Rotational partition function for CO2 molecule

[DannyJ108]

Homework Statement

Find the rotational partition function for a CO2 molecule. Assume ideal gas and classical approximation

Relevant Equations

$\zeta^r= \frac T {\sigma \theta_r}$

Hello fellow physicists,

I need to calculate the rotational partition function for a CO2 molecule. I'm running into problems because I've found examples were they say this rotational partition function is:

$\zeta^r= \frac T {\sigma \theta_r} = \frac {2IkT} {\sigma \hbar^3}$

Where $\zeta^r$ : rotational partition function for the molecule
$T$ : temperature
$\sigma$ : symmetry number
$\theta_r$ : characteristic rotational temperature
$I$ : moment of inertia
$K$ :Boltzmann factor

The problem is that I've read that $\zeta^r$ mentioned before is ONLY valid for DIATOMIC molecules. There's another more complicated formula used for polyatomic molecules:

$\zeta^r= \frac {\left( \pi I_1 I_2 I_3 \right)^{1/2}} {\sigma \hbar^3} \left( 2kT \right)^{3/2}$

But I've read this formula is for asymmetric polyatomic molecules with different inertia moments, whereas CO2 only has one moment of inertia.

Now I don't know what formula to use. Can you guys help me out?

This is a link (http://myweb.liu.edu/~nmatsuna/PHS702/statmech/lect7/stat.mech.8.html) for polyatomic molecules and it says that the $\zeta^r$ for a linear polyatomic molecule (which is the case of CO2) is the first formula I wrote out.

This other one (http://faculty.washington.edu/gdrobny/Lecture453_17_2013.pdf) says that $\zeta^r$ is only valid for diatomic molecules, but then proceeds to write the partition function with that formula.

I'm so confused. Thanks in advance for your kind help.

Regards.

 

[mjc123]

This other one (http://faculty.washington.edu/gdrobny/Lecture453_17_2013.pdf) says that ζr is only valid for diatomic molecules, but then proceeds to write the partition function with that formula.

It says that the formula it gives for the total partition function is only valid for diatomics; the difference for linear polyatomics is in the vibrational component, not the rotational.