phys 369 09 hw 11 solution

phys 369 09 hw 11 solution - Phys. 369, Fall 2009 Homework...

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Phys. 369, Fall 2009 Homework #11 Solution 1. (22 points) a) The diameter of the molecules is 10 2r a d i u s 3 . 7 61 0 m . d = × The collision cross section is 21 9 2 4.44 10 m . d σπ ==× The number density of the gas is 5 24 3 23 0.5 1.013 10 7.75 10 m . 1.381 10 (273 200) P n kT ×× == = × ××+ The mean free path is 7 24 19 11 2.05 10 m. 2 2 7.75 10 4.44 10 n σ = × ×××× A b) The average speed of the molecules is 1/2 1/2 23 27 8 8 1.381 10 473 m 598 . 28 1.661 10 s kT v m ππ ⎛⎞ ××× = ⎜⎟ × ⎝⎠ The collision rate is 91 7 598 22 . 9 2 1 0 s . 2.05 10 coll v nv Γ= = × × A c) The heat capacity per mole at constant volume is 5 , v f cR R so 55 . v AA c R k NN The thermal conductivity is 24 7 23 5 1.227 1.227 2 W 1.227 7.75 10 598 2.05 10 2.5 1.381 10 0.0403 m K v t A c kn v n v k N −− × × × × × × × = d) The viscosity is 27 5 19 5 28 1.661 10 598 0.347 0.347 2.17 10 Pa s. 4.44 10 32 2 mv mv π η σσ === = × × e) The distribution function (,) f xt for the displacement of the particle in the x -direction obeys the diffusion equation 2 2 self f f D tx ∂∂ = with the initial condition (,0 ) () . f xx δ = As we showed in HW 9, problem 1, the solution is 2 4 1/2 1 (,) 4 self x D t self fx t e Dt =
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The rms displacement in the x -direction is () 2 rms self x tD t = .
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This note was uploaded on 11/06/2010 for the course PHY 369 taught by Professor Staff during the Fall '08 term at University of Texas at Austin.

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phys 369 09 hw 11 solution - Phys. 369, Fall 2009 Homework...

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