The rms velocity u_{rms},mean velocity u_{av} | vedclass

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Question

(B) The formulas for the velocities are:$u_{rms} = \sqrt{\frac{3RT}{M}}$$u_{av} = \sqrt{\frac{8RT}{\pi M}}$$u_{mp} = \sqrt{\frac{2RT}{M}}$Calculating

Vedclass · Accepted Answer

$\frac{u_{av}}{u_{mp}} = 1.12$

Vedclass · Answer

(B) The formulas for the velocities are:$u_{rms} = \sqrt{\frac{3RT}{M}}$$u_{av} = \sqrt{\frac{8RT}{\pi M}}$$u_{mp} = \sqrt{\frac{2RT}{M}}$Calculating the ratios:$1$. $\frac{u_{rms}}{u_{av}} = \frac{\sqrt{3}}{\sqrt{8/\pi}} = \sqrt{\frac{3\pi}{8}} \approx 1.085$$2$. $\frac{u_{av}}{u_{mp}} = \frac{\sqrt{8/\pi}}{\sqrt{2}} = \sqrt{\frac{4}{\pi}} \approx 1.128 \approx 1.12$$3$. $\frac{u_{rms}}{u_{mp}} = \frac{\sqrt{3}}{\sqrt{2}} = \sqrt{1.5} \approx 1.225$Comparing these with the given options,the ratio $\frac{u_{av}}{u_{mp}} = 1.12$ is correct.

The rms velocity $u_{rms}$,mean velocity $u_{av}$ and most probable velocity $u_{mp}$ of a gas differ from each other at a given temperature. Which of the following ratios regarding them is correct?

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