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Dust particles are10μ³¾in diameter. They are pulverized rock, with ÒÏ≈2500kg/m3. If you treat dust as an ideal gas, what is the rms speed of a dust particle at20°C?

Short Answer

Expert verified

In ideal gas state the rms speed of a dust particle at20°Cis9.6·10-5m/s.

Step by step solution

01

Formula for root mean square 

Root mean square speed can be given as,

vrms=3kBTm

where is the mass of one particle.

The volume and density of a particle can be used to compute its mass,

m=ÒÏV

02

Calculation for root square mean 

Root mean square of speed,

vrms=3kBTÒÏV

substitute the volume of a sphere with diameterd.

We have,

V=43Ï€°ù3=43Ï€d22=16Ï€»å3

vrms=3kBTÒÏ16Ï€»å3=18kBTÏ€ÒÏd3

vrms=18·1.38·10-23·293π·2500·1·10-53

vrms=9.6·10-5m/s

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