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Unformatted text preview: PHYS 445 Lecture 17 - Ideal gas in detail 17 - 1 2001 by David Boal, Simon Fraser University. All rights reserved; further resale or copying is strictly prohibited. Lecture 17 - Ideal gas in detail What's Important: phase space of non-interacting particles Maxwell-Boltzmann distribution Text : Reif Phase space of non-interacting particles An ideal gas is one in which particles are essentially non-interacting because their number density is sufficiently low. Because of the energy scales involved, the rotational and vibrational motion of the gas particles can be separated from their translational motion, allowing the particles to be treated as point objects for the time being. As introduced in an earlier lecture, the number of states available for translational motion is proportional to the phase space volume ( E ) d 3 r d 3 p for a single particle. In the canonical ensemble, each state E is weighted by exp(- E ), so the probability of a particle being in the phase space volume element d 3 r d 3 p is just [ probability of r , p ] d 3 r d 3 p exp(- E ) d 3 r d 3 p or P ( r , p ) d 3 r d 3 p exp(- p 2 / 2 m ) d 3 r d 3 p (17.1) the last relationship following because the energy is not position-dependent.the last relationship following because the energy is not position-dependent....
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- Spring '08