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kinetic_theory_of_gases

# kinetic_theory_of_gases - Kinetic Theory of Gases...

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Kinetic Theory of Gases: Elementary Ideas 17th February 2010 1 Kinetic Theory: A Discussion Based on a Sim- plified View of the Motion of Gases 1.1 Pressure: Consul Engel and Reid (Ch. 33.1) for a discussion of the derivation for the pressure of a rarefied collection of particles of mass m . In the following, we provide a connection from the one-dimensional version to the full scalar pressure. The connection is not quite direct from the discussion of Engel and Reid. In 3-D, for a collection of many particles (on the order of Avogadro num- ber), using average values of velocity and velocity components (in Carte- sian coordinates); these are not generalized coordinates (as physicists would consider), the total kinetic energy is: KE total = N 2 m ( ~v · ~v ) = N 2 m ( v 2 x + v 2 y + v 2 z ) = N 2 m v 2 x + N 2 m v 2 y + N 2 m v 2 z = ( KE ) x + ( KE ) y + ( KE ) z The last equality is really just a notational trick; there really does not exist a thermodynamic or kinetic property ( KE ) x or ( KE ) y or ( KE ) z ! The lowercase m is mass. The velocity is a vector so the v 2 we treat casually is really a dot product . The pressure components for the x , y , and z directions as we determined in class are: 1

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