Question

The molecules of a given mass of a gas have a rms velocity of 200 $m/s$ at ${27}^{\circ }C$ at a pressure of $1.0\times {10}^{5}N/m^2$ . When the temperature is ${127}^{\circ }C$ and pressure is $0.5\times {10}^{5}N/m^2$, the rms velocity in $m/s$ will be:

• A. $\frac{400}{\sqrt{3}}$
• B. $100\sqrt{2}$
• C. $\frac{200}{\sqrt{3}}$
• D. None of these

Answer 1

The correct option is A $\frac{400}{\sqrt{3}}$

Change in pressure will not affect the rms velocity of molecules. So will calculate the effect of temperature

$v_{rms}\propto \sqrt{T}$
$\frac{v_{{300}^{\circ }}}{v_{{400}^{\circ }}}=\sqrt{\frac{300}{400}}=\sqrt{\frac{3}{4}}$

$\frac{200}{v_{400}}=\sqrt{\frac{3}{4}}$

$v_{400}=\frac{200\times 2}{\sqrt{3}}=\frac{400}{\sqrt{3}}m/s$