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# lec24 - MIT OpenCourseWare http/ocw.mit.edu 8.044...

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MIT OpenCourseWare http://ocw.mit.edu 8.044 Statistical Physics I Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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Polyatomic Gases 1 Non-interacting, identical Z = N ! Z N Find Z 1 1 Each molecule has # atoms 3# position coordi- nates 3# = 3 + n r + (3# 3 n r ) C.M. rotation n v , vibration 8.044 L24B1
MONATOMIC DIATOMIC LINEAR TRI. NON-LINEAR TRI. Xe HS CO 2 H 2 O 3 3 3 9 3 2 4 9 3 2 1 6 3 0 0 3 8.044 L24B2

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C.M. Motion: Particle in a box ∆ E s kT classical Rotation: (H 2 ν rot = 3 . 65 × 10 12 Hz 175 K ) Q.M. Vibration: (H 2 ν vib = 1 . 32 × 10 14 Hz 6 , 320 K ) Q.M. H CM + H vib + H rot problem separates H = 8.044 L24B3
Vibration n v 1 2 1 K i H vib = + 2 ω i 2 a ˙ i K i a i 2 i =1 2 n v 1 dimensional harmonic oscillators, use Q.M. ˆ 2 H ψ n = n ψ n n = ( n + 1 n = 0 , 1 , 2 , · · · The energy levels are non-degenerate. 8.044 L24B4

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� � 2 hω/kT / e n /kT p ( n ) = e ( n + 1 ε n =0 h ω e ( n + 1 hω/kT 1 hω/kT e ¯ 2
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