Question

The average speed of an ideal gaseous molecule at ${27}^{\circ }C$ is $0.3m{s}^{-1}$. The average speed at ${927}^{\circ }C$ would be:

• A. 0.3 ms${}^{-1}$
• B. 0.6 ms${}^{-1}$
• C. 0.9 ms${}^{-1}$
• D. 1.2 ms${}^{-1}$

Answer 1

The correct option is B 0.6 ms${}^{-1}$

$U_{AV}=\sqrt{(\frac{8RT}{\pi m})}$

Given:

$U_{AV}=0.3m/s$ at $300K$

$\therefore U_1=0.3=\sqrt{(\frac{8R\times 300}{\pi m})}$-------(1)

At $T=273+927=1200K$

$\therefore U_2=\sqrt{(\frac{8R\times 1200}{\pi m})}$-------(2)

$\therefore \frac{U_2}{0.3}=\sqrt{(\frac{1200}{300})}$

$\Rightarrow U_2=0.6m/s$

Hence, the correct answer is option B.