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Semester Plan

Semester Plan. Quizzes will generally be on Wednesdays Quiz 12 Wednesday Standards 33–36 Make-ups generally on Tuesdays. Semester 1 Standards. Count toward year grade Do not count toward semester 2 grade Still can be made up this semester Revise! Revise! Revise!. Thermodynamic Paths.

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Semester Plan

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  1. Semester Plan • Quizzes will generally be on Wednesdays • Quiz 12 Wednesday • Standards 33–36 • Make-ups generally on Tuesdays

  2. Semester 1 Standards • Count toward year grade • Do not count toward semester 2 grade • Still can be made up this semester • Revise! Revise! Revise!

  3. Thermodynamic Paths energy transfers § 15.1–15.4

  4. Definitions System: bodies and surroundings exchanging energy (usually not exchanging matter) State: unique set of p, V, T, (n or N) (state variables) Process: change in state of a system

  5. Internal Energy U U SKi + SSVij i i j<i • Ki = kinetic energy of molecule i wrt com • Vij = intermolecular potential energy of i and j Does not include potential or kinetic energy of bulk object Each thermodynamic state has a unique U (U is a state function)

  6. Monatomic Ideal Gas U = S ½ mivi2 = S 3/2 kT = 3/2 NkT = 3/2 nRT

  7. Question All other things being equal, adding heat to a system increases its internal energy U. • True. • False.

  8. Question All other things being equal, lifting a system to a greater height increases its internal energy U. • True. • False.

  9. Question All other things being equal, accelerating a system to a greater speed increases its internal energy U. • True. • False.

  10. Question All other things being equal, doing work to compress a system increases its internal energy U. • True. • False.

  11. Energy Transfer Conventions Q: heat added to the systemsurroundings  systemBecause of a temperature difference W: work done by the systemsystem  surroundingsAchieved by a volume change

  12. Work W • The surroundings exert pressure on the system. • If the system expands, it does work on the surroundings. • So, W > 0, • and the surroundings do negative work on the system.

  13. First law of Thermodynamics DU = Q – W U is a state function

  14. Conservation of Energy DU of a system = heat added to the system + work done on the system

  15. Work and Heat Q and W depend on the path taken between initial and final states. DU = Q – Wis path-independent

  16. pV Diagrams • W = area under pV curve • Direction matters Source: Y&F, Figure 19.6a

  17. Question What is this system doing? • Expanding • Contracting • Absorbing heat at constant volume • Absorbing heat at constant pressure Source: Y&F, Figure 19.6b

  18. Question What is the sign of the work W for this process? • + • – • 0 • Cannot be determined Source: Y&F, Figure 19.6b

  19. Question What is this system doing? • Expanding at constant volume • Expanding at constant temperature • Expanding at constant pressure Source: Y&F, Figure 19.6c

  20. Question How is the temperature of this ideal gas changing? • Increasing • Decreasing • Remaining constant • Cannot be determined Source: Y&F, Figure 19.6c

  21. Simple Case Expansion at constant pressure W = pDV Source: Y&F, Figure 19.6c

  22. Question The work done by a thermodynamic system in a cyclic process (final state is also the initial state) is zero. • True. • False. Source: Y&F, Figure 19.12

  23. W Cyclic Process W 0 Is the system a limitless source of work? (Of course not.) Source: Y&F, Figure 19.12

  24. Cyclic Processes DU = U1 – U1 = 0 so Q – W = 0 so Q = W • Total work output = total heat input

  25. Work out = Heat in Does this mean cyclic processes convert heat to work with 100% efficiency? (Of course not.) Waste heat is expelled, not recovered.

  26. Types of Processes cool names, easy rulesSummarized in Table 15.1

  27. Reversible • An infinitesimal change in conditions reverses the direction • Requires no non-conservative processes • no friction • no contact between different temperatures • An ideal concept • not actually possible • some processes can get close

  28. Constant pressure • “Isobaric” • W = PDV

  29. Constant Volume • “Isochoric” • W = 0

  30. Constant Temperature • “Isothermal” • Ideal gas: W = nRT ln(Vf/Vi)

  31. No Heat Flow • “Adiabatic” • Q = 0 • W: more complicated • PfVfg = PiVig • g = heat capacity ratio CP/CV CP for constant pressure CV for constant volume

  32. Specific Heats of Ideal Gases § 15.6

  33. Constant Volume or Pressure • Constant volume: heating simply makes the molecules go faster • Constant pressure: As the molecules speed up, the system expands against the surroundings, doing work • It takes more heat to get the same DT at constant pressure than at constant volume

  34. Constant Volume U = 3/2 nRT for a monatomic gas DU = 3/2 nRDT DU = Q – W = Q Q = 3/2 nRDT Molar specific heat CV = Q/(nDT) CV = 3/2 R

  35. Constant Pressure U = 3/2 nRT DU = 3/2 nRDT DU = Q – W W = PDV = nRDT Q = DU + W = 3/2 nRDT + nRDT = 5/2 nRDT Molar specific heat CV = Q/(nDT) CV = 5/2 R

  36. Heat Capacity Ratio g = CP/CV = (5/2)/(3/2) = 5/3 For a monatomic ideal gas

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