# 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 $227^{\circ}C,$ then rms speed of the molecules will be : Option 1) $100\: m/s$ Option 2)  $80\sqrt{5}\; m/s$ Option 3) $100\sqrt{5}\; m/s$ Option 4) $80\: m/s$

$V_{rms}=\sqrt{\frac{3RT}{M}}$

$\frac{V_{1}}{V_{2}}=\sqrt{\frac{T_{1}}{T_{2}}}$

$\frac{200}{V_{2}}=\sqrt{\frac{400}{500}}$

$V_{2}=200\sqrt{\frac{5}{4}}$

$V_{2}=100\sqrt{5}\; m/s$

Option 1)

$100\: m/s$

Option 2)

$80\sqrt{5}\; m/s$

Option 3)

$100\sqrt{5}\; m/s$

Option 4)

$80\: m/s$

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