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  4. At what temperature is the rms velocity of hydrogen molecule equal to that of an oxygen molecule at 47 °C?

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Q. At what temperature is the rms velocity of hydrogen molecule equal to that of an oxygen molecule at $47\,{}^{\circ}C$?

Kinetic Theory

Solution:

$v_{rms} = \sqrt{\frac{3RT}{m}}$
Now, rms velocity of $H_{2}$ molecule = rms velocity of $O_{2}$ molecule
$\sqrt{\frac{3R\times T}{2}}= \sqrt{\frac{3R\times\left(47+273\right)}{32}}$
$T = \frac{2\times320}{32} = 20\,K$