Question

The rms velocity of gas molecules of a given amount of a gas at ${27}^{\circ }\text{C}$ and $1.0\times {10}^5{\text{N m}}^{-2}$ pressure is $200{\text{m sec}}^{-1}$. If temperature and pressure are respectively ${127}^{\circ }\text{C}$ and $0.5\times {10}^5{\text{N m}}^{-2}$, the rms velocity will be:

• A. $\frac{400}{\sqrt{3}}{\text{ms}}^{-1}$
• B. $100\sqrt{2}{\text{ms}}^{-1}$
• C. $100\frac{\sqrt{2}}{3}{\text{ms}}^{-1}$
• D. $50\sqrt{\frac{2}{3}}{\text{ms}}^{-1}$

Answer 1

The correct option is A $\frac{400}{\sqrt{3}}{\text{ms}}^{-1}$

$v_{rms}\propto \sqrt{T}$ (Does not depend on pressure)
$\frac{v_{rm{s}_1}}{v_{rm{s}_2}}=\sqrt{\frac{T_1}{T_2}}\Rightarrow \frac{200}{v_{rm{s}_2}}=\sqrt{\frac{300}{400}}$
$v_{rm{s}_2}=\frac{400}{\sqrt{3}}\text{m/s}$