Question

The molar mass of a certain gas $B$ is double than that of $A$. Also the RMS velocity of gas $A$ is $200{\text{ms}}^{-1}$ at a certain temperature. RMS velocity of gas $B$ at the temperature half of the temperature of $A$ is:

• A. $200{\text{ms}}^{-1}$
• B. $300{\text{ms}}^{-1}$
• C. $400{\text{ms}}^{-1}$
• D. $100{\text{ms}}^{-1}$

Answer 1

The correct option is D $100{\text{ms}}^{-1}$

$u_{\text{rms}}=\sqrt{\frac{3RT}{M}}$

$u_A=\sqrt{\frac{3RT}{M_A}}$ at temperature $T$,

$u_B=\sqrt{\frac{3R\left(T/2\right)}{M_B}}$ at temperature $\left(T/2\right)$

$\frac{u_B}{u_A}=\sqrt{\frac{M_A}{2M_B}}=\sqrt{\frac{M_A}{4M_A}}=\sqrt{\frac{1}{4}}=\frac{1}{2}$
(as $M_B=2M_A$)
$\therefore u_B=\frac{u_A}{2}=100{\text{ms}}^{-1}$