# lec28 - 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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± ² ³ Normal modes of the radiation ﬁeld in a rectangular cavity with conducting walls ± r, t ) ω = L n x + n y + n z E n x ,n y ,n z ² ( ± πc 2 2 2 Harmonic oscillators V D ( ω )= π 2 c 3 ω 2 0 8.044 L28B1
± Classical Statistical Mechanics ( ω ) > = k B T u ( ω, T )= ( ω ) > D ( ω ) = k B T ω 2 V π 2 c 3 u ( T )= u ( T ) = 0 u( ω , T) CLASSICAL MEASURED ω 8.044 L28B2

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Quantum Statistical Mechanics ¯ ( ω ) > = e hω/kT 1 hω/ 2 ¯ D ( ω ) ¯ h ω 3 u ( ω, T )= ( ω ) > = π 2 c 3 e 1 + z. p. term ¯ V du ( T ) To ﬁnd the location of the maximum, set =0 . The maximum occurs at ¯ 2 . 82. 8.044 L28B3
± ² ³ hω/ 2 kT (1 e ¯ hω/kT ) 1 Z = Z i Z i = e ¯ states i The ﬁrst factor in the expression for Z i comes from the zero-point energy. F ( V, T )= ln

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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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lec28 - MIT OpenCourseWare http:/ocw.mit.edu 8.044...

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