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UPCET / UPSEE RMS Speed — practice questions

Explore 4 free RMS Speed questions in UPCET / UPSEE Physics. Open each question or exercise to read its content, reference answers and available explanation.

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RMS Speed questions and exercises with answers

Showing questions 1–4 of 4.

The **rms speed** of gas molecules at absolute temperature $T$ is:Read the answer and worked solution →The rms speed of N₂ at 300 K (M = 28 g/mol) is approximately (use $R = 8.314$ J/(mol·K)):Read the answer and worked solution →If the temperature of a gas is doubled (at constant volume), the rms speed changes by a factor of:Read the answer and worked solution →The rms speed of helium atom at 300 K is approximately (M_He = 4 g/mol):Read the answer and worked solution →

Worked practice questions

The **rms speed** of gas molecules at absolute temperature $T$ is:

  1. $\sqrt{3RT/M_0}$ (also $\sqrt{3 k_B T/m}$)
  2. $\sqrt{2RT/M_0}$
  3. $RT/M_0$
  4. $3RT/M_0$
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Correct answer: A. $\sqrt{3RT/M_0}$ (also $\sqrt{3 k_B T/m}$)

$v_{rms} = \sqrt{\overline{v^2}} = \sqrt{3RT/M_0} = \sqrt{3k_B T/m}$, where $M_0$ is molar mass, $m$ is molecular mass.

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The rms speed of N₂ at 300 K (M = 28 g/mol) is approximately (use $R = 8.314$ J/(mol·K)):

  1. 170 m/s
  2. 517 m/s
  3. 1000 m/s
  4. 5170 m/s
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Correct answer: B. 517 m/s

$v_{rms} = \sqrt{3RT/M_0} = \sqrt{3 \times 8.314 \times 300/0.028} = \sqrt{2.673 \times 10^5} \approx 517$ m/s.

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If the temperature of a gas is doubled (at constant volume), the rms speed changes by a factor of:

  1. 2
  2. $\sqrt 2$ ≈ 1.414
  3. 4
  4. $1/\sqrt 2$
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Correct answer: B. $\sqrt 2$ ≈ 1.414

$v_{rms} \propto \sqrt T$. Double T ⇒ $v_{rms}$ rises by $\sqrt 2 \approx 1.41$.

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