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JEE Main 20199 AprilMorning Shift
Exam
JEE Main
Year
2019
Date
9 April
Shift
Morning Shift
Subject
Physics
Chapter
Kinetic Theory of Gases

JEE Main 2019 · 9 April · Morning Shift · Physics · Kinetic Theory of Gases

For given gas at 1atm pressure, rms speed of the molecules is 200m...

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

Options

  1. A100m/s100m / s
  2. B80m/s80m / s
  3. C805m/s80\sqrt{5}m / s
  4. D1005m/s100\sqrt{5}m / s

Correct answer

D. 1005m/s100\sqrt{5}m / s

Step-by-step solution

Vrms=3RTM⇒Vrms∝T{V}_{rms} = \sqrt{\dfrac{3RT}{M}} ⇒ {V}_{rms} ∝ \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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