All Problems 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 \(1 \mathrm{~cm}^{3}\) of nitrogen per second.
2.228. (a) \(v=\sqrt{2} \pi d^{2} n\langle v\rangle=0.74 \cdot 10^{10} \mathrm{~s}^{-1}\) (b) \(v=1 / 2 \sqrt{2} \pi d^{2} n^{2}\langle v\rangle=1.0 \times 10^{29} \quad \mathbf{s}^{-1} \cdot \mathrm{cm}^{-3}, \quad\) where \(\quad n=p_{0} / k T_{0}\) \(\langle v\rangle=\sqrt{8 R T / \pi M}\)