625_Physics ProblemsTechnical Physics

625_Physics ProblemsTechnical Physics - Chapter 21 P21.64...

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Chapter 21 627 P21.64 (a) The effect of high angular speed is like the effect of a very high gravitational field on an atmosphere. The result is: The larger-mass molecules settle to the outside while the region at smaller r has a higher concentration of low-mass molecules. (b) Consider a single kind of molecules, all of mass m. To cause the centripetal acceleration of the molecules between r and rd r + , the pressure must increase outward according to Fm a rr = . Thus, PA P dP A nmAdr r −+ = af bg ej ω 2 where n is the number of molecules per unit volume and A is the area of any cylindrical surface. This reduces to dP nm rdr = 2 . But also Pn kT B = , so dP k Tdn B = . Therefore, the equation becomes dn n m rdr B = 2 giving dn n m rdr n n B r 0 2 0 zz = or ln n m r n n B r 0 22 0 2 = F H G I K J ln n n m r B 0 2 2 2 F H G I K J = and solving for n : nn e mr k T B = 0 2 . P21.65 First find v av 2 as v N vNd v v av 2 = z 1 2 0 . Let a m B = 2 . Then, v Na N ve a a a m av dv B av 2 == = z 4 4 3 8 3 12 32 4 0 32 12 2 2 π The root-mean square speed is then
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .

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