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Lect24-Phys172s10-(12.3-12.5-Entropy)

# Lect24-Phys172s10-(12.3-12.5-Entropy) - PHYS 172 Modern...

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Spring 2011 PHYS 172: Modern Mechanics Lecture 24 – Entropy Read 12.3 – 12.5 Exam 3 results: Multiple choice: 42.5/70 = 60.7% Handwritten: grading in progress EXAM PROBLEM OVERVIEW : NEXT LECTURE What is my grade? (see announcement on the course web page) 1. Calculate (estimate) your total score Total score = FEX*0.2 + (Ex1+Ex2+Ex3)*0.1 + (Lab + HW + Rec)*0.15 + Lec*0.05 2. Compare with the grade cutoff table in syllabus. Your score will be not lower than that. Cutoffs may be lowered by 1..2% depending on exam 3 and final exam difficulty levels. Averages: EX1 = 63.5% Lab = 90 % Lec = 84 % EX2 = 58.4% HW = 88 % EX3 = 59 % Rec = 90 % ( blue = expected averages) 2 Equilibrium Only 500 oscillators (500/3 molecules) and 100 quanta: Ω ~10 114 Take logarithm! ( ) ( ) 1 ! ! 1 ! q N q N + - Ω = -

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3 Entropy Definition of entropy ln S k Ω k = 1.4 × 10 -23 J/K (Boltzmann constant) Ludwig Boltzmann 1844-1906 entropy: en - in (Greek) trope – turning turning pure states to mixed ones 4 Additivity of entropy ( ) 1 2 ln ln S k k Ω = Ω Ω ( ) 1 2 ln ln k = Ω + Ω 1 2 ln ln k k = Ω + Ω 1 2 tot S S S = +
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