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The root mean square speed of molecules of a given mass of a gas at 27°C and 1 atmosphere pressure is 200 m s⁻¹. The root mean square speed of molecules of the gas at 127°C and 2 atmosphere pressure is x/√3 m s⁻¹. The value of x will be _____.
- 200
- 300
- 400
- 500
Correct answer: 400
Solution
rms speed depends only on temperature: v2/v1 = sqrt(T2/T1) = sqrt(400/300) = 2/sqrt3. So v2 = 200 x 2/sqrt3 = 400/sqrt3 m/s. Thus x = 400 (pressure has no effect).
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