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(D) The root mean square velocity $(U_{rms})$ is given by the formula $U_{rms} = \sqrt{\frac{3RT}{M}}$.Since $U_{rms} \propto \sqrt{T}$,the ratio of v

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Doubled

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(D) The root mean square velocity $(U_{rms})$ is given by the formula $U_{rms} = \sqrt{\frac{3RT}{M}}$.Since $U_{rms} \propto \sqrt{T}$,the ratio of velocities is $\frac{U_2}{U_1} = \sqrt{\frac{T_2}{T_1}}$.Given $T_1 = 27 + 273 = 300 \, K$ and $T_2 = 927 + 273 = 1200 \, K$.Substituting the values: $\frac{U_2}{U_1} = \sqrt{\frac{1200}{300}} = \sqrt{4} = 2$.Therefore,$U_2 = 2 	imes U_1$,which means the velocity is doubled.

The temperature of the gas is raised from $27\,^oC$ to $927\,^oC$. The root mean square velocity is:

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