lec21 - 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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± 3 1 / 2 ² 1 ±/ 2 <±> e p ( p x )= e 4 πm 1 / 2 N e 3 N<±> 1 = e 4 πm < ± > ±/ 2 <±> 2 Now use ± = p 2 / 2 m and <±> = <p x >/ 2 m . x p ( p x )= ³ 1 e p 2 / 2 <p 2 > x x 2 π<p 2 > x 8.044 L13B15
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Homework problem on classical harmonic oscillators 1 p ( p i ,q i )= (2 π/ω ) <±> exp[ ±/ <±> ] 1 2 = (2 π/ω ) kT exp[ p i / 2 mkT ] exp[ ( 2 / 2 kT ) q i ] = ··· 2
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Ensembles Microcanonical: E and N fixed Starting point for all of statistical mechanics Difficult to obtain results for specific systems Canonical: N fixed, T specified; E varies Workhorse of statistical mechanics Grand Canonical: T and µ specified; E and N vary Used when the the particle number is not fixed 8.044 L21B1
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2 1 1 IS THE SUBSYSTEM OF INTEREST. 2, MUCH LARGER, IS THE REMAINDER OR THE "BATH".
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This note was uploaded on 11/08/2011 for the course PHYSICS 8.004 taught by Professor Staff during the Spring '08 term at MIT.

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lec21 - MIT OpenCourseWare http:/ocw.mit.edu 8.044...

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