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Unformatted text preview: Physics 212: Statistical mechanics II, Fall 2005 Midterm : ends 11 a.m., Thursday, 11/10/05 Directions : The allotted time is 80 minutes. The 5 problems count equally. No books or notes are allowed, and please ask for help only if a questions meaning is unclear. 1. Consider a dilute gas of N 1 classical point particles described by a Hamiltonian with shortranged twoparticle interactions: the interaction potential is V (  x 1 x 2  ) and there is no external potential. (a) (6 points) Let f N (0 , x 1 , p 1 , x 2 , x 2 , . . . , x N , p N ) be the Nparticle distribution function at t = 0. Suppose that at t = 0, f N = 1 /V inside a small volume V of Nparticle phase space, and 0 elsewhere, so that the integral of f N over all phase space is 1. State Liouvilles theorem. (b) (10 points) Assume that the gas is threedimensional and has many collisions. Write the Boltzmann equation collision term in terms of the oneparticle distribution f and use it to argue that the system will evolve toward a locally Maxwellian distribution. Write the most general suchthat the system will evolve toward a locally Maxwellian distribution....
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 Fall '06
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 mechanics, Statistical Mechanics

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