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Q.

For a gas at a temperature T the root mean square velocity v_rms, the most probable speed v_mp, and the average speed v_av obey the relationship

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a

$ν_{av} > ν_{rms} > ν_{mp}$

b

$ν_{rms} > ν_{av} > ν_{mp}$

c

$ν_{mp} > ν_{av} > ν_{rms}$

d

$ν_{mp} > ν_{rms} > ν_{av}$

answer is B.

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Detailed Solution

$V_{av} = \sqrt{\frac{8 KT}{πm}}, V_{rms} = \sqrt{\frac{3 KT}{m}}, V_{mp} = \sqrt{\frac{2 KT}{m}}$

$∴ V_{rms} > V_{av} > V_{mp}$

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For a gas at a temperature T the root mean square velocity vrms, the most probable speed vmp, and the average speed vav obey the relationship