First slide

Kinetic theory of ideal gases

Question

At what temperature is the rms velocity of hydrogen molecule equal to that of an oxygen molecule at 47^o C?

Moderate

A

10 K
B

20 K
C

30 K
D

40 K

Solution

$v_{rms} = \sqrt{\frac{3 RT}{M}}$
Now, rms velocity of H₂ molecule = rms velocity of O₂ molecule
$\begin{array}{l} \sqrt{\frac{3 R \times T}{2}} = \sqrt{\frac{3 R \times (47 + 273)}{32}} \\ T = \frac{2 \times 320}{32} = 20 K \end{array}$

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