14.2 The Boltzmann factor e (- ε /kT) December 7, 2010
Aims <ul><li>Examine one derivation of the Boltmann factor </li></ul><ul><li>Use the Boltzmann factor </li></ul><ul><li>St...
Getting extra energy by chance <ul><li>Processes happen when the energy  ε  per particle is a multiple of the average kine...
Think about playing pool…
How many will get lucky? <ul><li>A small fraction  f  will get this extra energy </li></ul><ul><li>This come from the othe...
How often you get lucky? <ul><li>The chances of hitting ten heads in a row is 1 in 2 10  which means every 1000 ish turns ...
 
 
 
 
Flying high Dense Less dense Gravity Diffusion
 
fraction of molecules mgh The idea is generally applicable
Hotter goes faster
 
 
 
rate of reaction is proportional to exp(-e/kT)
Soft matter
Soap, cell membranes and wristwatches
The molecules don’t care
Quick check questions (page 132)
Questions 1-7 (pg 134)
Test
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14.2 boltzmann factor

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Introduction to the Boltmann factor, 14.2 Advancing Physics

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14.2 boltzmann factor

  1. 1. 14.2 The Boltzmann factor e (- ε /kT) December 7, 2010
  2. 2. Aims <ul><li>Examine one derivation of the Boltmann factor </li></ul><ul><li>Use the Boltzmann factor </li></ul><ul><li>State what is proportional to the rate of a reaction </li></ul>
  3. 3. Getting extra energy by chance <ul><li>Processes happen when the energy ε per particle is a multiple of the average kinetic energy kT per particle </li></ul><ul><li>The multiple can be as high as 20 or 30 </li></ul><ul><li>To achieve this it must get lucky </li></ul>
  4. 4. Think about playing pool…
  5. 5. How many will get lucky? <ul><li>A small fraction f will get this extra energy </li></ul><ul><li>This come from the other particles </li></ul><ul><li>With a large number of particles the fraction f who get more energy will remain the same </li></ul><ul><li>The chances of getting lucky decreases with the number of collision required </li></ul><ul><li>A particle needs a run of luck… </li></ul>
  6. 6. How often you get lucky? <ul><li>The chances of hitting ten heads in a row is 1 in 2 10 which means every 1000 ish turns it will happen </li></ul><ul><li>Particles at room temperature interact billions of times per second so they get lucky often (10, 20 even 30 kT) </li></ul>
  7. 11. Flying high Dense Less dense Gravity Diffusion
  8. 13. fraction of molecules mgh The idea is generally applicable
  9. 14. Hotter goes faster
  10. 18. rate of reaction is proportional to exp(-e/kT)
  11. 19. Soft matter
  12. 20. Soap, cell membranes and wristwatches
  13. 21. The molecules don’t care
  14. 22. Quick check questions (page 132)
  15. 23. Questions 1-7 (pg 134)
  16. 24. Test

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