# Groupwork 3 Rotational Temperatures

Using the rigid rotator, we can write the expression for the rotational partition function, that is,

$$q_{rot}(T)=\sum_Jg_Je^{-\epsilon_J/k_BT}=\sum_J(2J+1)e^{-hB(J(J+1))/k_BT}=\sum_J(2J+1)\epsilon^{-\Theta_{rot}(J(J+1))/T}$$

where $$\Theta_{rot}=\frac{hB}{k_B}$$ is the characteristic rotational temperature.

In the high temperature limit, $$q_{rot}(T)=\frac{T}{\sigma\Theta_{rot}}$$ where σ is the symmetry number

(σ =1 for heteronuclear diatomic molecule, σ =2 for homonuclear diatomic molecule).

The figure below shows the rovibrational absorption spectrum of CO gas.  What was the temperature of the CO gas measured in the spectrum below?

Some potentially useful information:

$$h=6.626x10^{-34}J*s$$        $$k_B=1.38x10^{-23}J/K$$        $$1eV=1.602x10^{-19}$$        $$J=8065.54cm^{-1}$$        $$B=1.9313cm^{-1}$$