Question:
If the temperature $T$ of oxygen molecule is raised to $9T$, then its root mean square speed $v$ is increased to
If the temperature $T$ of oxygen molecule is raised to $9T$, then its root mean square speed $v$ is increased to
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For gas molecules:
- $v \propto \sqrt{T}$
- If temperature becomes $n$ times, speed becomes $\sqrt{n}$ times
Updated On: Apr 30, 2026
- $3v$
- $2v$
- $\sqrt{2}v$
- $\sqrt{3}v$
- $\sqrt{\frac{3}{2}}v$
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The Correct Option is A
Solution and Explanation
Concept:
Root mean square speed:
\[
v \propto \sqrt{T}
\]
Step 1: Write proportional relation.
\[ \frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}} \]
Step 2: Substitute given values.
\[ \frac{v_2}{v} = \sqrt{\frac{9T}{T}} = \sqrt{9} \]
Step 3: Simplify.
\[ v_2 = 3v \]
Step 1: Write proportional relation.
\[ \frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}} \]
Step 2: Substitute given values.
\[ \frac{v_2}{v} = \sqrt{\frac{9T}{T}} = \sqrt{9} \]
Step 3: Simplify.
\[ v_2 = 3v \]
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