Molecular basis for pressure and the ideal-gas law.

If a molecule, with radius r, averages n collisions as it travels distance L, then the average distance between collisions is L/n, and is called the mean free path λ, \lambda =\frac{1}{4\sqrt{2}\pi (\frac{N}{V})r^{2}}.

The mean free path is independent of temperature.

The mean time between collisions is temperature dependent.

Assumptions for ideal gas:

  • # of molecules N is large
  • They obey Newton’s laws
  • Short-range interactions with elastic collisions
  • Elastic collisions with walls  (an impulse…..pressure)
  • What we call temperature T is a direct measure of the average translational kinetic energy
  • What we call pressure p is a direct measure of the number density of molecules, and how fast they are moving (vrms)
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