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Kinetic Theory of Gases. Overview. Assume atomic picture of gases Simpler than solids/liquids, as interactions can be neglected Predict behavior E.g., relations between P and V , P and T … Test in lab experiments. Basic Picture. Gas consists of noninteracting particles

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Presentation Transcript
  • Assume atomic picture of gases
    • Simpler than solids/liquids, as interactions can be neglected
  • Predict behavior
    • E.g., relations between P and V, P and T…
  • Test in lab experiments
basic picture
Basic Picture
  • Gas consists of noninteracting particles
  • They move around randomly
  • Temperature corresponds to (average) speed of particles
    • Hotter  faster
  • Pressure a manifestation of collisions with container walls
basic processes
Basic Processes
  • Thermal expansion
  • Evaporation
    • A cooling process
  • Dissolving solids in liquids
  • Reaction rates
more on temperature
More on Temperature
  • Prediction of kinetic theory:

v is the average speed

T is the temperature (in Kelvins)

m is the mass of a gas particle

kB is Boltzmann’s constant

  • Note that
more on pressure
More on Pressure

Weight W

  • Canonical example: container wih movable piston
  • P is the average force per unit area due to collisions with walls
    • Average because it fluctuates
  • Weight on piston balances this force, in equilibrium
    • W tells us P of gas
now change something
Now change something…
  • E.g. add weight to the piston (T = const)
  • Forces out of equilibrium; piston drops
  • Collision rate increases until forces again balance
  • P has increased, V decreased
  • In fact,


computer simulation
Computer Simulation
  • Allows changing N, W, v
  • Replaces tedious mathematical analysis
  • Explore all relations encoded in the Ideal Gas Law: PV = NkBT
  • Most of these relations are qualitatively obvious, some even quantitatively so!
another example
Another Example
  • Increase T keeping P fixed
    • Note: doubling T means increasing v by
  • Faster particles means harder collisions and more rapid
  • Piston rises, reducing collision rate
  • Equilibrium is restored
  • Model gives

(constant P)

another example10
Another Example
  • Increase N with P and T held fixed
  • More particles means more collisions, piston rises
  • Reduced collision rate restores equilibrium
  • In detail:

(constant T, P)

a slightly more complicated one
A slightly more complicated one…
  • Increase T with V and N held constant
  • Do it in two steps:
    • Increase T with P unchanged
    • Increase W to return V to its original value
  • Result:

(constant V, N)

verifying the predictions
Verifying the Predictions
  • These relations are simple predictions of atomic/kinetic theory
  • If they are found to hold in experiments, we gain confidence that the atomic picture is correct!
  • Several of them are easily checked in lab exercises
sample exercises
Sample Exercises
  • Calculate v for gas at room temperature
  • It may take a few seconds for a smell to reach you from across a room, e.g. from a perfume bottle. What does this suggest about the path taken by the perfume particles?
  • R. P. Feynman, et al., The Feynman Lectures on Physics, v. I (Addison Wesley, 1970)