The average distance that a molecule travels between two successive collisions is called the average free path.

| June 3, 2021 | education

The average distance that a molecule travels between two successive collisions is called the average free path. Estimate the average free path of a molecule in air under normal conditions (T = 273 K, P = 10 ^ 5 Pa). The diameter of the molecules is taken equal to d = 3.7×10 ^ -10 m.

Let us find the average distance that a molecule travels between two successive collisions.

L = 1 / (√2 * n * D ^ 2 * n). n = P / (K * T). Hence we have. Where L is the average path length of air molecules. K = 1.38 * 10 ^ -23 – Boltzmann’s constant. T = 273 K – gas temperature. D = 3.7 * 10 ^ -10 – The diameter of the gas molecules. P = 10 ^ 5 Pa – gas pressure. Where n = 3.14.

L = K * T / (√2 * n * P * D ^ 2) = 1.38 * 10 ^ -23 * 273 / (√2 * 3.14 * 10 ^ 5 * (3.7 * 10 ^ – 10) ^ 2) = 376.74 * 10 ^ -23 / (60.79 * 10 ^ -15) = 6.19 * 10 ^ -8 (m).



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