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Thermodynamics and Statistical Mechanics

Thermodynamics and Statistical Mechanics. Kinetic Theory of Gases. Mixing of Two Ideal Gases. Change of Gibbs Function. An expression is needed for the specific Gibbs function. Specific Gibbs Function. Specific Entropy. Specific Gibbs Function. Specific Gibbs Function.

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Thermodynamics and Statistical Mechanics

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  1. Thermodynamics and Statistical Mechanics Kinetic Theory of Gases Thermo & Stat Mech - Spring 2006 Class 14

  2. Mixing of Two Ideal Gases Change of Gibbs Function An expression is needed for the specific Gibbs function. Thermo & Stat Mech - Spring 2006 Class 14

  3. Specific Gibbs Function Thermo & Stat Mech - Spring 2006 Class 14

  4. Specific Entropy Thermo & Stat Mech - Spring 2006 Class 14

  5. Specific Gibbs Function Thermo & Stat Mech - Spring 2006 Class 14

  6. Specific Gibbs Function Thermo & Stat Mech - Spring 2006 Class 14

  7. Mixing of Two Ideal Gases Thermo & Stat Mech - Spring 2006 Class 14

  8. For the Same Pressure Thermo & Stat Mech - Spring 2006 Class 14

  9. For the Same Pressure Thermo & Stat Mech - Spring 2006 Class 14

  10. For the Same Volume Thermo & Stat Mech - Spring 2006 Class 14

  11. For the Same Volume Thermo & Stat Mech - Spring 2006 Class 14

  12. Basic Assumptions • 1. A macroscopic volume contains a large number of molecules. • 2. The separation of molecules is large compared to molecular dimensions. • 3. No forces exist between molecules except those associated with collisions • 4. The collisions are elastic. Thermo & Stat Mech - Spring 2006 Class 14

  13. Basic Assumptions • When no external forces are applied: • 5. The molecules are uniformly distributed within a container. • 6. The directions of the velocities of the molecules are uniformly distributed. • The fraction of molecules with speeds in the range v to v + dv is: f (v) dv Thermo & Stat Mech - Spring 2006 Class 14

  14. Molecular Speeds • f (v) is the probability density. Thermo & Stat Mech - Spring 2006 Class 14

  15. Gas Pressure Thermo & Stat Mech - Spring 2006 Class 14

  16. Gas Pressure Thermo & Stat Mech - Spring 2006 Class 14

  17. Gas Pressure Thermo & Stat Mech - Spring 2006 Class 14

  18. Molecular Flux Thermo & Stat Mech - Spring 2006 Class 14

  19. Molecular Flux Thermo & Stat Mech - Spring 2006 Class 14

  20. Molecular Flux Thermo & Stat Mech - Spring 2006 Class 14

  21. Gas Pressure Thermo & Stat Mech - Spring 2006 Class 14

  22. Ideal Gas Law Thermo & Stat Mech - Spring 2006 Class 14

  23. Molecular Kinetic Energy Thermo & Stat Mech - Spring 2006 Class 14

  24. Equipartition of Energy Thermo & Stat Mech - Spring 2006 Class 14

  25. Internal Energy Thermo & Stat Mech - Spring 2006 Class 14

  26. Heat Capacities Thermo & Stat Mech - Spring 2006 Class 14

  27. Maxwell Velocity Distribution • Consider a gas at equilibrium. The number of molecules in any range of velocity does not change. Collisions cause individual molecules to change velocity, but the distribution does not change. For every collision that changes the distribution, there must be one that changes it back. Thermo & Stat Mech - Spring 2006 Class 14

  28. Molecular Collisions Thermo & Stat Mech - Spring 2006 Class 14

  29. Molecular Collisions Thermo & Stat Mech - Spring 2006 Class 14

  30. Maxwell Distribution Thermo & Stat Mech - Spring 2006 Class 14

  31. Evaluation of Constants Thermo & Stat Mech - Spring 2006 Class 14

  32. Maxwell Distribution Thermo & Stat Mech - Spring 2006 Class 14

  33. Maxwell Distribution Thermo & Stat Mech - Spring 2006 Class 14

  34. Some Molecular Speeds Thermo & Stat Mech - Spring 2006 Class 14

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