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The Kelvin Scale

At what tempe...

Question

At what temperature is the average velocity of $O_{2}$ molecule equal to the root mean square velocity at $27^{\circ} C$ ?

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Solution

$u_{avg} = u_{rms}$
$\sqrt{\frac{8 R T_{1}}{π M}} = \sqrt{\frac{3 R T_{2}}{M}}$
$\frac{8 R T_{1}}{π M} = \frac{3 R \times 300}{M}$
$T_{1} = 353.57 K$
Therefore, $T_{1} = {80.57}^{\circ} C$

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