Lecture04-03.1.Boltzmann_Distribution

# Lecture04-03.1.Boltzmann_Distribution - Last Time...

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1 Last Time Fundamental assumption: A closed system is equally likely to be in any accessible state. Ensemble average Two systems in thermal contact Entropy Temperature ( ) ( ) ( ) 1 1 2 1 s g s g s g s s = - Last Time 0 th Law: with 1 st Law: Heat is energy (energy conservation) 2 nd Law: Left alone, entropy will not decrease 3 rd Law: Entropy approaches a constant as T 0. A B C

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2 Temperature and Energy Common misconception : “temperature is the measure of thermal energy” Example : which glass takes more energy to heat up by 1 degree? Water Vodka Example: Einstein’s model of solid & τ (U) Solid can be represented as a set of one- dimensional harmonic oscillators Each oscillator has quantized energy levels One atom = three one-dimensional oscillators Oscillators can exchange energy s k m &
3 Distributing energy: 4 quanta 3 ways: 4-0-0 quanta 6 more ways: 2-2-0 quanta 1-1-2 quanta 6 ways: 3-1-0 quanta 15 microstates The same macrostate s k m Distributing energy among 1D oscillators ( ) ( ) 1 ! ! 1 ! q N g q N + - = - Number of ways: # of oscillators # of energy quanta Entropy: ( ) log g σ = U U τ

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4 Temperature of a binary system Spin excess: ↑↑↑↑↑↑↑↑↓↓↓↓ ½N s 2 N N s - B 2 U smB = - s s=0 2 2 0 s N g g e - 4 1 4 2 2 s s s U s U N mB mBN σ - ± = = - = ² ³ ´ µ 2 U s mB = - 2 mBN s τ = ( ) 2 0 log 2 g s N = - See more in: * Kittel, Appendix E * http://www.xs4all.nl/~johanw/PhysFAQ/ParticleAndNuclear/neg_temperature.html Today Chapter 3 (part 1) Boltzmann Distribution Boltzmann factor Partition Function Two State System: energy and heat capacity Definition: reversible process Pressure Thermodynamic Identity
5 Probabilities

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## Lecture04-03.1.Boltzmann_Distribution - Last Time...

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