# Vibrational energy at low temperatures

1. Mar 4, 2013

### Cisneros778

1. The problem statement, all variables and given/known data
I would like to get a better picture of the degree of freedom of vibration.

Predicting the value of heat capacity for water vapor turns out to be 6R, but the experimental value is 3.038R
In my notes it then says, "contributions to the heat capacity can be considered classically only if En~hv<< kT...... Energy levels with En>=kT contribute little, if at all, to the heat capacity." So only at very high temperatures can we consider vibrations as degrees of freedom. At lower temperatures, the vibrational degrees of freedom are omitted.

2. Relevant equations

3 atoms,
Translational = 3 x 1/2kT = 3/2kT
Rotational = 3 x 1/2kT= 3/2kT
Vibrational = 0
No potential relation, ideal gas scenario. So the sum off energies equal 3kT=3R

3. The attempt at a solution

I'm considering now, to simplify my analysis, two bonded atoms. When given heat, they will not be excited until at very high temperatures... But I think they are still interacting amongst each other since they are bonded. So is it because they are at an equilibrium distance that they do not feel each other's force and do not vibrate as much?
I hope I am not being too confusing.

2. Mar 5, 2013

### clamtrox

No, but the energy levels of the system are quantized! So if, say, the difference between two energy levels is E ~*kT, then the atoms cannot really "vibrate" in a classical sense: they can just transition to the first excited state and back again. If you want to consider classical vibration, then you must have kT >> E, so that there is enough energy to excite the system high enough that quantum effects are no longer important.