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March 18, 2009 - Boltzmann no change just S S = kln#states...

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March 19, 2009
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Boltzmann no change just S S = kln(#states) Classroom 100 seats if 1 student can sit in any of 100 seats S = 1 kln(100) =4.6k 2 students S = 2 k ln(100) = kln(100) 2
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Illustrate with two seats , 2 students total states = S n S # of seats (states) n # of students 2 2 = 4 Seat 1 Seat 2 1,2 0 0 1,2 1 2 2 1
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Number of states gets huge when S,n Increase 100 seats 2 students 100 2 = 10,000 = (10 2 ) 2 =10 4 If 100 seats, 100 students 100 100 = (10 2 ) 100 = 10 200
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Remember power n x entropy for one student gives total entropy S = (100)k ln(100) =100k(4.6) 460k = 1.4x10 -23 (460) = 640x10 -23 = 6.4x10 -21 Entropy only gets “large” for large number of molecules (or students)
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Case 1 1 student in room of 100 seats If choice completely random can pick any one of 100 S = k ln(100) Case 2 1 student always sits in same seat (1 state) S = kln(1) = 0 no randomness S = 0
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Third Law of Thermodynamics Perfect atomic crystal at 0K Each atom rests in a specific spot and has no vibrational (or other) motions O O O O O O X O O O O O At 0K, x is always in the same state (seat) only one state
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