Life as a Molecule: The Kinetic Theory Adventure

1. N2 O2 N2 H2O N2 N2 O2 N2 N2 Kinetic Theory (or life as a molecule) Kinetic Theory

2. Objective • Be able to define temperature and pressure • Be able to perform simple calculations using the Ideal Gas Law Kinetic Theory

3. Reading • Wallace and Hobbs, pp. 64, 74 • Bohren and Albrecht • pp. 1-30 Kinetic Theory

4. Kinetic Theory • Once Upon A Time There Was A Molecule Kinetic Theory

5. Kinetic Theory • The molecule had no size or internal structure, but it was a happy molecule. Her name was Point Mass. m = mass Kinetic Theory

6. Kinetic Theory • One day, Point Mass decided to move. He only moved in one direction. He moved a a constant speed. x - direction velocity = vx Kinetic Theory

7. Kinetic Theory • He had momentum! momemtum = mvx x - direction velocity = vx Kinetic Theory

8. Kinetic Theory • He had so much momentum, he could not slow down when he saw the wall! Kinetic Theory

9. Kinetic Theory • He hit the wall! OUCH! Area A x x Kinetic Theory

10. Kinetic Theory • But much to his surprise, he rebounded! His collision was perfectly elastic! No energy was lost in the collision. Kinetic Theory

11. Kinetic Theory • He had the same momentum leaving the wall as he had before the collision, but in the opposite direction. momentum Kinetic Theory

12. Kinetic Theory • His change in momentum was Change in Momentum Kinetic Theory

13. Kinetic Theory • The force exerted on Point Mass by the wall was or Kinetic Theory

14. Kinetic Theory • Point Mass had other friends who are molecules identical to himself. Kinetic Theory

15. Kinetic Theory • They all move at the same velocity vx Kinetic Theory

16. Kinetic Theory • The molecules do not interact between themselves ... Kinetic Theory

17. x x Kinetic Theory • …but they all interacted with the wall Kinetic Theory

18. Kinetic Theory • The number of molecules (N) in a given volume (V) is the number density (n) V = Volume N = # of molecules n = number density Kinetic Theory

19. Kinetic Theory • The flux of molecules headed toward the wall is ... vx 1/2 moving towards at vx 1/2 moving away at vx vx Kinetic Theory

20. Kinetic Theory • The number of molecules striking the wall (A) during a time period (t) is ... A vx vx t Kinetic Theory

21. Kinetic Theory • The total time integrated force on the wall (A) is ... A Kinetic Theory

22. Kinetic Theory • The time-averaged force on the wall is ... A Kinetic Theory

23. Kinetic Theory • The average force per unit area is ... A Kinetic Theory

24. Kinetic Theory • …Which is pressure! A Kinetic Theory

25. Kinetic Theory • Lets modify one assumption. The molecules are moving at different speeds. Kinetic Theory

26. Kinetic Theory • Let’s replace vx2 with an average. Kinetic Theory

27. Kinetic Theory • In reality, the molecules are moving in all directions (not just x). Kinetic Theory

28. Kinetic Theory • Substitute back into the equation Kinetic Theory

29. Kinetic Theory • This looks like Kinetic Energy! Monatomic Gas KE Kinetic Theory

30. Kinetic Theory • Definition of Temperature • Temperature is a measure of the average KE of the molecules! • where k = Boltzmann Constant • = 1.38 x 10-23 J/K Kinetic Theory

31. Kinetic Theory • Substitute temperature into pressure Kinetic Theory

32. Kinetic Theory • Ideal Gas Law where ... p = pressure V = volume N = number of molecules T = temperature k = Boltzman Constant or Kinetic Theory

33. Kinetic Theory • Monatomic Molecules • Energy Is a Result of Atom’s Motion Only Kinetic Theory

34. Kinetic Theory • Polyatomic Molecules • Energy Is a Result of • Atom’s Motion • Rotation, Vibration and Oscillation of Molecule Kinetic Theory

35. Kinetic Energy Due to Rotation & Vibration Total Molecular Energy Kinetic Energy Due to Motion + = Kinetic Theory • Polyatomic Molecules • Need to Account for Other Forms of Molecular Energy Kinetic Theory

36. Kinetic Energy Due to Rotation & Vibration Total Molecular Energy Kinetic Energy Due to Motion + = Kinetic Theory • Polyatomic Molecules • More Complex Molecules Have More Rotational & Vibrational Energy Kinetic Theory

37. Kinetic Energy Due to Rotation & Vibration Total Molecular Energy Kinetic Energy Due to Motion + = Kinetic Theory • Polyatomic Molecules • More Complex Molecules Have More Rotational & Vibrational Energy Kinetic Theory

38. Kinetic Energy Due to Rotation & Vibration Total Molecular Energy Kinetic Energy Due to Motion + = Kinetic Theory • Polyatomic Molecules • Low Pressure • Approximates Ideal Gas • High Pressure • Deviates More Kinetic Theory

39. Kinetic Theory • Summary • pressure is a measure of the total kinetic energy of molecules, the force per unit area of these molecules • temperature is proportional to the average kinetic energy of molecules • from this kinetic theory viewpoint, we can derive the perfect gas law: Kinetic Theory

40. Kinetic Theory • We will return to the perfect gas law from a macroscopic point of view and derive exactly the same relationship: where ... p = pressure V = volume, n = number of moles N = number of molecules T = temperature k = Boltzmann constant m = mass, M = molecular weight or Kinetic Theory