Equipartition theorem and molecule of CO

  • Context: Graduate 
  • Thread starter Thread starter fluidistic
  • Start date Start date
  • Tags Tags
    Molecule Theorem
Click For Summary
SUMMARY

The discussion centers on the application of the equipartition theorem to the carbon monoxide (CO) molecule, which possesses five degrees of freedom: three vibrational and two rotational. Participants clarify that the equipartition theorem is valid primarily in the classical limit, where molecules are excited to high quantum numbers. It is established that at low temperatures, the theorem does not apply as expected, leading to confusion regarding energy distribution in vibrational and rotational modes. The conversation emphasizes the necessity of understanding the classical versus quantum mechanical perspectives when applying the equipartition theorem.

PREREQUISITES
  • Understanding of the equipartition theorem in thermodynamics
  • Knowledge of molecular degrees of freedom, specifically for diatomic molecules
  • Familiarity with quantum mechanics and energy quantization
  • Basic principles of rotational and vibrational spectroscopy
NEXT STEPS
  • Study the implications of the equipartition theorem in classical thermodynamics
  • Explore the quantum mechanics of molecular vibrations and rotations
  • Learn about the energy distribution in diatomic molecules at various temperatures
  • Investigate the differences between classical and quantum mechanical models of gas behavior
USEFUL FOR

Students and researchers in physical chemistry, molecular physics, and thermodynamics, particularly those interested in the behavior of gases and the application of the equipartition theorem.

fluidistic
Gold Member
Messages
3,932
Reaction score
283
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:
 
Physics news on Phys.org
The equipartition theorem applies only in the classical limit. I.e., when (on average) the molecules are excited to high quantum numbers.
 
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.
 

Similar threads

Understanding the Equipartition Theorem for Ideal Gases
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Questions about my Understanding of Thermodynamics and Statistical Mechanics
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Emission of photons by vibrational relaxation of molecules
  • · Replies 12 ·
Replies
12
Views
7K
Interpreting Energy diagrams for polyatomic molecules
  • · Replies 6 ·
Replies
6
Views
4K
Graduate Collisional excitation: selection rules for rotations?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Question about chiral molecules
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Atom as a harmonic oscillator of radition
  • · Replies 14 ·
Replies
14
Views
3K
Undergrad Vibrational cooling of a molecule
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Some questions about heat and temperature
  • · Replies 7 ·
Replies
7
Views
2K
Graduate When to use collective and when shell model?
  • · Replies 0 ·
Replies
0
Views
1K