TS EAMCET · Physics · Kinetic Theory of Gases
If the temperature of a gas is increased from \(127^{\circ} \mathrm{C}\) to \(527^{\circ} \mathrm{C}\), then the rms speed of the gas molecules
- A increases by 4 times
- B becomes \(\sqrt{2}\) times
- C becomes half
- D decreases by \(\sqrt{2}\) times
Answer & Solution
Correct Answer
(B) becomes \(\sqrt{2}\) times
Step-by-step Solution
Detailed explanation
\(T_1 = 127 + 273 = 400 \mathrm{K}\) \(T_2 = 527 + 273 = 800 \mathrm{K}\) \(\frac{v_{rms,2}}{v_{rms,1}} = \sqrt{\frac{T_2}{T_1}}\) \(\frac{v_{rms,2}}{v_{rms,1}} = \sqrt{\frac{800}{400}} = \sqrt{2}\) rms speed becomes \(\sqrt{2}\) times.
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