Question

The molecules of a given mass of gas have an rms velocity of $200 \, m \, s^{- 1}$ at $27 \, ^\circ C$ and pressure $1 \, atm$ . When the temperature is $127 \, ^\circ C$ and pressure is $2 \, atm$ , the rms velocity in $m \, s^{- 1}$ will be?

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

Answer 1

Answer: (C)

RMS velocity doesn't depend upon pressure, it depends upon temperature only,
$ie., \, v_{rms} \propto \sqrt{T}$ .
$\Rightarrow \frac{v_{1}}{v_{2}}=\sqrt{\frac{T_{1}}{T_{2}}} \, \Rightarrow \, \frac{200}{v_{2}}=\sqrt{\frac{\left(\right. 273 + 27 \left.\right)}{\left(\right. 273 + 127 \left.\right)}}=\sqrt{\frac{300}{400}}$
$\Rightarrow \, v_{2}=\frac{400}{\sqrt{3}}ms^{- 1}$