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Lect26

# Lect26 - PHYS 172 Modern Mechanics Lecture 26 Kinetic...

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PHYS 172: Modern Mechanics Lecture 26 - Kinetic theory of gases; pressure Read 12.8 Fall 2011 1

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Exam 3 Results Machine-graded part: Average = 42/70 Hand-graded part: Average = 14/30 2
S = k B ln ! P ( ! E ) " e # ! E kT 1 T ! " S " E int Counting states Entropy Temperature Boltzmann distribution C = ! E atom ! T = 1 N ! E system ! T Heat capacity Summary of Statistical Mechanics (Ch 12) = ( q + N 1 )! q !( N 1 )! 3

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Boltzmann Distribution 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6 7 Quanta on Atom A Probability ratio Probability of ! E above ground state Probability of being in ground state ~ " A ! E ( ) e # ! E kT ! e # ! E kT Boltzmann Distribution 4
Distribution of Speeds in a Gas X- Component Speed Distribution 5

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( v ) ! v 2 e " 1 2 mv 2 kT Use this “distribution function” to calculate averages: K trans = 3 2 kT v rms = 3 kT m This is determined by assuming that all of a molecule’s energy is kinetic energy, and then averaging over all directions (see page 399-400). The Maxwell-Boltzmann
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Lect26 - PHYS 172 Modern Mechanics Lecture 26 Kinetic...

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