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,PAPdP AnmAdrr−+= −afbgejω2where nis the number of molecules per unit volume and Ais the area of any cylindricalsurface. This reduces to dPnmrdr=ω2.But also Pnk TB=, so dPk TdnB=. Therefore, the equation becomesdnnmk TrdrB=ω2giving dnnmk TrdrnnBr020zz=ωorlnnmk TrnnBra f02202=FHGIKJωlnnnmk TrB0222FHGIKJ=ωand solving for n: nn emrk TB=0222ω.P21.65First find vav2as vNv N dvvav2=∞z120. Let amk TB=2.Then, vNaNv eaaak Tmav dvBav2===−−∞−z4438
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