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  4. A fixed mass of gas at constant pressure occupies a volume V. The gas undergoes a rise in temperature so that the root mean square velocity of molecules is doubled. The new volume will be

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Q. A fixed mass of gas at constant pressure occupies a volume $V$. The gas undergoes a rise in temperature so that the root mean square velocity of molecules is doubled. The new volume will be

Haryana PMTHaryana PMT 2002Kinetic Theory

Solution:

Using $c = \sqrt{T}$ , we get, $\frac{c_2}{c_1} = \sqrt{\frac{T_2}{T_1}}$
Then $\frac{2c}{c} = \sqrt{\frac{T_2}{T}}$ $i.e.$ 4 = $\frac{T_2}{T}$
$i.e. $ $T_2$ = 4T
Since V $\propto$ T, so new volume is four times.