Lect09 - 213 M i dter m comi ng up Monday November 8 @ 7 pm...

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Lecture 9 Pg 1 213 Midterm coming up… Monday November 8 @ 7 pm (conflict exam @ 5:15pm) Covers: Lectures 1-10 + ½ of 11 HW 1-4 Discussion 1-4 Labs 1-2 Review Session Sunday November 7, 3-5 PM, 228 Natural History Bldg.
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Lecture 9 Pg 2 Lecture 9 Examples and Problems Counting microstates of combined systems Volume exchange between systems Definition of Entropy and its role in equilibrium The second law of thermodynamics Statistics of energy exchange General definition of temperature Why heat flows from hot to cold
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Lecture 9 Pg 3 When the numbers are small, and the whole distribution matters, the average and the most likely may not be very close. Consider 3 particles (A, B, C) in a system with 6 multiple occupancy cells partitioned by a movable barrier: Take N L =1 (particle A) and N R =2 (particles B and C). 1 ) Calculate the entropy for each partition position. 2) What are the most likely and average partition positions? Note: We are interested in the volume on the left and right, V L and V R , so we’ll express our answers in terms of them. V L + V R = 6. Exercise: Microstates and Entropy A A BC B C A B C Some possible microstates: 1 2 3 4 5
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Lecture 9 Pg 4 Worksheet for this problem L R = L R σ = ln( ) V L = 1 1 5 2 = 25 25 3.22 V L = 2 V L = 3 V L = 4 V L = 5
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Lecture 9 Pg 5 Solution L R = L R σ = ln( ) V L = 1 1 5 2 = 25 25 3.22 V L = 2 2 4 2 = 16 32 3.47 V L = 3 3 3 2 = 9 27 3.30 V L = 4 4 2 2 = 4 16 2.77 V L = 5 5 1 2 = 1 5 1.61 tot = 105 The most likely V L = 2 . The average <V L > = (1*25 + 2*32 + 3*27 + 4*16 + 5*5) / 105 = 259/105 = 2.47
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Graph the Results Most probable V L : σ = ln(32) = 3.47 1 in this example 2 L R L R N N V V   = =     V L 1 2 3 4 5 40 30 20 10 0 L R V L Notice that the most likely position occurs when: What is the probability, P(2), that V L = 2? 32
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This note was uploaded on 02/21/2011 for the course PHYS 213 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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Lect09 - 213 M i dter m comi ng up Monday November 8 @ 7 pm...

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