Five gas molecules chosen at random are found to have speed of 500, 600, 700, 800 and 900 m/s. Find the rms speed. Is it the same as the average speed ?

Open in App

Solution

RMS speed will be

$v_{r m s} = \sqrt{\frac{V_{1}^{2} + V_{2}^{2} + V_{3}^{2} + V_{4}^{2} + V_{5}^{2}}{5}} = \sqrt{\frac{500^{2} + 600^{2} + 700^{2} + 800^{2} + 900^{2}}{5}} = 100 \sqrt{\frac{25 + 36 + 49 + 64 + 81}{5}} = 714 m / s$

Also, average velocity is

$v_{a v} = \frac{V_{1} + V_{2} + V_{3} + V_{4} + V_{5}}{5} = \frac{500 + 600 + 700 + 800 + 900}{5} = 700 m / s$

Answer is $714 m / s$ and $700 m / s$

Suggest Corrections

Similar questions

500 m/s, 600 m/s, 700 m/s, 800 m/s

900 m/s

500, 600, 700, 800

900 m/s

v_{1} = \sqrt{\frac{x_{1} R T}{M}}

v_{2} = \sqrt{\frac{x_{2} R T}{M}}

v_{3} = \sqrt{\frac{x_{3} R T}{M}}

v_{4} = \sqrt{\frac{x_{4} R T}{M}}

300

6.21 \times 10^{- 21}

484

600

Join BYJU'S Learning Program