The Kinetic Theory of Gases (cont.)

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Chapter 21

• The Kinetic Theory of Gases (cont.)

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Outline

• The Boltzmann distribution law (21.5)
• Distribution of molecular speeds (21.6)

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The Boltzmann distribution law

• nV(E) number density or the distribution
  function.
• nV(E)dE the number of molecules per unit volume
  with energy between E and EdE.
• Physical meaning of the Boltzmann distribution
  law
• The probability of finding the molecules in a
  particular energy state varies exponentially as
  the negative of the energy divided by kBT.

4
Example 21.5 Thermal excitation of atomic energy
levels

• Consider a gas at a temperature of 2500 K whose
  atoms can occupy only two energy levels separated
  by 1.50 eV (1eV 1.60 x 10-19 J).
• Determine the ratio of the number of atoms in the
  higher energy level to the number in the lower
  energy level.
• Answer 9.64 x 10-4.

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Distribution of molecular speeds

• Maxwell-Boltzmann speed distribution
• Nv dv the number of molecules with speeds
  between v and v dv.
• N the total number of molecules
• Root-mean-square, average, and most probable
  speeds (derivation see Problems 41, 62)

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Homework

• Ch. 21, P. 665, Problems 41, 62.