Question

If the velocities of molecules of gas are -2,3,4,1,-6(m/s) respectively then find the root mean square velocities ​

Answer 1

Therefore the root mean square velocity is 3.633 m/s.

Given : the velocities of molecules of gas are -2, 3, 4, 1 , - 6 ( in m/s) respectively.

To find : The root mean square velocity.

solution : if v₁ , v₂ , v₃ , v₄ .... are velocities.

then, root mean square velocity is given by,

v = $\sqrt{\frac{v_1^2+v_2+v_3^2+v_4^2+.....}{n}}$

where n is number of observations.

here -2, 3 , 4 , 1 , -6 are velocities of molecules of gas respectively.

number of observations, n = 5

so, root mean square velocity = $\sqrt{\frac{(-2)^2+(3)^2+(4)^2+(1)^2+(-6)^2}{5}}$

= $\sqrt{\frac{4+9+16+1+36}{5}}$

= $\sqrt{\frac{66}{5}}$

= 3.633 m/s

Therefore the root mean square velocity is 3.633 m/s .