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Phys105_ps11_2009 - Physics 105 Problem Set 11 Due Friday 3...

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Physics 105, Problem Set 11 Due: Friday, December 18, 2009, 3 PM. Reading: K&K Chapters 11, 12, 13 with particular emphasis on 11.3-11.5, 12, 13.1-13.3. Knight’s Chapter 36 (on E-reserves on PHY103 website) contains additional discussion of relativity. Problem 1. Pressure of a gas: First consider one atom of mass m bouncing elastically inside a perfect cube of interior size L × L × L = V (volume V ). The atom bounces elastically of the interior walls of the cube. Assume the walls have infinite mass and are oriented perpendicular to the x , y and z axes. When the atom bounces, the impulse is normal to the wall that it bounces off of. The initial velocity of the atom is ~v = ( v x , v y , v z ). (a) What is the time-averaged force that this atom exerts on a wall whose surface is perpendicular to the x axis? Now assume that there are N 1 such atoms inside the cube. The atoms may have different masses m i . The directions ˆ v i of their velocities are random and equally likely to point in any direction on the unit sphere. The total kinetic energy of these atoms is
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