14_562ln08

14_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 #14: Low and High-T Limits for q rot and q vib Reading: Hill, pp. 153-159, Maczek pp. 51-53 TEMPERATURE DEPENDENCE OF E rot AND C V rot Low T limit of E rot : T ) = 0 lim E rot = lim ( 6Nk θ r e 2 θ r T 0 T 0 e 2 θ r lim C V rot = lim 12Nk θ r 2 T = 0 T 0 T 0 T 2 Low T Limit High T Limit rot 2 rot C V 12 θ r e 2 θ r T C v 1 nR T 2 nR E rot 6 θ r e 2 θ r T E rot T nR nR Note maximum in C R v 1.624 at T = 1.0 if we retain the two-term formula for the low-T θ rot 1.0 C V rot nR E rot nR 1.0 T/ θ rot limit. Actual maximum, derived from the full q V rot , is C V /nR = 1.098 at T/ θ rot = 0.8. [Rapid
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5.62 Spring 2008 Lecture 14, Page 2 change in C V is a signal of a gap in the level spacing measured in units of kT. What gap would be relevant here? At what value of T/ θ rot would you expect the most rapid change in C V ?] QUANTUM BEHAVIOR
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14_562ln08 - MIT OpenCourseWare http:/ocw.mit.edu 5.62...

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