2009.04.13-ECE659-L35-notes

2009.04.13-ECE659-L35-notes - qV kT u d B E dtVI F e F F F...

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ECE 659 Quantum Transport: Atom to Transistor Lecture 35: Entropy Supriyo Datta Spring 2009 Notes prepared by Samiran Ganguly
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( 29 ( 29 1 1 d u d u d u F f f I dE F f f - - - 1 2 , , 0, 1 u d d u f f f f F F = = = = 2 μ 1 Second law of Thermodynamics: ln B S k W S = ( 29 ( 29 ( 29 ( 29 ( 29 2 1 1 2 2 1 2 1 1 1 u d E kT E kT kT f F f F f f e e e - - - - - = - = = 1 2 ln u B d F qV k T F = - = 1 dS dE T = S E hotter colder
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N spins: W: 1 way 2 N ways Change in entropy: ln 2 0 ln 2 N B B E S k T E Nk T ∆ = - + Total spin: tanh 2 B qV s N k T = S V Another way to see this: 2 2 2 2 tanh 2 qV kT u d qV kT qV kT u d qV kT
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Unformatted text preview: qV kT u d B E dtVI F e F F F e e s F F e e qV k T--= =--= = + + = 1 impurity flip = 1 electron flow For 1 electron flow, changes by 2 s 2 q ds I dt dQ dt = tanh 2 2 2 B qs qN qV Q k T = = dQ E dtV VdQ dt = = Q V tanh V Q Q V = N T 2 qN 2 B k T q This gives: ln 2 ln 2 B E Q V Nk T = =...
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2009.04.13-ECE659-L35-notes - qV kT u d B E dtVI F e F F F...

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