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# p212p2 - Physics 212 Statistical mechanics II Fall 2006...

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Physics 212: Statistical mechanics II, Fall 2006 Problem set 2 : due on Thursday 9/28/05, based on lectures IV-VIII 1. A quick numerical problem: Suppose that a sphere of radius 1 mm moves at 1 mm/sec through a monatomic helium gas at room temperature and atmospheric pressure (1 atm = 10 5 Pa). Estimate the viscosity coefficent of the gas η mkT/a 2 , where a is the particle size. What is the viscous drag force on the sphere from Stokes’s law? Estimate the Reynolds number. 2. In our derivation of zeroth-order hydrodynamics, we assumed “equipartition”: each quadratic term in a classical energy function contains an energy k B T/ 2 at high temperature. For example, the mean energy of a particle in an ideal gas in 3D is 3 k B T/ 2, since there is no potential energy and there are three components in the kinetic energy. Starting from the quantum harmonic oscillator in 1D, H = p 2 2 m + kx 2 2 , (1) compute the mean kinetic energy at temperatures k B T ¯ , where ω is the fundamental frequency, and show that equipartition is satisfied.

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p212p2 - Physics 212 Statistical mechanics II Fall 2006...

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