Kinetic theory of ideal gases

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Question

The molecules of a given mass of gas have rms speed 200 m s^-1 at 27 °C and 10⁵ N m^-2 pressure. When the absolute temperature is doubled and the pressure is halved, then rms speed (in m s^-1) of the molecules of the same gas is _______.

Moderate

Solution

$v_{rms} = \sqrt{\frac{3 RT}{m}} \Rightarrow \frac{v_{{rms}_{2}}}{v_{{rms}_{1}}} = \sqrt{\frac{T_{2}}{T_{1}}} = \sqrt{\frac{2 \times 300}{300}}$
$∴ v_{{rms}_{2}} = v_{{rms}_{1}} \sqrt{2} = 200 \sqrt{2} {ms}^{- 1} = 282 .8 {ms}^{- 1}$

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