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(B) The root mean square speed $(v_{rms})$ of an ideal gas is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$.From this relation, we can see th

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$2 v$

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(B) The root mean square speed $(v_{rms})$ of an ideal gas is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$.From this relation, we can see that $v_{rms} \propto \sqrt{T}$.Let $v_1$ be the speed at temperature $T_1 = 120 \,K$ and $v_2$ be the speed at temperature $T_2 = 480 \,K$.Given $v_1 = v$.Using the proportionality, we have: $\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}}$.Substituting the values: $\frac{v_2}{v} = \sqrt{\frac{480}{120}}$.$\frac{v_2}{v} = \sqrt{4} = 2$.Therefore, $v_2 = 2v$.

The temperature of an ideal gas is increased from $120 \,K$ to $480 \,K$. If at $120 \,K$, the root mean square speed of gas molecules is $v$, then at $480 \,K$ it will be

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