Effect of Leakage on RMS Speed – Rankers Physics

Kinetic Theory of Gases: Practice Problem & Solution

The root mean square speed of \(\text{H}_2\) molecules contained in a vessel is \(300\text{ m/s}\). If half of the gas leaks out at constant temperature, then the rms speed of the remaining molecules in the vessel will be
\(150\text{ m/s}\)
\(600\text{ m/s}\)
\(300\text{ m/s}\)
\(900\text{ m/s}\)

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 root mean square speed of molecules is given by \(v_{\text{rms}} = \sqrt{\frac{3RT}{M}}\). Since the temperature \(T\) and molecular mass \(M\) of the remaining gas remain constant, the rms speed does not change and remains \(300\text{ m/s}\).

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