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Cube-Root of Fractional Numbers

At what tempe...

Question

At what temperature 1 atm of $H_{2}$ and $O_{2}$ (NTP) $U_{r m s}$ is equal?

37 K

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17 K

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512 K

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27 K

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Solution

The correct option is C 17 K
$U_{r m s} H_{2} = \sqrt{\frac{3 R T_{1}}{2}}$
$U_{r m s} O_{2} = \sqrt{\frac{3 R T_{2}}{32}}$
$\Rightarrow \frac{T_{1}}{2} = \frac{T_{2}}{32}$ $(T_{2} = 273 K)$
$\Rightarrow T_{1} = \frac{2 \times 273}{32} = 17 K$

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