Question

The ratio of the root mean square speed of $H_2$ gas at $50\text{K}$ and that of $O_2$ gas at $800\text{K}$ is:

• A. 4
• B. 2
• C. 1
• D. 0.25

Answer 1

The correct option is C 1

$u\left(H_2\right)$ at $50\text{K}=\sqrt{\frac{3R\times 50}{2}}$
$u\left(O_2\right)$ at $800\text{K}=\sqrt{\frac{3R\times 800}{32}}$
$\frac{u\left(H_2\right)}{u\left(O_2\right)}=\sqrt{\frac{50\times 32}{2\times 800}}=1$
$\therefore$ ratio of rms of $H_2\left(50\text{K}\right)\text{and}{O}_2\left(800\text{K}\right)$
$\frac{u\left(H_2\text{at}50\text{K}\right)}{u\left(O_2\text{at}800\text{K}\right)}=1$