lec16 - MIT OpenCourseWare http://ocw.mit.edu 8.044...

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Unformatted text preview: 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 . EXAMPLE 2 Level System Ensemble of N "independent" systems ENERGY | 1 > N = N + N 1 E = N 1 | 0 > 0 8.044 L16B1 SURFACE MOLECULES IONS IN A CRYSTAL LOWEST LYING STATES 0 0 0 E N 1 NO WORK POSSIBLE (JUST HEAT FLOW) ENERGY 8.044 L16B2 1 when N 1 = 0 or N N ! ( E ) = N 1 !( N N 1 )! Maximum when N 1 = N/ 2 T = (or - S(E) E = N/2 ) S ( E ) = k ln ( E ) E = N T = 0 E T > 0 T < 0 8.044 L16B3 ln N ! N ln N N S ( E ) = k [ N ln N N 1 ln N 1 ( N N 1 ) ln( N N 1 ) N + N 1 + N N 1 ] 1 S S N 1 k = = = [ 1 ln N 1 +1+ln( N N 1 )] T E N N 1 E 1 / k N N 1 k N = ln = ln N 1 N 1 1 8.044 L16B4 N N 1 1 = e /kT N N 1 = e /kT +1 N E = N 1 = e /kT +1 1.0 N 1 /N or E/ N /kT ~ e ~ 0.5 1 2 3 kT/ 4 8.044 L16B5 e...
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lec16 - MIT OpenCourseWare http://ocw.mit.edu 8.044...

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