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

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

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

Rotation Rotation energies: Degeneracy r is the rotational temperature

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

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

Vibrations - continuation Partition function Vibrational temperature

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

Characteristic Temperatures Characteristic temperature of vibration of diatomic molecules Substance θvib(K) H2 6140 O2 2239 N2 3352 HCl 4150 CO 3080 NO 2690 Cl2 810 Characteristic temperature of rotation of diatomic molecules Substance θrot(K) H2 85.4 O2 2.1 N2 2.9 HCl 15.2 CO 2.8 NO 2.4 Cl2 0.36

Partition function Q and free energy F translation rotation vibrations electronic

Energy translation rotation vibrations electronic

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

Heat capacity Translation rotation vibrations

Heat capacity for diatomic molecules

Chemical potential