CO2 Molecule Vibrational Modes and Heat Capacity | Thermal Physics Problem

[kottur]

Homework Statement

Consider a CO2 molecule, which is linear and has vibrational modes with frequency
corresponding to 2565 cm-1 (an asymmetric stretch), 1480 cm-1 (a symmetric stretch)
526 cm-1 (bends). Sketch a curve showing how the constant volume heat capacity of CO2
gas varies with temperature and mark the values of plateaus. (Recall: the spacing between
rotational levels is smaller than the spacing between the vibrational levels).

The Attempt at a Solution

I don't have a clue where to start!

 

[FactorsOf2]

Assume you can treat the CO2 gas classically and try using these main ideas:

1) Equipartition of Energy theorem says that each degree of freedom (for example translational motion along x-axis) which shows up quadratically in the total energy of the molecule contributes an average 1/2k_BT to the energy of the molecule.

2) Some degrees of freedom ('modes') require more energy to excite and so they do not contribute to the total energy at lower temperatures. For example, only the three translational degrees of freedom ('x', 'y' and 'z') contribute for the lowest temperatures.

3) The wavenumbers (cm^-1) corresponding to each vibrational mode listed are related to the energy of the mode.

4) Constant Vololume heat capacity is defined as dE_tot/dT


Bit hand-wavey but I think that's the idea.