Class 12 Physics · Chapter 1 · Test 2
RMS Speed and Boltzmann
35 MCQs
35 questions · 30 min · 35 marks
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Sample questions
The first 5 of 35. Try each one, then tap to see the answer.
Question 1
The root mean square (rms) speed is the:
- AAverage of the velocities
- BSquare root of the average of the squares of the speeds
- CSquare of the average speed
- DMaximum speed of the molecules
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Answer: B
The rms speed is the square root of the mean of the squared speeds.
Question 2
The rms speed of a gas molecule of mass m at temperature T is:
- Asqrt(kBT/m)
- Bsqrt(kBT/3m)
- Csqrt(3kBT/m)
- Dsqrt(3m/kBT)
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Answer: C
From (1/2)m<v^2> = (3/2)kBT we get vrms = sqrt(3kBT/m).
Question 3
In terms of molar mass M and the gas constant R the rms speed is:
- Asqrt(3RT/M)
- Bsqrt(RT/3M)
- Csqrt(3M/RT)
- Dsqrt(RT/M)
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Answer: A
Using kB = R/NA and M = mNA the expression becomes sqrt(3RT/M).
Question 4
In terms of pressure P and density ρ the rms speed is:
- Asqrt(Pρ/3)
- Bsqrt(P/3ρ)
- Csqrt(3ρ/P)
- Dsqrt(3P/ρ)
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Answer: D
From P = (1/3)ρ<v^2> we get vrms = sqrt(3P/ρ).
Question 5
An ideal gas has density 4.5 kg m^-3 at pressure 9.3 × 10^5 Pa and temperature 504 K. Its rms speed is about:
- A787 m s^-1
- B249 m s^-1
- C62 m s^-1
- D3150 m s^-1
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Answer: A
<v^2> = 3P/ρ = 6.2 × 10^5 m^2 s^-2 so vrms = 787 m s^-1.
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