1 / 43

Due to Monday Holiday (Presidents Day 2/18), 2/14 Thursday DL Section (1,3,4) cancelled.

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. Quiz 5 10-10:20am TODAY Have your calculator ready. Cell phone calculator NOT allowed. Closed book.

ami
Download Presentation

Due to Monday Holiday (Presidents Day 2/18), 2/14 Thursday DL Section (1,3,4) cancelled.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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 TODAYHave 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 19Quiz 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. Particle Model of Matter What is the world made of? What holds the world together? Where did the universe come from?

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

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

  7. How big(small) is an atom, anyways? 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. ... 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 Richard P. Feynman

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

  12. PEmass-spring [-] Displacement from equilibrium y [+]

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

  14. PEmass-spring direction of force Dy [-] Displacement from equilibrium y [+]

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

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

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

  18. 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| ~Force PEmass-spring Equilibrium [-] Displacement from equilibrium y [+]

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

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

  21. Particle Model of Ebond Particle Model of Ethermal Example H2O What is Ebond in terms of KE and PE of individual atom (atom pair)? What is Ethermal in terms of KE and PE of individual atom (atom pair)?

  22. Particle Model of Ebond • Ebond for a substance is the amount of energy required to break apart “all” the bondsi.e. we define Ebond = 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. Ebond = ∑all pairs(PEpair-wise) • A useful approximation of the above relation is , Ebond ~ -(total number of nearest neighbor pairs)x() => Ebond of the system is determined by both the depth of the pair-wise potential well and the number of nearest-neighbors.

  23. A B 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 Etot greater? a) Situation A has a greater Etot b) Situation B has a greater Etot c) Both have the same Etot d) Impossible to tell

  24. A B 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 Etot greater? a) Situation A has a greater Etot

  25. A B 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 Etot greater? b) Situation B has a greater Etot

  26. A B 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 Ethermal greater? a) Situation A has a greater Ethermal b) Situation B has a greater Ethermal c) Both have the same Ethermal d) Impossible to tell

  27. A KE B KE 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 Ethermal greater? a) Situation A has a greater Ethermal b) Situation B has a greater Ethermal c) Both have the same Ethermal d) Impossible to tell

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

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

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

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

  32. Particle Model of Ethermal Ethermal is the energy associated with the random microscopic motions and vibrations of the particles. • We increased Ethermal 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 Ethermal Ethermal is the energy associated with the random microscopic motions and vibrations of the particles. • We increased Ethermal 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 Ethermal Ethermal is the energy associated with the random microscopic motions and vibrations of the particles. • We increased Ethermal 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 Ethermal increases BOTH KEaverage and PEaverage

  35. Particle Model of Ethermal and Ebond The energy associated with the random motion of particles is split between PEoscillation and KE .

  36. Mass on Spring Energy KE PE Etot position As we increase Etot we increase PEave and KEave PEave = KEave = Etot/2

  37. Particle Model of Ethermal and Ebond The energy associated with the random motion of particles is split between PEoscillation and KE .

  38. Particle Model of Ethermal and Ebond The energy associated with the random motion of particles is split between PEoscillation and KE . • For particles in liquids and solids, let’s not forget the part • of PE hat correspond to Ebond of the system. • Ebond 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 Ethermal and Ebond The energy associated with the random motion of particles is split between PEoscillation and KE . • For particles in liquids and solids, let’s not forget the part • of PE hat correspond to Ebond of the system. • Ebond 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, • KEall atoms = (1/2)Ethermal • PEall atoms = PEbond + PEoscillation = Ebond (PEbond )+ (1/2)Ethermal (PEoscillation) • => KEall atoms + PEall atoms = Ethermal + Ebond

  40. Particle Model of Ethermal and Ebond The energy associated with the random motion of particles is split between PEoscillation and KE . • For particles in liquids and solids, let’s not forget the part • of PE hat correspond to Ebond of the system. • Ebond 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, • KEall atoms = (1/2)Ethermal • PEall atoms = PEbond + PEoscillation = Ebond (PEbond )+ (1/2)Ethermal (PEoscillation) • => KEall atoms + PEall atoms = Ethermal + Ebond • In the gas phase, there are no springs, so there is no PEoscillation orPEbond

  41. Intro to Equipartition of Energy • 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.

  42. Intro to Equipartition of Energy • 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”.

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

More Related