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Equipartition Theorem

A mixture of ...

Question

A mixture of $n_{1}$ moles of a monoatomic gas and $n_{2}$ moles of a diatomic gas has $\frac{C_{p}}{C_{v}} = γ = 1.5$ . Then,

n_{1} = 2 n_{2}

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2 n_{1} = n_{2}

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n_{1} = n_{2}

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2 n_{1} = 3 n_{2}

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Solution

The correct option is C $n_{1} = n_{2}$
$\frac{C_{P}}{C_{V}} = 1.5$
Also $C_{P} = C_{V} + R$
$⟹ C_{V} = 2 R = \frac{f_{m i x}}{2} R$
$⟹ f_{m i x} = 4$

$⟹ \frac{3 n_{1} + 5 n_{2}}{n_{1} + n_{2}} = 4$
$⟹ n_{1} = n_{2}$

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