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Transport Phenomena

Problem 2.228

For the case of nitrogen under standard conditions find: (a) the mean number of collisions experienced by each molecule per second; (b) the total number of collisions occurring between the molecules within 1 cm31 \mathrm{~cm}^{3} of nitrogen per second.

Reveal Answer
2.228. (a) v=2πd2n⟨v⟩=0.74⋅1010 s−1v=\sqrt{2} \pi d^{2} n\langle v\rangle=0.74 \cdot 10^{10} \mathrm{~s}^{-1} (b) v=1/22πd2n2⟨v⟩=1.0×1029s−1⋅cm−3,v=1 / 2 \sqrt{2} \pi d^{2} n^{2}\langle v\rangle=1.0 \times 10^{29} \quad \mathbf{s}^{-1} \cdot \mathrm{cm}^{-3}, \quad where n=p0/kT0\quad n=p_{0} / k T_{0} ⟨v⟩=8RT/πM\langle v\rangle=\sqrt{8 R T / \pi M}
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