Question

at a given temperature the ratio of RMS and average velocities is?

Answer 1

Root-mean-square speed is the measure of the speed of particles in a gas which is most convenient for problem solving within the kinetic theory of gases. It is defined as the square root of the average velocity-squared of the molecules in a gas. 

Sol. 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

R.M.S velocity=
$\sqrt{ \frac{3rt}{m} }$
Average velocity
$\sqrt{ \frac{8rt}{\pi \times m} }$
Dividing both equations
we get
$\frac{rms}{average} = \sqrt{ \frac{24}{\pi} }$
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