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Lecture 11b Polyatomic ideal gas
Model - translation, rotation, vibration Rotational partition function Vibrational partition function - harmonic oscillator Thermodynamic functions Problems
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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
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Translation Consider a single diatomic molecule is the box
M =m1+m2
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Rotation Rotation energies: Degeneracy
r is the rotational temperature
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Rotation - continuation
Unless temperature is very low: If two atoms are the same we overcounted states by - symmetry number
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Vibrations Vibrations - harmonic oscillator - frequency
Near potential minimum With reduced mass
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Vibrations - continuation
Partition function Vibrational temperature
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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
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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
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Partition function Q and free energy F
translation rotation vibrations electronic
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Energy translation rotation vibrations electronic
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For a diatomic molecule system
Discussing the relationship of T and Cv
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Heat capacity Translation rotation vibrations
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Heat capacity for diatomic molecules
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Chemical potential
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