The molecular velocities of two gases at same temperature are $u_{1}$ and $u_{2}$ , their molar masses are $m_{1}$ and $m_{2}$ respectively. Which of the following expression is correct?

$\frac{m_{1}}{u_{1}^{2}} = \frac{m_{2}}{u_{2}^{2}}$

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$m_{1} u_{1} = m_{2} u_{2}$

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$\frac{m_{1}}{u_{1}} = \frac{m_{2}}{u_{2}}$

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$m_{1} u_{1}^{2} = m_{2} u_{2}^{2}$

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Solution

The correct option is D
$m_{1} u_{1}^{2} = m_{2} u_{2}^{2}$

If molecular velocities are root mean square type at temperature $T$ then

$u_{1} = \sqrt{\frac{3 R T}{m_{1}}}$

$u_{2} = \sqrt{\frac{3 R T}{m_{2}}}$

$\frac{u_{1}^{2}}{u_{2}^{2}} = \frac{m_{1}}{m_{2}}$

$m_{1} u_{1}^{2} = m_{2} u_{2}^{2}$

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