• # question_answer For a given gas at 1 atm pressure, rms speed of the molecule is 200 m/s at $127{}^\circ C.$ At 2 atm pressure and at$~227{}^\circ C,$the rms speed of the molecules will be :             [JEE Main 9-4-2019 Morning] A) $80\text{ }m/s$                      B) 100 5 m/sC) $80\sqrt{5}m/s$                    D) $100\text{ }m/s$

${{V}_{rms}}=\sqrt{\frac{3RT}{{{M}_{\text{w}}}}}\Rightarrow {{\text{v}}_{rms}}\propto \sqrt{T}$ Now,$\frac{\text{v}}{200}=\sqrt{\frac{500}{400}}\Rightarrow \frac{\text{v}}{200}=\frac{\sqrt{5}}{2}$ $\Rightarrow \text{v}=100\sqrt{5}m/s$ Option