ExamBro
ExamBro
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

  1. A twice.
  2. B half.
  3. C four times.
  4. D one-fourth.
Verified Solution

Answer & Solution

Correct Answer

(A) twice.

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \text { We know } \mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}} \\ \Rightarrow \mathrm{v}_{\mathrm{rms}} & \propto \sqrt{\mathrm{T}} \\ \therefore \quad & \frac{\mathrm{v}_{\mathrm{rms}}}{\mathrm{v}_{\mathrm{rms}}}=\sqrt{\frac{\mathrm{T}_1}{\mathrm{~T}_2}}=\sqrt{\frac{300}{1200}}=\sqrt{\frac{1}{4}} \\ & \frac{\mathrm{v}_{\mathrm{rms}_1}}{\mathrm{v}_{\mathrm{rms}}}-\frac{1}{2} \\ \therefore \quad \mathrm{v}_{\mathrm{rms}_2} & =2 \cdot \mathrm{v}_{\mathrm{rms1}}\end{aligned}\)
Same subject
Explore more questions on app