Chapter 20: Q. 39 (page 568)

Dust particles are $10 μm$ in diameter. They are pulverized rock, with $ρ \approx 2500 kg / m^{3}$ . If you treat dust as an ideal gas, what is the rms speed of a dust particle at $20 ° C$ $?$

Short Answer

Expert verified

In ideal gas state the rms speed of a dust particle at $20^{°} C$ is $9.6 \cdot 10^{- 5} m / s$ .

Step by step solution

Formula for root mean square

Root mean square speed can be given as,

$v_{rms} = \sqrt{\frac{3 k_{B} T}{m}}$

where is the mass of one particle.

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

$m = ρV$

Calculation for root square mean

Root mean square of speed,

$v_{rms} = \sqrt{\frac{3 k_{B} T}{ρV}}$

substitute the volume of a sphere with diameter $d$ .

We have,

$V = \frac{4}{3} {πr}^{3} = \frac{4}{3} π {(\frac{d}{2})}^{2} = \frac{1}{6} {πd}^{3}$

$v_{rms} = \sqrt{\frac{3 k_{B} T}{ρ \frac{1}{6} {πd}^{3}}} = \sqrt{\frac{18 k_{B} T}{{πρd}^{3}}}$

$v_{rms} = \sqrt{\frac{18 \cdot 1.38 \cdot 10^{- 23} \cdot 293}{π \cdot 2500 \cdot {(1 \cdot 10^{- 5})}^{3}}}$

$v_{rms} = 9.6 \cdot 10^{- 5} m / s$

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Dust particles are $10 μm$ in diameter. They are pulverized rock, with $ρ \approx 2500 kg / m^{3}$ . If you treat dust as an ideal gas, what is the rms speed of a dust particle at $20 ° C$ $?$

Short Answer

Step by step solution

Formula for root mean square

Calculation for root square mean

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Dust particles are10μmin diameter. They are pulverized rock, with ρ≈2500kg/m3. If you treat dust as an ideal gas, what is the rms speed of a dust particle at20°C?

Short Answer

Step by step solution

Formula for root mean square

Calculation for root square mean

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Engineering Physics

Radiation

Measurements

Quantum Physics

Modern Physics

Famous Physicists

Study anywhere. Anytime. Across all devices.

Dust particles are $10 μm$ in diameter. They are pulverized rock, with $ρ \approx 2500 kg / m^{3}$ . If you treat dust as an ideal gas, what is the rms speed of a dust particle at $20 ° C$ $?$