Molecular velocities of two gases at the same temperature are $U_{1}$ and $U_{2}$ and their molecular 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 C $m_{1} U_{1}^{2} = m_{2} U_{2}^{2}$
$m_{1}$ , $m_{2}$ are the molecular masses.
$U_{1}$ , $U_{2}$ are the molecular velocities.
$K_{t r a n s l a t i o n a l a v e r a g e} = \frac{1}{2} m {(v^{2})}_{a v e r a g e} = \frac{3}{2} k_{B} T$
where $k_{B}$ = Boltzmann's constant, m = mass of gas molecule, T = temperature, v = molecular velocity.
For same temperature, $m_{1} U_{1}^{2} = m_{2} U_{2}^{2}$ is valid equation.

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