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Kinetic theory of gases. Boltzmanns Law and Maxwell distribution

Problem 2.75

Calculate at the temperature t=17∘Ct=17^{\circ} \mathrm{C} : (a) the root mean square velocity and the mean kinetic energy of an oxygen molecule in the process of translational motion; (b) the root mean square velocity of a water droplet of diameter d=0.10μmd=0.10 \mu \mathrm{m} suspended in the air.

Reveal Answer
 (a) vsq=3RT/M=0.47 km/s,⟨ε⟩=3/2kT=6.0⋅10−21 J (b) vsq=32kT/πρd3=0.15 m/s\text { (a) } v_{s q}=\sqrt{3 R T / M}=0.47 \mathrm{~km} / \mathrm{s},\langle\varepsilon\rangle=3 / 2 k T=6.0 \cdot 10^{-21} \mathrm{~J} \text { (b) } v_{s q}=3 \sqrt{2 k T / \pi \rho d^{3}}=0.15 \mathrm{~m} / \mathrm{s}
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