The root mean square (rms) velocity of an ide | vedclass

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(C) The root mean square (rms) velocity of an ideal gas is given by the formula:$v_{	ext{rms}} = \sqrt{\frac{3RT}{M}}$From this expression, we can se

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$2 v$

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(C) The root mean square (rms) velocity of an ideal gas is given by the formula:$v_{	ext{rms}} = \sqrt{\frac{3RT}{M}}$From this expression, we can see that the rms velocity is directly proportional to the square root of the absolute temperature:$v_{	ext{rms}} \propto \sqrt{T}$Let $v_1 = v$ at temperature $T_1 = T$.When the temperature is increased to $T_2 = 4T$, let the new rms velocity be $v_2$.Using the proportionality $v_{	ext{rms}} \propto \sqrt{T}$, we have:$\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}}$$\frac{v_2}{v} = \sqrt{\frac{4T}{T}}$$\frac{v_2}{v} = \sqrt{4} = 2$$v_2 = 2v$Therefore, the new rms velocity is $2v$.

The root mean square (rms) velocity of an ideal gas at temperature $T$ is $v$. If the temperature is increased to $4 T$, the rms velocity of the gas is

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