MasterPhysics 5 soln

# MasterPhysics 5 soln - PHYS-408 Fall 2008 Mastering Physics...

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PHYS-408 Fall 2008 Mastering Physics Assignment #5 Solutions Problem 18.3 (a) At what pressure will the mean free path in room-temperature 20 degree(s) C nitrogen be 1.0 m? λ = 1 π N V r 2 For an ideal gas, pV = Nk B T N V = p k B T = 1 p k B T r 2 p k B T = 1 πλ r 2 p = k B T r 2 For most diatomic molecules, r = 1.0 × 10 10 m So p = 1.38 × 10 23 J / K ( ) 293 K ( ) 4 1 m ( ) 1.0 × 10 10 m ( ) 2 = 0.0228 N / m 2 Problem 18.12 At 100 degree(s) C the rms speed of nitrogen molecules is 576 m/s. Nitrogen at 100 degree(s) C and a pressure of 2.0 atm is held in a container with a 10 (cm) * 10 (cm) square wall. (a) Estimate the rate of molecular collisions (collisions/s) on this wall. Knowing the RMS velocity results from the average of the components of the velocity: v RMS 2 = v x 2 ( ) ave + v y 2 ( ) ave + v z 2 ( ) ave There is no preferred direction, so v x 2 ( ) ave = v y 2 ( ) ave = v z 2 ( ) ave v x 2 ( ) ave = 1 3 v RMS 2 So v x = 1 3 v RMS

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Note that, on average, half of the molecule have this velocity component forward, and half are backwards.
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MasterPhysics 5 soln - PHYS-408 Fall 2008 Mastering Physics...

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