Question

For a given gas at 1 atm pressure, rms speed of the molecules is 200 m/s at ${127}^{\circ }C.$ At 2 atm pressure and at ${227}^{\circ }C$, the rms speed of the molecules will be:

• A. $100\sqrt{5}m/s$
• B. $80m/s$
• C. $80\sqrt{5}m/s$
• D. $100m/s$

Answer 1

The correct option is A $100\sqrt{5}m/s$

$V_{rms}=\sqrt{\frac{3RT}{M}}$
$T_1={127}^{\circ }C=400K$
$T_2={227}^{\circ }C=500K$
$\therefore \frac{V_{rms1}}{V_{rms2}}=\sqrt{\frac{T_1}{T_2}}$
$\Rightarrow \frac{200}{V_{rms2}}=\sqrt{\frac{400}{500}}$
$V_{rms2}=100\sqrt{5}m/s$.