Temperature as a measure of the kinetic energy of molecules

[Karol]

Homework Statement

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?

Homework Equations

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

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

 

[Bystander]

Homework Statement

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?

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

2. Homework Equations

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

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

And, is this your answer?

 

[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

 

[haruspex]

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

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

 

[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.

 

[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.

 

[haruspex]

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.

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

 

[Karol]

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

 

[haruspex]

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

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

 

[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?

 

[haruspex]

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.

How do you think temperature is defined?

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?

It probably depends on what you mean by direct measurement. E.g. you could infer it from Doppler shifts in spectra.

 

[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...

 

[haruspex]

I read from the site hyperphysics and they define temperature as related to kinetic energy.

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.

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...

That would be very challenging even now. You cannot see the molecules, so how direct can that be?

 

[Karol]

Thanks