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…..

Cont.

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

Monoatomic ideal gases

Monoatomic Gases =Bolztmann

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.

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

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 

Fraction of population in excited states

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

Translation Contribution by state Translation partition function q translation

Q of ideal gas

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

for an ideal monoatomic gas Internal energy

for a monoatomic gas Pressure

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

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

Reference 