Question

Gas molecules has RMS speed $200\text{m/s}$ at ${27}^{\circ }\text{C}$ and $1\text{atm}$ pressure. If the RMS speed changes to $\frac{x}{\sqrt{3}}\text{m/s}$ when temperature becomes ${127}^{\circ }\text{C}$ and pressure becomes $2\text{atm}$, then the value of $x$ is

• A. $100$
• B. $200$
• C. $300$
• D. $400$

Answer 1

The correct option is D $400$

We know that, RMS speed is given by,

$v=\sqrt{\frac{3RT}{M}}$

$\Rightarrow 200=\sqrt{\frac{3R\times (27+273)}{M}}$

$\Rightarrow 200=\sqrt{\frac{900R}{M}}$

$\Rightarrow \sqrt{\frac{R}{M}}=\frac{20}{3}.......\left(1\right)$

Also, when temperature becomes ${127}^{\circ }\text{C}\left(400\text{K}\right)$,

$v^{\prime }=\sqrt{\frac{3R\times 400}{M}}$

$\Rightarrow v^{\prime }=20\sqrt{3}\times \frac{20}{3}$ [ from $\left(1\right)$]

$\Rightarrow v^{\prime }=\frac{400}{\sqrt{3}}\text{m/s}=\frac{x}{\sqrt{3}}\text{m/s}$ (Given)

$\Rightarrow x=400$

$\begin{array}{c}\text{Why this question}?\\ \text{Trick - Here the data of pressure is given to confuse}\\ \text{you. We know that the RMS speed}v=\sqrt{\frac{3RT}{M}}\end{array}$