06 Lecture 10 January 25 - CHEM 350 Lecture 10, January 25,...

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CHEM 350 Lecture 10, January 25, 2010 Fluctuations (continued) The number of atoms on a given side varies from frame to frame – though not by much – these are local fluctuations which occur even though our system is in equilibrium For a small number of particles, say 4 particles: sometimes find all four in one half of the container. This is highly unlikely in principle when there are many particles, but how unlikely is it? For N particles we have 2 N configurations, of which only one will correspond to all N particles in a particular half of the container. Probability = 1 2 N (1) Probability measure relative frequency with which an event occurs. If C ( n ) is the number of possible ways of distributing the N atoms in the container so that n of them are found in a specified half, then the probability of finding n atoms in that half is P n = C ( n ) 2 N . For n = 0 or n = N , we have 1 configuration C ( N ) = C (0) = 1 (2) Thus, if N is large and n is close to 0 or to N, then C ( n ) ± 2
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This note was uploaded on 04/11/2010 for the course CHEM 1101 taught by Professor Leroy during the Spring '10 term at University of Toronto- Toronto.

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06 Lecture 10 January 25 - CHEM 350 Lecture 10, January 25,...

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