hit other molecules near by which deliver forward this fast movement. it's called conduction.

6. Nov 18, 2014

### BiGyElLoWhAt

I think the textbook definition of temperature is solely kinetic energy, but there are times when potential energy can be called a "temperature". This is not the same temperature, though. One example where I've seen it used this way is in a setup for optical tweezers. You shine a laser on a molecule, and it moves to the center of the beam (or wherever the high intensity point is). I think the reason this gets called a temperature is because the molecule moves along the potential gradient (which does work), thus actually increasing the kinetic energy of the molecule. The "temperature" function here is essentially the potetential function. Whether or not this is a good way to look at it, I don't know, but it definitely helped to understand how the setup was working.

7. Nov 18, 2014

### haruspex

Yes, but also what happens to the fast moving molecule when it hits slower ones?

8. Nov 18, 2014

### Karol

Oh, the fast ones, i guess, slow down, so the body cools

9. Nov 19, 2014

### haruspex

Certainly the KE is shared out - until what point? Does that sound like what temperature does?

10. Nov 19, 2014

### Karol

Until the whole lump has the same KE, and temperature also shares out until all parts have the same temp.
This shows they are direct proportionally related, but it's not yet a proof.
But i have another question. i heard that the kinetic theory of gases relates pressure and volume to average kinetic energy, but has anyone actually measured the velocities of molecules in gas? how do you do that?

11. Nov 19, 2014

### haruspex

How do you think temperature is defined?
It probably depends on what you mean by direct measurement. E.g. you could infer it from Doppler shifts in spectra.

12. Nov 19, 2014

### Karol

I read from the site hyperphysics and they define temperature as related to kinetic energy.
By direct measurement of velocity of molecules i mean a simpler experiment than a Doppler shift in spectra, a more classical one with less sophisticated equipment and preferably one that was made long ago...

13. Nov 20, 2014

### haruspex

That makes it easy. But temperature was discussed by physicists before the KE connection was known. At that time, it would have been based on the observations that (1) the hotness of a body can be measured in a consistent way by expansion of a liquid, and (2) that objects which measure differently on that scale, placed adjacently, come to be equal. If you define it in those terms, and you have a theory of atoms and molecules as mobile particles, then transfer of KE is a persuasive model.
That would be very challenging even now. You cannot see the molecules, so how direct can that be?

14. Nov 20, 2014

Thanks