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Lecture 12—Ideas of Statistical Mechanics Chapter 4, Monday February 4 th

Lecture 12—Ideas of Statistical Mechanics Chapter 4, Monday February 4 th. Finish the model for a rubber band Demonstration Spins on a lattice. Reading: All of chapter 4 (pages 67 - 88) ***Homework 4 due Thu. Feb. 7th**** Assigned problems, Ch. 4 : 2, 8, 10, 12, 14

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Lecture 12—Ideas of Statistical Mechanics Chapter 4, Monday February 4 th

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  1. Lecture 12—Ideas of Statistical Mechanics Chapter 4, Monday February 4th • Finish the model for a rubber band • Demonstration • Spins on a lattice Reading: All of chapter 4 (pages 67 - 88) ***Homework 4 due Thu. Feb. 7th**** Assigned problems, Ch. 4: 2, 8, 10, 12, 14 Exam 1: Fri. Feb. 8th (in class), chapters 1-4 Review: Thu. 7th at 5:30pm, tentatively in NPB1220

  2. Rubber band model Dimensionless length: d n+ = # of forward links; n- = # of backward links N = n+ + n- = total # of links Length l = (n+-n-)d = (2n+-N)d

  3. Rubber band model Sterling’s approximation: ln(N!) = NlnN-N d

  4. Rubber band model Sterling’s approximation: ln(N!) = NlnN-N d

  5. Rubber band model 2nd law: dU = TdS + Fdl

  6. A simple model of spins on a lattice Magnetic moment m Quantum spins in a magnetic field B n1 = # of ‘up’ spins; n2 = # of ‘down’ spins N = n1 + n2 = total # of spins Energy U = -(n1-n2)e = (N- 2n1)e

  7. Statistical Mechanics – ideas and definitions 64 An example: Coin toss again!! width

  8. A simple model of spins on a lattice Magnetic moment m Quantum spins in a magnetic field B n1 = # of ‘up’ spins; n2 = # of ‘down’ spins N = n1 + n2 = total # of spins Energy U = -(n1-n2)e = (N- 2n1)e

  9. A simple model of spins on a lattice

  10. A simple model of spins on a lattice

  11. A simple model of spins on a lattice

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