1. Lecture 11b Polyatomic ideal gas
Model - translation, rotation, vibration
Rotational partition function
Vibrational partition function - harmonic oscillator
Thermodynamic functions
Problems

2. Single polyatomic molecule
Translational, rotational, vibrational and electronic energies additive
qt - evaluated last lecture
qr and qv - will evaluated today
Typically with De - binding energy

3. Translation Consider a single diatomic molecule is the box
M =m1+m2

4. Rotation Rotation energies: Degeneracy
r is the rotational temperature

5. Rotation - continuation
Unless temperature is very low:
If two atoms are the same we overcounted states by
 - symmetry number

6. Vibrations Vibrations - harmonic oscillator - frequency
Near potential minimum
With reduced mass

7. Vibrations - continuation
Partition function
Vibrational temperature

8. Ideal Gases Molecular Energies
The schematic below gives an indication of the relative spacing between energy levels for the various energies
electronic
vibrational
rotational
translational

9. Characteristic Temperatures
Characteristic temperature of vibration of diatomic molecules
Substance θvib(K) H O N
HCl CO NO Cl
Characteristic temperature of rotation of diatomic molecules
Substance θrot(K) H O N
HCl CO NO Cl

10. Partition function Q and free energy F
translation rotation
vibrations electronic

11. Energy
translation rotation
vibrations electronic

12. For a diatomic molecule system
Discussing the relationship of T and Cv

13. Heat capacity
Translation rotation vibrations

14. Heat capacity for diatomic molecules

15. Chemical potential