# (Thermal) Vibrational degrees of freedom

• argon
In summary, the conversation discusses the number of vibrational degrees of freedom for a molecule such as CO2. While there are 3 translational and 2 rotational degrees of freedom, there is confusion over the number of vibrational degrees of freedom. Some sources claim 4, while others claim 8. The discrepancy may be due to the different definitions of vibrational degrees of freedom for non-linear and linear molecules. Additionally, the conversation suggests looking at the problem in terms of coordinates to determine the minimum number needed to pinpoint the exact position of the CO2 molecule.
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.

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.

## What are thermal vibrational degrees of freedom?

Thermal vibrational degrees of freedom refer to the ways in which molecules can store and transfer thermal energy through their vibrations. These vibrations occur in three dimensions and can be quantified by the number of vibrational modes in a molecule.

## How do thermal vibrational degrees of freedom affect the properties of a substance?

The number of thermal vibrational degrees of freedom in a substance can affect its specific heat, thermal conductivity, and other thermodynamic properties. This is because the energy stored in these vibrations contributes to the overall internal energy of the substance.

## How are thermal vibrational degrees of freedom related to temperature?

The average kinetic energy of a molecule is directly proportional to the temperature of the substance. This means that as the temperature increases, the molecules will have more thermal energy and thus more vibrational degrees of freedom.

## What is the relationship between thermal vibrational degrees of freedom and molecular mass?

The number of thermal vibrational degrees of freedom in a molecule is inversely proportional to its mass. This means that lighter molecules will have more vibrational modes and thus more thermal energy at a given temperature compared to heavier molecules.

## How do thermal vibrational degrees of freedom differ from rotational degrees of freedom?

Thermal vibrational degrees of freedom refer to the energy stored and transferred through molecular vibrations, while rotational degrees of freedom refer to the energy stored and transferred through molecular rotations. Both types of degrees of freedom contribute to the overall internal energy of a substance, but they have different effects on its properties.

Replies
15
Views
2K
• Quantum Physics
Replies
1
Views
806
• Introductory Physics Homework Help
Replies
8
Views
4K
• Introductory Physics Homework Help
Replies
5
Views
2K
Replies
9
Views
7K
• Atomic and Condensed Matter
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
11
Views
1K
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
9
Views
10K
• Special and General Relativity
Replies
7
Views
2K