MHT CET · Physics · Kinetic Theory of Gases
The temperature of an ideal gas is increased from \(27^{\circ} \mathrm{C}\) to \(927^{\circ} \mathrm{C}\). The r.m.s. speed of its molecules becomes
- A twice.
- B half.
- C four times.
- D one-fourth.
Answer & Solution
Correct Answer
(A) twice.
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { We know } \mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}} \\ \Rightarrow \mathrm{v}_{\mathrm{rms}} & \propto \sqrt{\mathrm{T}} \\ \therefore \quad & \frac{\mathrm{v}_{\mathrm{rms}}}{\mathrm{v}_{\mathrm{rms}}}=\sqrt{\frac{\mathrm{T}_1}{\mathrm{~T}_2}}=\sqrt{\frac{300}{1200}}=\sqrt{\frac{1}{4}} \\ & \frac{\mathrm{v}_{\mathrm{rms}_1}}{\mathrm{v}_{\mathrm{rms}}}-\frac{1}{2} \\ \therefore \quad \mathrm{v}_{\mathrm{rms}_2} & =2 \cdot \mathrm{v}_{\mathrm{rms1}}\end{aligned}\)
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