Six molecules of an ideal gas have velocities | vedclass

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(B) The average speed $\overline{V}$ is calculated as the arithmetic mean of the velocities: $\overline{V} = \frac{1 + 3 + 5 + 5 + 6 + 5}{6} = \frac{2

Vedclass · Accepted Answer

$V_{rms} > \overline{V}$

Vedclass · Answer

(B) The average speed $\overline{V}$ is calculated as the arithmetic mean of the velocities: $\overline{V} = \frac{1 + 3 + 5 + 5 + 6 + 5}{6} = \frac{25}{6} \approx 4.16 \,m/s$. The root mean square speed $V_{rms}$ is calculated as the square root of the mean of the squares of the velocities: $V_{rms} = \sqrt{\frac{1^2 + 3^2 + 5^2 + 5^2 + 6^2 + 5^2}{6}} = \sqrt{\frac{1 + 9 + 25 + 25 + 36 + 25}{6}} = \sqrt{\frac{121}{6}} = \frac{11}{\sqrt{6}} \approx 4.49 \,m/s$. Comparing the two values, we find that $4.49 > 4.16$, therefore $V_{rms} > \overline{V}$.

Six molecules of an ideal gas have velocities $1, 3, 5, 5, 6$ and $5 \,m/s$ respectively. At any given temperature, if $\overline{V}$ and $V_{rms}$ represent average and rms speed of the molecules, then

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