Kinetic Theory

JEE Main level, single correct, medium

60 of 168

Question 60 of 168

For given gas at 1atm1atm pressure, rmsrms speed of the molecules is 200m/s200m/s at 127∘C.127^{\circ}C. At 2atm2atm pressure and at 227∘C,227^{\circ}C, the rmsrms speed of the molecules will be:

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Answer: (D) 1005m/s100\sqrt{5}m/s

Vrms=3RTM⇒Vrms∝T{V}_{rms}=\sqrt{\dfrac{3RT}{M}}\Rightarrow {V}_{rms}\propto \sqrt{T}
V1V2=T1T2\dfrac{{V}_{1}}{{V}_{2}}=\sqrt{\dfrac{{T}_{1}}{{T}_{2}}}
200V2=400500\dfrac{200}{{V}_{2}}=\sqrt{\dfrac{400}{500}}
V2=1005m/s{V}_{2}=100\sqrt{5}m/s

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