Degrees of freedom of a water molecule

[LCSphysicist]

Homework Statement

List all the degrees of freedom, or as many as you can, for a
molecule of water vapor. (Think carefully about the various ways in which the
molecule can vibrate.)

Relevant Equations

There is no.

Well, first of all is really good to say that we don't can appeal to quantum mechanics...
So, i can see:
Three degree of freedoms in translation on a space xyz +3 degree
Three normal modes of vibration, but each normal mode has with it a potential and vibrational kinetic energy, so +6 degree

The problem is rotation, how can i know what directions can i molecule rotation?

 

[haruspex]

but each normal mode has with it a potential and vibrational kinetic energy

Yes, but the two forms of energy do not constitute separate modes.

Wrt rotation, I believe water molecules are sufficiently nonlinear to be counted as having three rotational degrees of freedom.

 

[ehild]

Yes, but the two forms of energy do not constitute separate modes.

Wrt rotation, I believe water molecules are sufficiently nonlinear to be counted as having three rotational degrees of freedom.

The H-O bonds enclose 105 degrees, so the molecule is definitely nonlinear. The rotational modes are around three axes, two of them in the molecular plane and one perpendicular to it.

http://www.xaktly.com/Water.html

 

[vela]

Yes, but the two forms of energy do not constitute separate modes.

It does if you're counting degrees of freedom for the equipartition theorem.

 

[LCSphysicist]

Yes, but the two forms of energy do not constitute separate modes.

Wrt rotation, I believe water molecules are sufficiently nonlinear to be counted as having three rotational degrees of freedom.

As @vela said, i need to account the two types of energy, potential and kinect ;)

The H-O bonds enclose 105 degrees, so the molecule is definitely nonlinear. The rotational modes are around three axes, two of them in the molecular plane and one perpendicular to it.
View attachment 266777
http://www.xaktly.com/Water.html

This is a really good image, so nonlinear molecules always has three degree wrt rotation?

...

Well, with this +3 deegre, we get 12, the answer...

 

[ehild]

This is a really good image, so nonlinear molecules always has three degree wrt rotation?

yes.

 

[haruspex]

It does if you're counting degrees of freedom for the equipartition theorem.

Ah, yes - I see why that is so. Thanks.

 

[wrobel]

any free rigid body has 6 degrees of freedom

 

[haruspex]

any free rigid body has 6 degrees of freedom

Yes, but my (limited) understanding is that for the purposes of equipartition a molecule that is essential a rod is not accorded one for a spin about that axis.