Mean free path and number density – Rankers Physics

Kinetic Theory of Gases: Practice Problem & Solution

On increasing the number density for a gas in a vessel, mean free path of the gas will
Decrease
Increase
Remain same
Become double

Solution Explained:

To solve this problem, we apply the core principles of Kinetic Theory of Gases. Understanding the underlying formula is key to arriving at the correct answer below:

The mean free path is given by \(\lambda = \frac{1}{\sqrt{2} n \pi d^2}\). Since \(\lambda\) is inversely proportional to the number density \(n\), increasing the number density decreases the mean free path.

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