Thermodynamics%20and%20Statistical%20Mechanics

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Thermodynamics and Statistical Mechanics

• Transport Processes

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Mean Free Path

• The average distance that a particles travels
  between collisions is called the mean free path,
  l. In order to have a collision, the centers of
  two particles of radius R must approach to within
  a distance of 2R d. The picture on the next
  slide illustrates this point.

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Collision Cross Section
s p d2
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Mean Free Path
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Mean Free Paths(?)
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Mean Free Path
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Some Molecular Speeds
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Effusion

• If there is a hole in a container of gas,
  molecules will escape through it. The rate at
  which they pass through the hole is equal to the
  flux of particles hitting the hole times the area
  of the hole, FA. Then the rate of change of the
  number of molecules in the container is

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Effusion Limit
If the hole is small equilibrium conditions
prevail, and F is known.
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Transport Processes

• 1. Molecular diffusion. The movement of the
  particles is of interest. This is particle
  transport.
• 2. Thermal conductivity. Particles carry energy
  from a high temperature region to a lower
  temperature region. This is energy transport.
• 3. Viscosity. Drag is created when particles move
  to a region which is moving at a different speed.
  This is momentum transport.

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Transport Processes
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Viscosity

• Consider a plate moving parallel to another plate
  with a layer of gas between them. The gas in
  contact with either plate is at rest relative to
  the plate, so there is a velocity gradient in the
  gas. A force F is applied to each plate to
  maintain the motion, and the area of the upper
  plate is A.

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Viscosity
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Viscosity

• Gas diffuses up and down, transferring x momentum
  from layer to layer. The gas that moves in the
  y direction is going slower than the layer it
  moves into, and the gas that moves in the y
  direction is going faster than the layer it moves
  into.

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Viscosity
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Viscosity

• First we need to know how far particles travel
  between collisions in the y direction. We must
  find the average value of y l cos q, averaged
  over the flux of molecules.

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Viscosity
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Viscosity
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Viscosity
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Diffusion
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Thermal Conductivity
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Thermal Conductivity
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Transport Processes