Lect23 - PHYS 172: Modern Mechanics Lecture 23 Entropy and...

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Fall 2011 PHYS 172: Modern Mechanics Lecture 23 – Entropy and Temperature Read 12.3 - 12.5 1
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First, an important reminder about multiplying probabilities : A deck of 52 cards has 4 aces. Starting from a randomly- shuffled deck, what is the probability that an ace is the first card dealt? P 1 = 4 52 = 0.0769 Once this happens, what is the probability that the second card is an ace? P 2 = 3 51 = 0.0588 So, what is the probability that the first two cards are aces? P two aces = P 1 ! P 2 = 4 52 ! 3 51 = (0.0769) ! (0.0588) = 0.00452 2
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Last Time Einstein Model of Solids ( ) ( ) 1 ! ! 1 ! q N q N + ! " # = ! # microstates (N oscillators, q quanta) Fundamental assumption of statistical mechanics Over time, an isolated system in a given macrostate (total energy) is equally likely to be found in any of its microstates (microscopic distribution of energy). ! E = ! k m = ! " 3
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These show the 15 different microstates where 4 quanta of energy are distributed among 3 oscillators (1 atom). The Fundamental Assumption of Statistical Mechanics A fundamental assumption of statistical mechanics is that in our state of macroscopic ignorance, each microstate (microscopic distribution of energy) corresponding to a given macrostate (total energy) is equally probable. 4
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The fundamental assumption of statistical mechanics is that, over time, an isolated system in a given macrostate is equally likely to be found in any of its microstates. Most likely case:
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This note was uploaded on 12/07/2011 for the course PHYS 172 taught by Professor ? during the Fall '08 term at Purdue.

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Lect23 - PHYS 172: Modern Mechanics Lecture 23 Entropy and...

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