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(B) The root mean square (rms) speed of gas molecules is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$, where $T$ is the absolute temperature

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becomes $\sqrt{2}$ times

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(B) The root mean square (rms) speed of gas molecules is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$, where $T$ is the absolute temperature in Kelvin.Since $v_{rms} \propto \sqrt{T}$, the ratio of the final rms speed $(v_2)$ to the initial rms speed $(v_1)$ is $\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}}$.Initial temperature $T_1 = 127^{\circ} C = 127 + 273 = 400 \ K$.Final temperature $T_2 = 527^{\circ} C = 527 + 273 = 800 \ K$.Substituting these values into the ratio formula: $\frac{v_2}{v_1} = \sqrt{\frac{800}{400}} = \sqrt{2}$.Therefore, the rms speed becomes $\sqrt{2}$ times the initial speed.

If the temperature of a gas is increased from $127^{\circ} C$ to $527^{\circ} C$, then the rms speed of the gas molecules

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