Thermodynamics and Statistical Mechanics

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Thermodynamics and Statistical Mechanics

• Kinetic Theory of Gases

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Mixing of Two Ideal Gases
Change of Gibbs Function
An expression is needed for the specific Gibbs
function.
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Specific Gibbs Function
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Specific Entropy
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Specific Gibbs Function
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Specific Gibbs Function
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Mixing of Two Ideal Gases
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For the Same Pressure
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For the Same Pressure
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For the Same Volume
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For the Same Volume
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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.

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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

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Molecular Speeds

• f (v) is the probability density.

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Gas Pressure
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Gas Pressure
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Gas Pressure
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Molecular Flux
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Molecular Flux
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Molecular Flux
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Gas Pressure
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Ideal Gas Law
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Molecular Kinetic Energy
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Equipartition of Energy
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Internal Energy
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Heat Capacities
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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.

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Molecular Collisions
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Molecular Collisions
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Maxwell Distribution
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Evaluation of Constants
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Maxwell Distribution
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Maxwell Distribution
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Some Molecular Speeds