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Equipartition Theorem

Calculate the...

Question

Calculate the ratio of average velocity of helium atom at $27^{o} C$ and methane molecule at $127^{o} C$ .

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Solution

We know,
$U_{a v g} = \sqrt{\frac{8 R T}{π M}}$
So,
$\frac{U_{a v g} (H e)}{U_{a v g} (C H_{4})} = \sqrt{\frac{T_{H e} \times M_{C H_{4}}}{T_{C H_{4}} \times M_{H e}}}$
$M_{H e} = 4$ , $M_{C H_{4}} = 16$
Hence,
$\frac{U_{a v g} (H e)}{U_{a v g} (C H_{4})} = \sqrt{3}$

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