# 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.