15_562ln08

15_562ln08 - MIT OpenCourseWare http:/ocw.mit.edu 5.62...

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MIT OpenCourseWare http://ocw.mit.edu 5.62 Physical Chemistry II Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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5.62 Lecture #15: Polyatomic Molecules: Rotation and Vibration Reading: Hill, pp. 151-153, 156-159 Maczek pp. 53, 58-63 VIBRATIONAL CONTRIBUTIONS TO MACROSCOPIC PROPERTIES (CONT.) High Temperature or Classical Limit of (E – E 0 ) vib : T θ vib E E 0 ( ) vib = Nk θ vib e θ vib T 1 Nk θ vib 1 + θ vib T +… 1 = NkT 1 1 e −θ v x 2 x 3 e x 1 + x + 2! + 3! for x < 1 This quantum result yields the same value for (E–E 0 ) vib as the classical approach when T θ vib or ε vib kT. Classical equipartition principle says that each vibrational degree of freedom contributes NkT to total average energy (but ony if T θ vib ). However, T θ vib is a condition that does not obtain very often. Other Thermodynamic Functions: = kTlnQ vib = Nk θ vib NkTlnq * vib A vib 2 * = Nk θ vib NkTln 2 T ) ( ( A E 0 ) vib = NkTln 1 e −θ v ( A E 0 ) vib = NkTln 1 ( e x ) x = θ vib /T, NkT = nRT ( A E 0 ) vib ( ) = ln 1 e x another Einstein function nRT * S VIB A = E – TS S = E A ( E E 0 ) ( A E 0 ) = T T This expresses the fact that entropy cannot depend on an arbitrary choice for the zero of energy.
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n 5.62 Spring 2008 Lecture 15, Page 2 nRx θ
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15_562ln08 - MIT OpenCourseWare http:/ocw.mit.edu 5.62...

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