Question 605: Thermodynamics & KTG

Question

A system consists of two types of gas molecules A and B having same number density 2 $$	imes$$ 1025/m3. The diameter of A and B are 10 $$\mathop A\limits^o $$ and 5 $$\mathop A\limits^o $$ respectively. They suffer collision at room temperature. The ratio of average distance covered by the molecule A to that of B between two successive collision is ____________ $$	imes$$ 10$$-$$2

Accepted Answer

$$\because$$ mean free path
$$\lambda  = {1 \over {\sqrt 2 \pi {d^2}n}}$$
$${{{\lambda _1}} \over {{\lambda _2}}} = {{d_2^2{n_2}} \over {d_1^2{n_1}}}$$
$$ = {\left( {{5 \over {10}}} ight)^2} = 0.25 = 25 	imes {10^{ - 2}}$$

Thermodynamics & KTG

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