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(A) The root mean square speed $(u_{rms})$ is directly proportional to the square root of the absolute temperature $(T)$: $u_{rms} = \sqrt{\frac{3RT}{

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get doubled

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(A) The root mean square speed $(u_{rms})$ is directly proportional to the square root of the absolute temperature $(T)$: $u_{rms} = \sqrt{\frac{3RT}{M}}$ For the same gas,$u_{rms} \propto \sqrt{T}$. Initial temperature $T_{1} = 30 + 273 = 303 \ K$. Final temperature $T_{2} = 930 + 273 = 1203 \ K$. Taking the ratio: $\frac{u_{2}}{u_{1}} = \sqrt{\frac{T_{2}}{T_{1}}} = \sqrt{\frac{1203}{303}} = \sqrt{3.97} \approx \sqrt{4} = 2$. Therefore,$u_{2} = 2u_{1}$. Thus,the root mean square speed of the gas gets doubled.

When the temperature of a gas is increased from $30^{\circ} C$ to $930^{\circ} C$,the root mean square speed of the gas would

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