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Question

(C) The average velocity $(v_{av})$ is calculated as the arithmetic mean of the velocities:$v_{av} = \frac{v_{1} + v_{2} + v_{3} + v_{4}}{N} = \frac{1

Vedclass · Accepted Answer

$0.583$

Vedclass · Answer

(C) The average velocity $(v_{av})$ is calculated as the arithmetic mean of the velocities:$v_{av} = \frac{v_{1} + v_{2} + v_{3} + v_{4}}{N} = \frac{1 + 3 + 5 + 7}{4} = \frac{16}{4} = 4 \ km/s$The root mean square $(RMS)$ velocity $(v_{rms})$ is calculated as the square root of the mean of the squares of the velocities:$v_{rms} = \sqrt{\frac{v_{1}^{2} + v_{2}^{2} + v_{3}^{2} + v_{4}^{2}}{N}} = \sqrt{\frac{1^{2} + 3^{2} + 5^{2} + 7^{2}}{4}} = \sqrt{\frac{1 + 9 + 25 + 49}{4}} = \sqrt{\frac{84}{4}} = \sqrt{21} \approx 4.583 \ km/s$The difference between the $RMS$ velocity and the average velocity is:$v_{rms} - v_{av} = 4.583 \ km/s - 4 \ km/s = 0.583 \ km/s$

The velocities of $4$ gas molecules are given by $1 \ km/s, 3 \ km/s, 5 \ km/s$ and $7 \ km/s$. Calculate the difference between the average velocity and the root mean square $(RMS)$ velocity. (in $km/s$)

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