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# Lect07 - 213 Midte com up rm ing Monday November 8 7...

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Lecture 7, p 1 213 Midterm coming up… Monday November 8, 7 pm (conflict exam at 5:15 pm) Covers: Lectures 1-10 + ½ of 11 HW 1-4 Discussion 1-4 Labs 1-2 Review Session Sun. November 7, 3-5 PM, 228 Nat. Hist. Bldg.

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Lecture 7, p 2 Lecture 7 Entropy and Exchange between Systems Reference for this Lecture: Elements Ch 6 Reference for Lecture 8: Elements Ch 7 Counting microstates of combined systems Volume exchange between systems Definition of Entropy and its role in equilibrium
Lecture 7, p 3 Review: Some definitions State: The details of a particular particle , e.g.: . what volume bin it is in . the orientation of its spin . Its velocity Microstate: The configuration of states for a set of particles , e.g.: . which bin each particle is in . the velocities of all the particles . the orientation of all the spins -- ↑↑↓↑↓ Macrostate: The collection of all microstates that correspond to a macroscopic property of the system , e.g.: . all the particles on the left side . A box of gas has a particular P, V, and T . 1/3 of the particles with their spins “up” . no particles as a gas (all as liquid)

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Lecture 7, p 4 ACT 1: Microstates Consider 10 coin flips. Which sequence is least likely? a. H H H H H H H H H H b. H H H H H T T T T T c. H T H T H T H T H T d. H H T H T T T H H H e. T T H T H H H T T H
Lecture 7, p 5 ACT 1: Solution Consider 10 coin flips. Which sequence is least likely? a. H H H H H H H H H H b. H H H H H T T T T T c. H T H T H T H T H T d. H H T H T T T H H H e. T T H T H H H T T H Each sequence is equally likely! Now, imagine that the coins are being flipped by random thermal motion. Each sequence is a microstate of the 10-coin system. In thermal equilibrium, every microstate is equally likely! If instead we ask which macrostate is least likely , it is the one with all the coins ‘heads’ (or ‘tails’). Why? Because there is only one corresponding microstate.

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Lecture 7, p 6 A New Definition In an isolated system in thermal equilibrium, each microstate is equally likely. We’ll learn later why the system must be isolated. So, the probability that you find some macro state A is just the fraction of all the microstates that correspond to A: P(A)= (A)/ total . To keep track of the large numbers of states, we define entropy , σ : σ (A) ln( (A)) P(A) e σ (A) In thermal equilibrium, the most likely macrostate is the one with the biggest entropy σ . We call that the “equilibrium state” even though there are really fluctuations around it. If the system is big (many particles), the relative size of these fluctuations is negligible. Entropy is the logarithm of the number of microstates.
Lecture 7, p 7 Last week we considered binomial (two-state) systems: Coins land with either heads or tails, electronic spins have magnetic moments m pointing either with or against an applied field, and 1-dimensional drunks can step a distance either left or right. We defined the terms “microstate” and “macrostate” to describe

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Lect07 - 213 Midte com up rm ing Monday November 8 7...

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