Equipartition theorem and molecule of CO

In summary, the equipartition theorem applies only in the classical limit for molecules that are excited to high quantum numbers. It does not apply for low temperatures or ground states.
  • #1
fluidistic
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If I understand the equipartition theorem more or less well, if I heat up a gas then the energy I have spent to heat it up should be equally distributed to the rotational part and vibrational part of the molecule dynamics.
Let's take the molecule of CO, I think it has 5 degrees of freedom. 3 vibrationals, 2 rotationals. I don't understand how does the equipartition theorem applies there: http://en.wikipedia.org/wiki/File:Vibrationrotationenergy.svg, taken from http://en.wikipedia.org/wiki/Rotational_spectroscopy#Structure_of_rotational_spectra. It seems that whenever I excitate the molecule, it will gain at least energy in the vibrational form. And if I'm lucky, in the rotational form too. But it seems forbidden to gain energy only in the rotational form. How does this agree with the equipartition theorem?! :confused:
 
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  • #2
The equipartition theorem applies only in the classical limit. I.e., when (on average) the molecules are excited to high quantum numbers.
 
  • #3
EmpaDoc said:
The equipartition theorem applies only in the classical limit. I.e., when (on average) the molecules are excited to high quantum numbers.

Thanks a lot. For some reason I thought it applied for low temperatures/ground states.
 

1. What is the equipartition theorem?

The equipartition theorem is a principle in statistical mechanics that states that, in thermal equilibrium, the energy of a system is equally distributed among all of its degrees of freedom. This means that each degree of freedom, such as translational, rotational, and vibrational motion, will have an average energy of 1/2kT, where k is the Boltzmann constant and T is the temperature.

2. How does the equipartition theorem apply to molecules of CO?

The equipartition theorem applies to molecules of CO by determining the average energy of each degree of freedom in the molecule. For CO, there are three translational degrees of freedom, two rotational degrees of freedom, and one vibrational degree of freedom. Therefore, the average energy for each degree of freedom would be 1/2kT, and the total average energy for the molecule would be the sum of these energies.

3. What is the significance of the equipartition theorem for understanding the behavior of molecules?

The equipartition theorem is significant because it helps us understand the distribution of energy within a molecule. It allows us to predict the average energy of each degree of freedom and how it contributes to the overall energy of the molecule. This information is important for understanding the physical properties and behavior of molecules, such as their ability to rotate, vibrate, and move.

4. Can the equipartition theorem be applied to all molecules?

Yes, the equipartition theorem can be applied to all molecules, as long as they are in thermal equilibrium. However, it is important to note that some molecules may have more or fewer degrees of freedom, depending on their structure and composition. In these cases, the average energy for each degree of freedom may differ, but the principle of equal distribution still applies.

5. How does the equipartition theorem relate to the specific heat capacity of a substance?

The equipartition theorem is closely related to the specific heat capacity of a substance. This is because the average energy of each degree of freedom, as determined by the theorem, contributes to the overall heat capacity of the substance. For example, the specific heat capacity of a gas at constant volume is directly proportional to the number of degrees of freedom it has, as predicted by the equipartition theorem.

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