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COMEDK2023Evening ShiftPhysicsKinetic Theory of GasesActual

The molecules of a given mass of a gas have root mean square speed of 120 ~m / s at 88^ C and 1 atmospheric pressure. The root mean square speed of the molecules at 127^ C and 2 atmospheric pressure is

Options

  1. A1.443 m/s
  2. B126.3 m/s
  3. C88.12 m/s
  4. D105.2 m/s

Correct answer

B. 126.3 m/s

Step-by-step solution

The root mean square speed v_ rms of gas molecules is given by the formula v_ rms = 3RT M . From this formula, it is evident that v_ rms depends only on the temperature T and the molar mass M of the gas. It is independent of the pressure P of the gas. Given v_ rms,1 = 120 m/s at T₁ = 88^ C = 88 + 273 = 361 K . We need to find v_ rms,2 at T₂ = 127^ C = 127 + 273 = 400 K . Taking the ratio of the two speeds: v_ rms,2 v_ rms,1 = T₂ T₁ Substituting the values: v_ rms,2 120 = 400 361 v_ rms,2 120 = 20 19 v_ rms,2 = 120

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