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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 short-ranged two-particle 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 N-particle distribution function at t = 0. Suppose that at t = 0, f N = 1 /V inside a small volume V of N-particle 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 three-dimensional and has many collisions. Write the Boltzmann equation collision term in terms of the one-particle 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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