Rankers Physics

Kinetic Theory of Gases: Practice Problem & Solution

Which of the following gases possesses maximum rms velocity, all being at the same temperature?
Oxygen
Air
Carbon dioxide
Hydrogen

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 (rms) velocity of a gas is given by:

\[
v_{\text{rms}} = \sqrt{\frac{3RT}{M}}
\]

where \( M \) is the molar mass. Since all gases are at the same temperature, the gas with the smallest molar mass will have the highest \( v_{\text{rms}} \).

Hydrogen has the smallest molar mass among the options, so it has the maximum rms velocity.

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