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Chapter 19 The Kinetic Theory of Gases

Chapter 19 The Kinetic Theory of Gases. Amedeo Avogadro (1776 -1856). Avogadro’s number Mole – amount of substance containing a number of atoms (molecules) equal to the number of atoms in a 12 g sample of 12 C This number is known as Avogadro’s number ( N A ):

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Chapter 19 The Kinetic Theory of Gases

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  1. Chapter 19 The Kinetic Theory of Gases

  2. Amedeo Avogadro (1776 -1856) • Avogadro’s number • Mole – amount of substance containing a number of atoms (molecules) equal to the number of atoms in a 12 g sample of 12C • This number is known as Avogadro’s number (NA): • NA = 6.02 x 1023 mol -1 • The number of moles in a sample • N – total number of atoms (molecules) • M – total mass of a sample, m – mass of a single atom (molecule)

  3. Ideal gases • Ideal gas – a gas obeying the ideal gas law: • R – gas constant • R = 8.31 J/mol ∙ K • k – Boltzmann constant • k = 1.38 x 1023 J/K

  4. Chapter 19 Problem 12

  5. Ideal gases

  6. Ideal gases • Root-mean-square (RMS) speed:

  7. Translational kinetic energy • Average translational kinetic energy: • At a given temperature, ideal gas molecules have the same average translational kinetic energy • Temperature is proportional to the average translational kinetic energy of a gas

  8. Internal energy • For the sample of n moles, the internal energy: • Internal energy of an ideal gas is a function of gas temperature only

  9. Work done by an ideal gas at constant temperature • Isothermal process – a process at a constant temperature • Work (isothermal expansion)

  10. Work done by an ideal gas at constant volume and constant pressure • Isochoric process – a process at a constant volume • Isobaric process – a process at a constant pressure

  11. Molar specific heat at constant volume • Heat related to temperature change: • Internal energy change:

  12. Molar specific heat at constant pressure • Heat related to temperature change: • Internal energy change:

  13. Chapter 19 Problem 41

  14. Adiabatic expansion of an ideal gas

  15. Adiabatic expansion of an ideal gas

  16. Chapter 19 Problem 56

  17. Free expansion of an ideal gas

  18. Degrees of freedom and molar specific heat • Degrees of freedom: • 3 translations, 3 rotations, 3 oscillations • In polyatomic molecules different • degrees of freedom contribute at • different temperatures

  19. Mean free path • In reality, molecules collide not only with the walls of the container, but also with each other • Mean free path: average distance traversed by a molecule between collisions

  20. James Clerk Maxwell (1831-1879) • Distribution of molecular speeds • Not all the molecules have the same speed • Maxwell’s speed distribution law: • P(v)dv – fraction of molecules with speeds in the range from v to v + dv

  21. Distribution of molecular speeds • Distribution function is normalized to 1: • Average speed: • RMS speed: • Most probable • speed:

  22. Chapter 19 Problem 94

  23. Answers to the even-numbered problems Chapter 19: Problem 2 (a) 0.0127; (b) 7.64 × 1021 atoms

  24. Answers to the even-numbered problems Chapter 19: Problem 28 0.32 nm

  25. Answers to the even-numbered problems Chapter 19: Problem 40 3.4 kJ

  26. Answers to the even-numbered problems • Chapter 19: • Problem 50 • 0.375 mol; • (b) 1.09 kJ; • (c) 0.714

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