1. Example Examples: Photon gas, an electromagnetic field in thermal equilibrium with its container To describe the state of the field, we need to know how many n are in each oscillator Photons are bosons  n=0,1,2,3…..

2. Cont.

3. Cont The average number of photons in a state j… Planck distribution

4. Monoatomic ideal gases

5. Monoatomic Gases =Bolztmann

6. Nuclear Contribution  for nuclear states ~10 6 ev  to populate an excited state, T>10 10 K  we can consider only the ground state Nuclear partition function q nuclear For most chemical problems (not nuclear!), q nuclear is just a const.

7. Electronic Contribution Electronic partition function q electronic  for electronic states, 400-700 nm (Uv-Vis); 33000–15000 cm -1 ; 4–1.8 ev; 160 kT – 70 kT; 6.6x10 -19 J – 3x10 -19 J Most cases @300K only ground state pop. T>10 4 K for pop. in excited state What is the degeneracy   1 of an electronic energy level?

8. Electronic degeneracy What is the degeneracy   1 of an electronic energy level? We have to go back to atomic electronic structure and Spectroscopic Term Symbols 2S+1 L j (for light atoms with RS S-L coupling)   1 =2 j +1 

9. Fraction of population in excited states

10. Translation Contribution by level Translation partition function q translation A single particle translation energy is given by

11. Translation Contribution by state Translation partition function q translation

12. Q of ideal gas

13. A(N,V,T) for ideal monoatomic gas

14. for an ideal monoatomic gas Internal energy

15. for a monoatomic gas Pressure

16. S for a monoatomic gas Entropy S(N,V,T)

17.  for a monoatomic ideal gas Chemical potential  (T,P)

18. Reference 