1 / 49

Chapter 3

Chapter 3. Interactions and Implications. Entropy. Entropy. Let’s show that the derivative of entropy with respect to energy is temperature for the Einstein solid. Let’s show that the derivative of entropy with respect to energy is temperature for the monatomic ideal gas.

jase
Download Presentation

Chapter 3

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. Chapter 3 Interactions and Implications

  2. Entropy

  3. Entropy

  4. Let’s show that the derivative of entropy with respect to energy is temperature for the Einstein solid.

  5. Let’s show that the derivative of entropy with respect to energy is temperature for the monatomic ideal gas.

  6. Let’s prove the 0th law of thermodynamics.

  7. An example with the Einstein Solid

  8. Heat Capacity, Entropy, Third Law Difficult to impossible Easy • Calculate W • Calculate S = kBln(W) • Calculate dS/dU = 1/T • Solve for U(T) • Cv = dU/dT Easy Easy – we’ll see a better way in Ch . 6 w/o needing W Easy

  9. Heat capacity of aluminum Let’s calculate the entropy changes in our heat capacity experiment.

  10. Heat Capacity, Entropy, Third Law What were the entropy changes in the water and aluminum? DS = Sf – Si = C ln(Tf/Ti)

  11. Heat Capacity, Entropy, Third Law As a system approaches absolute zero temperature, all processes within the system cease, and the entropy approaches a minimum.

  12. The Third Law It doesn’t get that cold. As a system approaches absolute zero temperature, all processes within the system cease, and the entropy approaches a minimum.

  13. Stars and Black Holes modeled as orbiting particles m1 Show the potential energy is equal to negative 2 times the kinetic energy. r r m2

  14. Stars and Black Holes modeled as orbiting particles m1 Show the potential energy is equal to negative 2 times the kinetic energy. r r m2

  15. Stars and Black Holes modeled as orbiting particles m1 What happens when energy is added? If modeled as an ideal gas what is the total energy and heat capacity in terms of T? r r m2

  16. Stars and Black Holes modeled as orbiting particles m1 Use dimensional analysis to argue potential energy should be of order -GM2/R. Estimate the number of particles and temperature of our sun. r r m2

  17. Stars and Black Holes modeled as orbiting particles m1 What is the entropy of our sun? r r m2

  18. Black Holes What is the entropy a solar mass black hole?

  19. Black Holes What are the entropy and temperature a solar mass black hole?

  20. S U

  21. Mechanical Equilibrium

  22. Mechanical Equilibrium

  23. Mechanical Equilibrium

  24. Diffusive Equilibrium

  25. Diffusive Equilibrium Chemical potential describes how particles move.

  26. The Thermodynamic Identity

  27. Diffusive Equilibrium Chemical potential describes how particles move.

  28. Diffusive Equilibrium Chemical potential describes how particles move.

  29. Diffusive Equilibrium Chemical potential describes how particles move.

  30. Diffusive Equilibrium Chemical potential describes how particles move.

  31. Entropy http://www.youtube.com/watch?v=dBXL93984cQ

  32. The Thermodynamic Identity

  33. The Thermodynamic Identity

  34. Paramagnet

  35. Paramagnet U +mB Down, antiparallel 0 -mB Up, parallel

  36. Paramagnet

  37. Paramagnet

  38. Paramagnet • M and U only differ by B

  39. Nuclear Magnetic Resonance wo = 900 MHz B = 21.2 T wo = g B g = 42.4 (for protons)

  40. Nuclear Magnetic Resonance S Inversion recovery Quickly reverse magnetic field B NmB Low U (negative  stable) Work on system lowers entropy but it will absorb any available energy to try and slide towards max S U M NmB B NmB High U (positive  unstable) Work on system lowers entropy but it will absorb any available energy to try and slide towards max S t

  41. Analytical Paramagnet

  42. Analytical Paramagnet

  43. Analytical Paramagnet

  44. Analytical Paramagnet

  45. Paramagnet

  46. Paramagnet Properties

  47. Paramagnet Properties

  48. Paramagnet Heat Capacity

  49. Magnetic Energies

More Related