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(B) The expressions for the different velocities of gas molecules are given by:$V_{rms} = \sqrt{\frac{3RT}{M}} = \sqrt{3} \cdot \sqrt{\frac{RT}{M}} \a

Vedclass · Accepted Answer

$
u_{rms} > 
u_{av} > 
u_{mp}$

Vedclass · Answer

(B) The expressions for the different velocities of gas molecules are given by:$V_{rms} = \sqrt{\frac{3RT}{M}} = \sqrt{3} \cdot \sqrt{\frac{RT}{M}} \approx 1.732 \sqrt{\frac{RT}{M}}$$V_{av} = \sqrt{\frac{8RT}{\pi M}} = \sqrt{\frac{8}{\pi}} \cdot \sqrt{\frac{RT}{M}} \approx 1.596 \sqrt{\frac{RT}{M}}$$V_{mp} = \sqrt{\frac{2RT}{M}} = \sqrt{2} \cdot \sqrt{\frac{RT}{M}} \approx 1.414 \sqrt{\frac{RT}{M}}$Comparing the coefficients,we find that $1.732 > 1.596 > 1.414$.Therefore,the correct relation is $
u_{rms} > 
u_{av} > 
u_{mp}$.

For a given gas at temperature $T$,the root mean square velocity is $\nu_{rms}$,the average velocity is $\nu_{av}$,and the most probable velocity is $\nu_{mp}$. Which of the following relations is correct?

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