(Thermal) Vibrational degrees of freedom

[argon]

Let's say I have a molecule such as CO2, where there are three atoms and a linear structure. I understand that there are 3 translational degrees of freedom and 2 rotational degrees of freedom (since it's symmetric). However, the number of vibrational degrees of freedom (DoF) confuses me.

My professor says there are 4 DoF. A quick Google search has people claiming 4.

I think the answer is 8 though. There are 4 vibrational modes (if this is correct) for CO2, and each mode gets a DoF from kinetic energy and one from potential energy. This makes 8.

There are also some websites claiming that for a non-linear molecule, there are 3N-6 vibrational modes and for a linear molecule there are 3N-5 vibrational modes. Some websites call these vibrational degrees of freedom instead, but this terminology is important to distinguish since it changes my answer by a factor of 2. Which is correct?

Assume sufficiently high temperatures for this discussion such that no modes are frozen out.

 

[1994Bhaskar]

Look at DOF in another way... Try to find the minimum number of coordinates you need to know the exact position of CO2 molecule , there are three atoms with each having x,y coordinates. Assume that you know the distance between Carbon And oxygen atoms.