Question

The ratio of root mean spuare velocity to average velocity of a gas molecule at a particular temperature is

Answer 1

. The two types of speeds are defined as; Root mean square speed (urms) = √(3RT/M) Average speed (uavg) = √(8RT/πM) For the same gas, at a given temperature, M and T are same, therefore u_rms/u_avg = √(3RT/M) ∶ √(8RT/πM) = √3 ∶ √(8/π )= √3 ∶ √2.54=1.085∶1

Answer 2

HELLO THERE!

From the concept of gaseous state, we know that:

Average velocity of a gas =

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

Root mean Square velocity of a gas =

$\sqrt{\frac{3RT}{M}}$

Now, the question asks for the ratio between them for a particular temperature, T. So T is same for both the velocities.

Hence,

$\frac{V_{rms}}{V_{avg}} = \frac{\sqrt{\frac{3RT}{M}}}{\sqrt{\frac{8RT}{\pi M}}}$

$= \frac{3\pi}{8}$

= 1.178

THANKS!