Find the rms speed of a dust particle.

AI Thread Summary
The discussion centers on calculating the root mean square (rms) speed of a dust particle, given its diameter of 13.0 micrometers and density of 2540 kg/m3. The user correctly converts the diameter to radius and calculates the volume of the particle using the formula for a sphere. They then determine the mass of the dust particle but express uncertainty about the final rms speed calculation, suspecting an error. The user seeks assistance in identifying any mistakes, particularly in the volume calculation. The conversation highlights the importance of accurate volume and mass calculations in determining the rms speed of particles treated as ideal gases.
nlingraham
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Homework Statement



Dust particles are 13.0 micrometers in diameter. They are pulverized rock, with ρ=2540 kg/m3 . If you treat dust as an ideal gas, what is the rms speed of a dust particle at 18.0 C?

Homework Equations



ρ=m/v
V=4/3∏r2
vrms=√(3kT/m)

The Attempt at a Solution



OK:

13 micrometers = 1.3*10-5 m, which makes radius 6.5*10-6 m

Then, V=(4/3)∏(6.5*10-6)2=1.7697*10-10 m3

m=ρv=(2540)(1.7697*10-10 m3)=4.495*10-7 kg

vrms=√(3*(1.38*10-23)*(273+18))/(4.495*10-7 kg))
=1.63*10-7 m/s

This isn't right though, anyone see where I went wrong?
 
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Check the volume of a sphere.
 
Thank you very much
 

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