Calculate the mean free path of air molecules at a pressure of .

Solution 38E The expression for mean free path is given by, kT = 2 …..(1), where k is Boltzmann’s constant, T is the temperature in absolute 4 2r P scale, r is the radius of air molecule and P is the pressure. Given, P = 3.50 × 10 13atm 13 5 5 P = 3.50 × 10 × 1.01 × 10 Pa (since 1 atm = 1.01 × 10 Pa) P = 3.53 × 10 8Pa 0 T = 27 C = 27 + 273 K = 300 K k = 1.38 × 10 23 J/K 10 r = 2.0 × 10 m Substituting these values in equation (1), = 1.38×102J/K × 300 K 4×3.14× 2×(2.0×1010m) ×3.53×108Pa 23 = 414×10 J 17.70×4×1020m ×3.53×108Pa = 1.65 × 10 m5 Therefore, the approximate mean free path of the air molecules at the given pressure is 1.65 × 10 m.