LectureT5

LectureT5 - Chapter 5 In this chapter we want to review the...

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5/20/2004 H133 Spring 2004 1 Chapter 5 In this chapter we want to review the concept of irreversibility in more detail and see how it comes from the multiplicity of states . In addition, we want to introduce the following new topics: ± Definition for Entropy ± Second Law of Thermodynamics. ± Entropy and disorder. Let’s start by reviewing what we learned last time. Here is the basic line of reasoning for Einstein Solids ± (1) Define an Einstein Solid ² Atoms locked in lattice but individual atoms were free to oscillate as simple harmonic oscillators around an equilibrium position. o 3-D Problem ± 3 x 1-D Problem. ± (2) Define a Macrostate for a single solid using ² U : Internal Energy which is related to temperature by ² N : Number of Atoms ± (3) The microstate of the solid is given by how much energy is stored in the 3N simple harmonic oscillators ² 3N integers required. ² Internal Energy (in terms of microstates) ² There are MANY microstates for each macrostate. T Nk U B 3 = ω ε { = = = 3 1 N i i n U () U q N q N q U N + = )! 1 3 ( ! ! 1 3 ) , (
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5/20/2004 H133 Spring 2004 2 Irreversibility…revisited ± (4) We can bring two Einstein Solids, A & B into thermal contact with one another and define the macrostate of the system by ± (5) The two solids can share the total energy in different ways. We call each of the ways a macropartition. ² The number of microstates for the macropartition is given by ² We defined a Macropartition Table to summarize all this information (at least for small N and q) ± (6) ASSUMPTION: All microstates are equally likely in the long run (i.e. if we wait a long time) ² Consequence: Since macropartitions have a different number of microstates, macropartitions are NOT equally likely. o The macropartitions with the most microstates are the most likely macropartitions. ± (7) For large N, most microstates are concentrated in a tight band of macropartitions, near the macropartition which has roughly equal energy per solid. B A AB = U A, N A U B, N B U sys =U A +U B 30 10 3 3 1 1:3 15 15 1 4 0 0:4 AB B A U B U A Macr o More Rows
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5/20/2004 H133 Spring 2004 3 Implications Based on the line of reasoning that we just outlined there are two statements that we would like to show: ± A) If the combined system is not in the most probable macropartition to begin with, it will rapidly and inevitably
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This note was uploaded on 06/03/2011 for the course H 133 taught by Professor Furnstahl during the Spring '11 term at Ohio State.

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LectureT5 - Chapter 5 In this chapter we want to review the...

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