# ps2rev - Statistical Physics I (8.044) Spring 2009...

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Statistical Physics I (8.044) Spring 2009 Assignment 2 February 11, 2009 Due February 18, 2009 Please remember to put your name and section number at the top of what you turn in. Readings You should have completed reading pages 1-86 of Atkins. You should be well into your reading of the Notes on Probability by Prof. Greytak. You will need to have read the ±rst section of these notes for this problem set. Problem Set 2 1. Partitioning Energy among Distinguishable Particles (12 points) Suppose that we have N atoms in a crystal, each of which is localized at a particular point. This means that the atoms are distinguishable, in that we can uniquely specify which one we are talking about by giving the coordinates of its location. Suppose further that each atom can exist in one of several possible energy states, with its energy taking on a value from a list of possible energies: 0 , ε, 2 ε, 3 ε, 4 ε, 5 ε, . . . [Making the possible energies discrete is inspired by quantum mechanics, but you need not know any quantum mechanics to do this problem.] Suppose that the total energy in the N -atom crystal is E , with E some integer multiple of ε . This problem is about counting the ways one can partition this energy E among the N atoms. (a) We shall initially consider only the speci±c example for which N = 7 and E = 4 ε . The “microstates” in this example are all possible ways of arranging the energy among the 7 speci±ed atoms. For example, the state where the ±rst atom has energy 4 ε while the other six atoms have zero energy is a di²erent microstate from the state where the second atom has 4 ε and the other six have zero. There are ±ve kinds of con±gurations possible, which we shall call “partitions”: Partition (a): 6 atoms with energy 0; 1 atom with energy 4 ε Partition (b): 5 atoms with energy 0; 1 atom with energy ε , and 1 atom with energy 3 ε Partition (c): 5 atoms with energy 0, 2 atoms with energy 2 ε each Partition (d): 4 atoms with energy 0, 2 atoms with energy ε each, and 1 atom with energy 2 ε Partition (e): 3 atoms with energy 0, 4 atoms with energy ε each 1

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How many microstates there are for each of the Fve partitions? If all microstates are equally probable, which partition is most probable?
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## This note was uploaded on 09/17/2009 for the course PHYSICS 8.044 taught by Professor Krishnarajagopal during the Spring '09 term at MIT.

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ps2rev - Statistical Physics I (8.044) Spring 2009...

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