If the absolute temperature of a sample of gas in a fixed volume container is quadrupled, then the root mean square speed in the initial state $U_{i}$ and that in the final state $U_{f}$ would be related as :

$u_{f} = \frac{u_{i}}{4}$

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$u_{f} = \frac{u_{i}}{2}$

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$u_{f} = 2 u_{i}$

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$u_{f} = 4 u_{i}$

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Solution

The correct option is C
$u_{f} = 2 u_{i}$

$u_{i} \propto \sqrt{T_{1}} (T_{2} = 4 T_{1})$

$\frac{u_{i}}{u_{f}} = \sqrt{\frac{T_{1}}{T_{2}}} = \sqrt{\frac{T_{1}}{4 T_{1}}} = \frac{1}{2}$

$u_{f} \propto 2 u_{i}$

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If the absolute temperature of a sample of gas in a fixed volume container is quadrupled, then the root mean square speed in the initial state Ui and that in the final state Uf would be related as :

The correct option is C uf=2ui ui∝√T1 (T2=4T1) uiuf=√T1T2=√T14T1=12 uf∝2ui

If the absolute temperature of a sample of gas in a fixed volume container is quadrupled, then the root mean square speed in the initial state $U_{i}$ and that in the final state $U_{f}$ would be related as :

The correct option is C
$u_{f} = 2 u_{i}$

$u_{i} \propto \sqrt{T_{1}} (T_{2} = 4 T_{1})$

$\frac{u_{i}}{u_{f}} = \sqrt{\frac{T_{1}}{T_{2}}} = \sqrt{\frac{T_{1}}{4 T_{1}}} = \frac{1}{2}$

$u_{f} \propto 2 u_{i}$