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lec14 - 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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Ω = Ω( E, V, N . . . ) Volume of the accessible region of phase space. 8.044 L14B1
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4. Entropy S ( E, V, N ) k ln Ω( E, V, N ) k ln Φ( E, V, N ) Differ only by ln N k ln ω ( E, V, N ) It is a state function. It is extensive. It is a logarithmic measure of the microscopic de- generacy associated with a macroscopic (that is, ther- modynamic) state of the system. k is Boltzmann’s constant, units of energy per 0 K . 8.044 L14B2
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5. Statistical Mechanical Definition of Temperature 1 2 dQ Total is microcanonical d /W 1 2 = 0 interaction between 1 & Find the most probable E 1 2 is so small that Ω can E be separated 1 8.044 L14B3
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p ( E 1 ) = = 1 ( E 1 )Ω 2 ( E E 1 ) Ω( E ) ln p ( E 1 ) = ln 1 ( E 1 )+ln Ω 2 ( E E 1 ) ln Ω( E ) 1 = ( S 1 ( E 1 )+ S 2 ( E E 1 ) S ( E ) ) k
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