Chapter 21627P21.64(a)The effect of high angular speed is like the effect of a very high gravitational field on anatmosphere. The result is:The larger-mass molecules settle to the outsidewhile the region at smaller rhas a higherconcentration of low-mass molecules.(b)Consider a single kind of molecules, all of mass m.To cause the centripetal acceleration ofthe molecules between rand rdr+, the pressure must increase outward according toFmarr∑=. Thus,PAP dP AnmAdr r−+=−afbgejω2where nis the number of molecules per unit volume and Ais the area of any cylindricalsurface. This reduces to dP nmrdr=2.But also PnkTB=, so dPk TdnB=. Therefore, the equation becomesdnnmrdrB=2giving dnnmrdrnnBr020zz=orlnnmrnnBr02202=FHGIKJlnnnmrB0222FHGIKJ=and solving for n: nnemrk TB=02.P21.65First find vav2as vNvNdvvav2=∞z120. Let amB=2.Then, vNaNveaaamav dvBav2===−−∞−z4438312 3240321222πThe 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 .