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Question: The average speed v and r.m.s. speed \(\bar{v}\) of the molecules are related as...

The average speed v and r.m.s. speed vˉ\bar{v} of the molecules are related as

A

vˉ=0.92v\bar{v} = 0.92v

B

vˉ2=0.29v2{\bar{v}}^{2} = 0.29v^{2}

C

vˉ=v\bar{v} = v

D

C=0.92CˉC = 0.92\bar{C}

Answer

C=0.92CˉC = 0.92\bar{C}

Explanation

Solution

vrms=3RTMv_{rms} = \sqrt{\frac{3RT}{M}} and vav=8RTπMv_{av} = \sqrt{\frac{8RT}{\pi M}}

Žvav=83πvrmsv_{av} = \sqrt{\frac{8}{3\pi}}v_{rms}Žv=0.92vˉv = 0.92\bar{v}