Why is average kinetic energy 3/2 RT for ideal gases?

[vijayram]

I have read Average translation kinetic energy is 1/2RT per degree of freedom and Average translation kinetic energy for an ideal gases is 3/2RT.How? Does it imply f=3 for all ideal gases?

 

[mfb]

There are three dimensions in our universe, so translation always has 3 degrees of freedom. Even if you constrain motion in one dimension: if the constraint is not too strong (or if you ignore quantum effects), it will have motion in that dimension.

 

[Cutter Ketch]

Yes, exactly. The ideal gas molecule has no structure, so it can't rotate or vibrate. All it can do it move in three dimensions. f=3. Atomic gasses (at least the ones that don't make dimers) approximate this case and differ from the ideal primarily only in that they take up space reducing the available volume. More complicated molecules can vibrate and rotate and each independent motion is another degree of freedom where energy can be stored. The gas has more capacity to store energy as a function of temperature.

 

[Cutter Ketch]

well this is weird. I keep trying to quote mfb's comment above about an ideal gas with f>3, and the app keeps quoting an entirely different post, one that doesn't even show up in the thread (on my browser anyway)

In any case, regarding the comment that an ideal gas can have degrees of freedom >3:

No volume, only perfectly elastic collisions, and no internal degrees of freedom is the definition of an ideal gas. I wouldn't be surprised if someone somewhere postulated and "an ideal diatomic gas" or similar, but in almost all contexts the meaning of "ideal gas" is extremely well established.

 

[Cutter Ketch]

Yes, exactly. The ideal gas molecule has no structure, so it can't rotate or vibrate. All it can do it move in three dimensions. f=3. Atomic gasses (at least the ones that don't make dimers) approximate this case and differ from the ideal primarily only in that they take up space reducing the available volume. More complicated molecules can vibrate and rotate and each independent motion is another degree of freedom where energy can be stored. The gas has more capacity to store energy as a function of temperature.

I know, replying to myself is goofy ...

I just wanted to correct myself in that the atoms in an atomic gasses also have to have negligible chemical interactions in order to be close to ideal. That means noble gasses for the most part.

 

[mfb]

I misunderstood the first post, then edited my post. I guess you opened the thread when the old text was there, but if you quote it the forum loads the current text. Ignore the old text.

I just wanted to correct myself

You can edit your posts.

 

[Cutter Ketch]

You can edit your posts.

Oh, that would be useful. I don't see a way to do it here (accessing by browser) do I need the app?

 

[mfb]

I don't know if it is possible via the app, it is certainly possible via the browser (bottom left of a post), but there is some time limit to it.