At what temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at 47°C ?

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Solution

Q.
At what temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at 47°C [2024]

1 80 K

2 – 73 K

3 4 K

4 20 K

Ans.
(4)

   $V_{r m s} = \sqrt{\frac{3 R T}{M}} \Rightarrow {(V_{r m s})}_{H_{2}} = {(V_{r m s})}_{O_{2}}$

$\Rightarrow \frac{T_{1}}{M_{1}} = \frac{T_{2}}{M_{2}}$

   $\Rightarrow T_{1} = \frac{M_{1}}{M_{2}} T_{2} = \frac{2}{32} (273 + 47)$

   $= \frac{2}{32} \times 320 = 20 K$

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