Question

If a gas contains 5 molecules with a velocity of 2 m/s, 10 molecules with a velocity of 3 m/s and 5 molecules with a velocity of 6 m/s.

(a) Calculate rms velocity (m/sec).
(b What average speeds (m/sec)?

• A. (a) $3.8m/s$ (b) $3.5m/s$
• B. (a) $3.5m/s$ (b) $3.8m/s$
• C. (a) $7.2m/s$ (b) $7.0m/s$
• D. None of these

Answer 1

The correct option is A (a) $3.8m/s$ (b) $3.5m/s$

The rms velocity is :

$u=\sqrt{\frac{u_1^2+u_2^2+....u_n^2}{n}}=\sqrt{\frac{5\times (2{)}^2+10\times (3{)}^2+5\times (6{)}^2}{20}}=3.8m/s$

The average velocity is :

$v=\frac{v_1+v_2+....+v_n}{n}=\frac{5\times 2+10\times 3+5\times 6}{20}=3.5m/s$