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The relationship between RMS speed (vrms) of gas molecules and temperature T is-
1. vrms ∝ T
2. vrms ∝ √T
3. vrms ∝ T2
4. vrms ∝ eT

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Correct Answer - Option 2 : vrms ∝ √T

The correct answer is option 2) i.e. vrms ∝ √T

CONCEPT:

  • Root-mean-square (rms) speed: The root-mean-square speed is a measure of the speed of gas molecules taking into account their molecular weight and temperature.
  • It is defined as the square root of the average velocity-squared of the gas molecules.

It is given by the equation:

\(v_{rms} = \sqrt{\frac{3 RT}{M}}\)

Where R is the universal gas constant = 8.314 J mol-1 K-1, T is the temperature of the gas and M is the molecular mass of gas.

EXPLANATION:

We know that, \(v_{rms} = \sqrt{\frac{3 RT}{M}}\)

∴ vrms ∝ √T

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