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# 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 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 ) = 1 e p 2 / 2 <p 2 > x x 2 π < p 2 > x 8.044 L13B15
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
2 1 1 IS THE SUBSYSTEM OF INTEREST. 2, MUCH LARGER, IS THE REMAINDER OR THE "BATH". ENERGY CAN FLOW BETWEEN 1 AND 2.

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