Lect05 - Lecture 5 Entropy and Exchange between systems...

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Physics 213: Lecture 5 Pg 1 Lecture 5 Lecture 5 Entropy and Exchange between systems Entropy and Exchange between systems Reference for this Lecture: Elements  Ch 6 Reference for Lecture 6: Elements  Ch 7 Counting microstates of combined systems Volume exchange between systems Definition of Entropy and its role in equilibrium
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Physics 213: Lecture 5 Pg 2 Review: Some definitions Review: Some definitions State: The details of a particular particle, e.g., what volume bin it is in, the orientation of its spin, what velocity it has, etc. Microstate: The configuration of states for a set of particles, e.g., which bin each particle is in, the specific orientation of the spins -- ↑↑↓↑↓ , etc. Macrostate: The collection of all microstates that satisfy some constraint, e.g., o all the particles on the left side o all the particles in any bin o 1/3 of the particles with their spins “up” o no particles as a gas (all as liquid)
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Physics 213: Lecture 5 Pg 3 ACT 1: Microstates ACT 1: Microstates Consider 10 coins (labeled by their position). Which microstate is least likely? a. HHHHH HHHHH b. HHHHH TTTTT c. HTHTH THTHT d. HHTHT TTHHH e. TTHTH HHTTH
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Physics 213: Lecture 5 Pg 4 Basic reminders and new definition Basic reminders and new definition When an isolated system can explore some number of microstates, they each become equally likely. So the probability that you find some macro state A is just the fraction of all the microstates that look like A. P(A)= (A)/ Ω, To keep track of the large numbers of states, we define Entropy (A) ln( (A)) P(A) e σ σ μ The most likely macrostate in equilibrium has the biggest net entropy σ . We call that the “equilibrium state” even though there are really small fluctuations around it. If the system is BIG (many particles), the relative size of these fluctuations is negligible.
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Physics 213: Lecture 5 Pg 5 Last lecture we considered binomial (two-state) systems: Last lecture we considered binomial (two-state) systems: Now we will study systems that occupy more than two Now we will study systems that occupy more than two states. This “bin problem” is directly related to particles in states. This “bin problem” is directly related to particles in gases and solids. gases and solids. Coins land with either heads or tails, electronic spins have magnetic moments m pointing either along or counter to an applied field, and 1-dimensional drunks can step a distance either left or right. We defined the terms “microstate” and “macrostate” to describe the spins, and by analogy the other systems: System One particular Microstate Macrostate (usually what we measure) Spins ↑↓↓↑↓↑↑↑↓↑ Total magnetic moment = μ (N up – N down ) Coins HTTHTHHHTH Net winnings = (N heads – N tails ) Steps RLLRLRRRLR Total distance traveled = (M right – M left ) (N = # drunks, or # particles diffusing) x Counting Microstates (revisited) Counting Microstates (revisited)
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Physics 213: Lecture 5 Pg 6 Counting arrangements of objects Counting arrangements of objects
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This note was uploaded on 12/11/2011 for the course PHYS 213 taught by Professor Kuwait during the Spring '09 term at University of Illinois at Urbana–Champaign.

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Lect05 - Lecture 5 Entropy and Exchange between systems...

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