Question

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

• A. $0.6\text{m/sec}$
• B. $0.3\text{m/sec}$
• C. $0.9\text{m/sec}$
• D. $3.0\text{m/sec}$

Answer 1

The correct option is A $0.6\text{m/sec}$

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