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Equipartition Theorem

A mixture Of ...

Question

A mixture Of $n_{2}$ moles of mono atomic gas and $n_{2}$ moles of diatomic gas has $\frac{C_{p}}{C_{V}} = y = 1.5$

n_{1} = n_{2}

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2 n_{1} = n_{2}

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n_{1} = 2 n_{2}

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2 n_{1} = 3 n_{2}

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Solution

The correct option is A $n_{1} = n_{2}$
$\begin{matrix} A s y_{m i x} = \frac{C_{p_{m i x}}}{C_{v_{m i x}}} w h e r e C_{p_{m i x}} = \frac{n_{1} C_{p_{1}} + n_{2} C_{p_{2}}}{n_{1} + n_{2}} a n d C_{v_{m i x}} = \frac{n_{1} C_{v_{1}} + n_{2} C_{v_{2}}}{n_{1} + n_{2}} S o, y_{m i x} = \frac{n_{1} C_{p_{1}} + n_{2} C_{p_{2}}}{n_{1} + n_{2}} G i v e n, f o r m o n o a t o m i c C_{p}, \frac{5}{2} R a n d C_{v_{1}} = \frac{3}{2} R F o r d i a t o m i c C_{p_{2}} = \frac{7 R}{2} a n d C_{v_{2}} = \frac{5}{2} R y_{m i x} = \frac{n_{1} \times \frac{5}{2} R + n_{2} \times \frac{7}{2} R}{n_{1} \times \frac{3}{2} R + n_{2} \times \frac{5}{2} R} = \frac{5 n_{1} + 7 n_{2}}{3 n_{1} + 5 n_{2}} = \frac{3}{2} 10 n_{1} + 14 n_{2} = 9 n_{1} + 15 n_{2} n_{1} = n_{2} H e n c e, o p t i o n A i s c o r r e c t a n s w e r . \end{matrix}$

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