Degrees of freedom of diatomic gas

[throneoo]

So I'm trying to figure out the average energy of diatomic gas molecules via the equipartition theorem at high temperature (such that it's translational , rotational and vibrational modes are activated)

and to do that I need to know the degree of freedom.

some websites claim it would be 6 , 3d translational motion , 2 rotational axis and 1 vibration along the bond between the atoms.

however, some sources state that they are actually one more: the motion/velocity along the bond.

so I'm now a bit confused which version is correct. I'm inclined towards the latter as I think only by including that d.o.f. can I fully describe the configuration of the gas molecules. I would think of the original 3 translational d.o.f. as the motion of the centre of mass only, which is why we need one more to describe the motion along the bond.

 

[Orodruin]

A system of two particles can never have more than six degrees of freedom! You can always describe the system using three spatial coordinates for each particle. The only question is whether or not there are additional constraints which lower the number of degrees of freedom.

 

[Andrew Mason]

So I'm trying to figure out the average energy of diatomic gas molecules via the equipartition theorem at high temperature (such that it's translational , rotational and vibrational modes are activated)

and to do that I need to know the degree of freedom.

some websites claim it would be 6 , 3d translational motion , 2 rotational axis and 1 vibration along the bond between the atoms.

however, some sources state that they are actually one more: the motion/velocity along the bond.

so I'm now a bit confused which version is correct. I'm inclined towards the latter as I think only by including that d.o.f. can I fully describe the configuration of the gas molecules. I would think of the original 3 translational d.o.f. as the motion of the centre of mass only, which is why we need one more to describe the motion along the bond.

How would motion/velocity along the bond differ from translational motion or vibration? The rotation about the axis along the bond does not count as there is no significant moment of inertia (the mass being concentrated in the nuclei which have negligible dimension compared to distance between nuclei).

AM

 

[DrDu]

The point is that the vibration counts as two degrees of freedom as far as the equipartition theorem is concerned, in the sense that the energy stored in the vibration is kT and not kT/2 as for the rotational and vibrational degrees of freedom. E.g. for a translation, the energy depends quadratically on momentum p. However in a vibration, the energy depends quadratically on both p and x, hence the doubling.

 

[Andrew Mason]

The point is that the vibration counts as two degrees of freedom as far as the equipartition theorem is concerned, in the sense that the energy stored in the vibration is kT and not kT/2 as for the rotational and vibrational degrees of freedom. E.g. for a translation, the energy depends quadratically on momentum p. However in a vibration, the energy depends quadratically on both p and x, hence the doubling.

Ok. I see what you are getting at. Whether a diatomic molecule has 6 or 7 degrees of freedom depends on whether you consider the vibrational mode to have one or two degrees of freedom. Vibration is the only mode that has potential energy associated with it. I would say it has one degree of freedom but two types of energy associated with vibration for purposes of the equipartition theorem (i.e. N=7 for purposes of the equipartion theorem when all modes are activated).

AM

 

[Orodruin]

Vibration is the only mode that has potential energy associated with it. I would say it has one degree of freedom but two types of energy associated with vibration for purposes of the equipartition theorem (i.e. N=7 for purposes of the equipartion theorem when all modes are activated).

The equipartition theorem relates to the number of (relevant) degrees of freedom in phase space, not configuration space.

 

[DrDu]

The equipartition theorem relates to the number of (relevant) degrees of freedom in phase space, not configuration space.

That's the problem, I don't think this is handled consistently in the literature.