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Lecture_24 - PHYS342 Fall2011 Lecture 24 Boltzmann Equation...

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PHYS 342 F ll 2011 Fall 2011 Lecture 24: Boltzmann Equation, N b f A il bl St t Number of Available States, Detailed Statistics for a Few Particles with Quantized Energies Ron Reifenberger Birck Nanotechnology Center Purdue University 1 Lecture 24 1
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The Maxwell-Boltzmann Factor: The System Inputs: N 4 d h bl l ( ll h d ) N=4 distinguishable particles (to illustrate the ideas) Equally spaced allowed energies 0 ε , 1 ε , 2 ε …. The allowed energies are now QUANTIZED. Add fi d f E 5 ( ill h id ) Add fixed amount of energy, say tot =5 ε (to illustrate the ideas) Let n 1 =number of particles with energy ε 1 , etc. How many available states does the system have for a 5 ε fixed total energy of 5 ε ? 1 2 6 ( , , ...... ) 5 tot r r r r E n n n n 2 2 4 r r N n
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State A : B : C : Possible States for a Fixed Energy of E tot =5 ε 4 ε 5 ε 4 ε 5 ε 3 ε 2 ε 3 ε 2 ε Microscopic Model 1 ε 0 ε 1 ε 0 ε State D : E : F : 4 ε 5 ε 4 ε 5 ε 3 ε 2 ε 3 ε 2 ε 3 1 ε 0 ε 1 ε 0 ε
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