Rotational Partition Function for a Diatomic Molecule (Quantum, High Temperature Approximation):

This formula from statistical mechanics describes the contribution of molecular rotation to the partition function (and thus thermodynamic properties) of a diatomic gas at temperatures that are high enough to excite rotational states but not so high that classical approximations are fully valid.


Work in Progress: 

Starting with: 
Z_rot ≈ (8π² I T k) / (σ h^2)

Replacing definitions:

Z_rot ≈ (8π² I T ( K_Hz Hz_kg kg_E )) / (σ ( Hz_kg kg_E  ) h)

Simplify:
 Z_rot ≈ (8π² I T K_Hz) / (σ h)

K_Hz = k/h, converts temperature to frequency 

h = Hz_kg kg_E
k = K_Hz Hz_kg kg_E
T is the input variable for the temperature.