Question

The average velocity of an ideal gas molecule at ${27}^{o}C$ is $0.3m/s$. The average velocity at ${927}^{o}C$ will be:

• A. $0.6m/s$
• B. $0.3m/s$
• C. $0.9m/s$
• D. $3.0m/s$

Answer 1

The correct option is A $0.6m/s$

The average velocity of a gas is given by the expression $u_{avg}=\sqrt{\frac{8RT}{\pi M}}$.
The expression for the average velocity of a gas at two different temperatures is $\frac{u_{avg}\left(T_1\right)}{u_{avg}\left(T_2\right)}=\sqrt{\frac{T_1}{T_2}}=\sqrt{\frac{300}{1200}}=\frac{1}{2}$
Thus $u_{avg}\left({927}^{o}C\right)=2\times u_{avg}\left({27}^{o}C\right)=0.6m{s}^{-1}$.