COMEDK · Physics · 14. Kinetic Theory of Gases
What is the ratio of the mean free paths of the molecules of two gases \(A\) and \(B\) having the molecular diameters \(2 \mathrm{~A}^0\) and \(3 \mathrm{~A}^0\) respectively under the identical conditions of pressure, temperature and volume?
- A \(\dfrac{\lambda_A}{\lambda_B}=9: 4\)
- B \(\dfrac{\lambda_A}{\lambda_B}=3: 2\)
- C \(\dfrac{\lambda_A}{\lambda_B}=4: 9\)
- D \(\dfrac{\lambda_A}{\lambda_B}=2: 3\)
Answer & Solution
Correct Answer
(A) \(\dfrac{\lambda_A}{\lambda_B}=9: 4\)
Step-by-step Solution
Detailed explanation
The mean free path \(\lambda\) of a gas molecule is given by the formula \(\lambda = \dfrac{k_B T}{\sqrt{2} \pi d^2 P}\), where \(k_B\) is the Boltzmann constant, \(T\) is the temperature, \(d\) is the molecular diameter, and \(P\) is the pressure. Under identical conditions of…
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