1. Due to Monday Holiday (Presidents Day 2/18), 2/14 Thursday DL Section (1,3,4) cancelled. (DL Section 7,10 meet as normal) 2/15 Friday DL Section 2,5,6 cancelled.

2. Quiz 5 10-10:20am TODAY Have your calculator ready. Cell phone calculator NOT allowed. Closed book Quiz 1 Re-evaluation Request Due this Thursday, 2/14. Quiz 2 Re-evaluation Request Due next Thursday, 2/21. Turn in you original Quiz along with the Re-evaluation Request Form. Note: It is possible for your grade to be lowered after the re-evaluation. Quiz 3 info (grades, ave score) will be posted this week. Quiz 4 graded, scores being recorded. Next lecture February 19 Quiz 6 will cover the material from today’s lecture (excluding equipartition) and material from DLM9 and 10, excluding FNTs for DLM11.

3. What is the world made of? What holds the world together? Where did the universe come from?

4. What is the world made of? What holds the world together? Where did the universe come from? Particle Model of Matter

5. Normal Matter : Particles Bouncing Around! Understand the particulate nature of matter

6. How big(small) is an atom, anyways?

7. 1 or 2 x 10 -10 m = 1 or 2Å (Angstrom) in radius

8. How big(small) is an atom, anyways? 1 or 2 x 10 -10 m = 1 to 2Å (Angstrom) in radius

9. Normal Matter : Particles Bouncing Around! Model Bonded Atoms as Masses on Spring ~ two atomic size particles interacting via“pair-wise potential”

10. Richard P. Feynman... I believe it is the atomic hypothesis... that all things are made of atoms--little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another... If all scientific information were to be lost, these would be the most valuable ideas to pass on to future generations. R.P. Feynman, Physics Nobel Laureate in 1965

11. r PE Distance between the atoms Repulsive: Atoms push apart as they get too close “pair-wise potential” a.k.a. Lennard-Jones Potential Flattening: atoms have negligible forces at large separation.

12. Displacement from equilibrium y[+][-] PE mass-spring

13. Displacement from equilibrium y[+][-] PE mass-spring Question: If the mass is displaced upwards, the following is true: a)The dot moves up and to the right, and the force vector points to the left. b)The dot moves up and to the right, and the force vector points to the right. c)The dot moves up and to the left, and the force vector points to the right. d)None of the above.

14. Displacement from equilibrium y[+][-] direction of force yy PE mass-spring

15. Displacement from equilibrium y[+][-] direction of force PE mass-spring

16. Displacement from equilibrium y[+][-] PE mass-spring On this side force pushes up On this side force pushes down Equilibrium Forces from potentials point in direction that (locally) lowers PE

17. Displacement from equilibrium y[+][-] PE mass-spring Equilibrium Potential Energy curve of a spring:  PE = (1/2) k (  x) 2 W (work) =  PE =F ||  x Force = -  PE /  x = - k x

18. Displacement from equilibrium y[+][-] PE mass-spring Equilibrium ~Force Potential Energy curve of a spring:  PE = (1/2) k (  x) 2 W (work) =  PE =F ||  x Force = -  PE /  x = - k x Force is always in direction that decreases PE Force is related to the slope -- NOT the value of PE The steeper the PE vs r graph, the larger the force |F|=|d(PE)/dr|

19. r PE Distance between the atoms Repulsive: Atoms push apart as they get too close “pair-wise potential” a.k.a. Lennard-Jones Potential Flattening: atoms have negligible forces at large separation.

20. PE KE E tot Separation (x10 -10 m) Energy (x10 -21 J)

21. Example H 2 O Particle Model of E bond Particle Model of E thermal What is E bond in terms of KE and PE of individual atom (atom pair)? What is E thermal in terms of KE and PE of individual atom (atom pair)?

22. E bond for a substance is the amount of energy required to break apart “all” the bonds i.e. we define E bond = 0 when all the atoms are separated The bond energy of a large substance comes from adding all the potential energies of particles at their equilibrium positions. E bond = ∑ all pairs (PE pair-wise ) A useful approximation of the above relation is, E bond ~ -(total number of nearest neighbor pairs)x(  ) => E bond of the system is determined by both the depth of the pair-wise potential well and the number of nearest-neighbors. Particle Model of E bond

23. A pair of atoms are interacting via a atom-atom potential. Only these two atoms are around. In two different situations, the pair have a different amount of total energy. In which situation is E tot greater? a) Situation A has a greater E tot b) Situation B has a greater E tot c) Both have the same E tot d) Impossible to tell A B

24. A pair of atoms are interacting via a atom-atom potential. Only these two atoms are around. In two different situations, the pair have a different amount of total energy. In which situation is E tot greater? a) Situation A has a greater E tot A B

25. A pair of atoms are interacting via a atom-atom potential. Only these two atoms are around. In two different situations, the pair have a different amount of total energy. In which situation is E tot greater? b) Situation B has a greater E tot A B

26. A pair of atoms are interacting via a atom-atom potential. Only these two atoms are around. In two different situations, the pair have a different amount of total energy. In which situation is E thermal greater? a) Situation A has a greater E thermal b) Situation B has a greater E thermal c) Both have the same E thermal d) Impossible to tell A B

27. A pair of atoms are interacting via a atom-atom potential. Only these two atoms are around. In two different situations, the pair have a different amount of total energy. In which situation is E thermal greater? a) Situation A has a greater E thermal b) Situation B has a greater E thermal c) Both have the same E thermal d) Impossible to tell A B KE

28. Okay. Now let us look at the same problem from the perspective of the KE and PE of individual atoms. initial final

29. Okay. Now let us look at the same problem from the perspective of the KE and PE of individual atoms. initial final

30. Particle Model of E thermal E thermal is the energy associated with the random microscopic motions and vibrations of the particles.

31. Particle Model of E thermal E thermal is the energy associated with the random microscopic motions and vibrations of the particles. We increased E thermal by putting more energy into the system

32. Particle Model of E thermal E thermal is the energy associated with the random microscopic motions and vibrations of the particles. We increased E thermal by putting more energy into the system KE and PE keep changing into one another as the atoms vibrate, so we cannot make meaningful statements about instantaneous KE and PE

33. Particle Model of E thermal E thermal is the energy associated with the random microscopic motions and vibrations of the particles. We increased E thermal by putting more energy into the system KE and PE keep changing into one another as the atoms vibrate, so we cannot make meaningful statements about instantaneous KE and PE We can make statements about average KE and PE.

34. Particle Model of E thermal E thermal is the energy associated with the random microscopic motions and vibrations of the particles. We increased E thermal by putting more energy into the system KE and PE keep changing into one another as the atoms vibrate, so we cannot make meaningful statements about instantaneous KE and PE We can make statements about average KE and PE. Increasing E thermal increases BOTH KE average and PE average

35. Particle Model of E thermal and E bond The energy associated with the random motion of particles is split between PE oscillation and KE.

36. Mass on Spring Energy position As we increase E tot we increase PE ave and KE ave PE ave = KE ave = E tot /2 E tot PE KE

37. Particle Model of E thermal and E bond The energy associated with the random motion of particles is split between PE oscillation and KE.

38. Particle Model of E thermal and E bond The energy associated with the random motion of particles is split between PE oscillation and KE. For particles in liquids and solids, let’s not forget the part of PE hat correspond to E bond of the system. E bond of the system is determined by both the depth of the pair-wise potential well and the number of nearest-neighbors.

39. Particle Model of E thermal and E bond The energy associated with the random motion of particles is split between PE oscillation and KE. For particles in liquids and solids, let’s not forget the part of PE hat correspond to E bond of the system. E bond of the system is determined by both the depth of the pair-wise potential well and the number of nearest-neighbors. For solids and liquids, KE all atoms = (1/2)E thermal PE all atoms = PE bond + PE oscillation = E bond (PE bond )+ (1/2)E thermal (PE oscillation ) => KE all atoms + PE all atoms = E thermal + E bond

40. Particle Model of E thermal and E bond The energy associated with the random motion of particles is split between PE oscillation and KE. For particles in liquids and solids, let’s not forget the part of PE hat correspond to E bond of the system. E bond of the system is determined by both the depth of the pair-wise potential well and the number of nearest-neighbors. For solids and liquids, KE all atoms = (1/2)E thermal PE all atoms = PE bond + PE oscillation = E bond (PE bond )+ (1/2)E thermal (PE oscillation ) => KE all atoms + PE all atoms = E thermal + E bond In the gas phase, there are no springs, so there is no PE oscillation or PE bond

41. If the atoms do not move too far, the forces between them can be modeled as if there were springs between the atoms. Each particle in a solid or liquid oscillates in 3 dimensions about its equilibrium positions as determined by its single-particle potential. Intro to Equipartition of Energy

42. Another way of saying is, each particle has six “ways” to store the energy associated with its random thermal motion. We call this “way” for a system to have thermal energy as a “mode”. Intro to Equipartition of Energy

43. Closed Book Don’t forget to fill in your DL section number! !!THIS QUIZ IS TWO-SIDED!!