Question

The root mean square velocity of the molecule of a gas is 184.2 m/s. The average velocity is​

Answer 1

RMS velocity = 184.2 m/s

$\mu_a_v=\sqrt{\frac{8RT}{\pi M} }$

$\mu_R_M_S = \sqrt[]{\frac{3RT}{M} }$

Take the ratio of the root mean square velocity and the average velocity of a molecule will be:

0.9215

Now, multiply

You will get: 0.9215 x 184.2 = 169.7403 m/s

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Answer 2

Given:

$u_{RMS} = 184.2m/s^{2}$

To Find:

The average velocity i.e. $u_{av}$

Solution:

$\mu_{av} =\sqrt{\frac{8RT}{\pi M} } \\\\\mu_{RMS}=\sqrt{\frac{3RT}{M} }$

Taking the ratio we get,

$\frac{\mu_{av}}{\mu_{RMS}} =\sqrt{\frac{8}{3 \pi} } \\\frac{\mu_{av}}{184.2} = \sqrt{\frac{8}{3\pi} } \\\mu_{av} =169.7403 m/s$

Hence the average velocity of the gas would be 169.74 m/s.

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