Example

Question:

Estimate the mean free path for a water molecule in water vapour at 373 K. Use information from Exercises 12.1 and Eq. (12.41) above.

Solution:

For water vapour, the effective molecular diameter \(d\) is the same as air. The number density is inversely proportional to temperature:
\[ n = 2.7 \times 10^{25} \times \frac{273}{373} = 2 \times 10^{25}\,\mathrm{m}^{-3} \]
Hence, mean free path \[ l = 4 \times 10^{-7}\,\mathrm{m} \]
Note: The mean free path is 100 times the interatomic distance (\(\sim 40\,\text{\AA} = 4 \times 10^{-9}\,\mathrm{m}\)) previously calculated. This large mean free path explains typical gaseous behaviour—gases cannot be confined without a container.