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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