For a given gas at 1,atm pressure,the rms spe | vedclass

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(B) The root mean square $(rms)$ speed of gas molecules is given by the formula: $V_{rms} = \sqrt{\frac{3RT}{M_w}}$.From this relation,it is clear tha

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

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(B) The root mean square $(rms)$ speed of gas molecules is given by the formula: $V_{rms} = \sqrt{\frac{3RT}{M_w}}$.From this relation,it is clear that $V_{rms} \propto \sqrt{T}$.Note that the $rms$ speed is independent of pressure.Given: $T_1 = 127\,^oC = 127 + 273 = 400\,K$ and $V_1 = 200\,m/s$.Given: $T_2 = 227\,^oC = 227 + 273 = 500\,K$.Using the proportionality: $\frac{V_2}{V_1} = \sqrt{\frac{T_2}{T_1}}$.$\frac{V_2}{200} = \sqrt{\frac{500}{400}} = \sqrt{\frac{5}{4}} = \frac{\sqrt{5}}{2}$.$V_2 = 200 	imes \frac{\sqrt{5}}{2} = 100\sqrt{5}\,m/s$.

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

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