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Find the rms speed of a dust particle.

  • Thread starter nlingraham
  • Start date
  • #1
16
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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?
 

Answers and Replies

  • #2
6,054
390
Check the volume of a sphere.
 
  • #3
16
0
Thank you very much
 

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