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

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$200/\sqrt{3} \ m/s$

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(B) The root mean square speed $(v_{rms})$ of gas molecules is given by the formula:$v_{rms} = \sqrt{\frac{3RT}{M}}$From this relation,it is clear that $v_{rms} \propto \sqrt{T}$.Note that $v_{rms}$ is independent of the pressure of the gas.Given:$T_1 = 27^{\circ} \ C = 27 + 273 = 300 \ K$$T_2 = 127^{\circ} \ C = 127 + 273 = 400 \ K$$(v_{rms})_1 = 100 \ m/s$Using the ratio formula:$\frac{(v_{rms})_1}{(v_{rms})_2} = \sqrt{\frac{T_1}{T_2}}$$\frac{100}{(v_{rms})_2} = \sqrt{\frac{300}{400}} = \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{2}$$(v_{rms})_2 = \frac{100 	imes 2}{\sqrt{3}} = \frac{200}{\sqrt{3}} \ m/s$.

The molecules of a given mass of a gas have root mean square speeds of $100 \ m/s$ at $27^{\circ} \ C$ and $1.00 \ \text{atm}$ pressure. What will be the root mean square speeds of the molecules of the gas at $127^{\circ} \ C$ and $2.0 \ \text{atm}$ pressure?

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