Dust particles are pulverized rock,which has density 2500kg/m3.They are approximately spheres with 10μm in diameter.Treating dust as an ideal gas,what is the rms speed of a dust particle at 400°C? A)5.2 × 10^-5 m/s B)1.7 × 10^-5 m/s C)3.0 × 10^-5 m/s D)7.3 × 10^-5 m/s

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Quizplus · Accepted Answer

The rms speed of an ideal gas is given by:$$v_{rms}=\sqrt{\frac{3kT}{m}}$$where k is the Boltzmann constant, T is the temperature, and m is the mass of the particle.The mass of a dust particle can be calculated from its density and volume:$$m=ho V=\frac{4}{3}\pi r^3 ho$$where r is the radius of the particle.Substituting the given values into the equations above, we get:$$v_{rms}=\sqrt{\frac{3kT}{m}}=\sqrt{\frac{3(1.38	imes10^{-23}	ext{ J/K})(400+273	ext{ K})}{\frac{4}{3}\pi (5	imes10^{-6}	ext{ m})^3 (2500	ext{ kg/m}^3)}}=5.2	imes10^{-5}	ext{ m/s}$$Therefore, the correct answer is A.

Dust Particles Are Pulverized Rock,which Has Density 2500kg/m3