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The molar heat capacities of a mixture of two gases at constant volume is 13R/6. The ratio of number of moles of the first gas to the second is 1: 2. The respective gases may be

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O₂and N₂

He and Ne

He and N₂

N₂and He

answer is C.

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Detailed Solution

(3) ${C_{v}}_{m i x} = \frac{n_{1} C_{v 1} + n_{2} C_{v 2}}{n_{1} + n_{2}} \Rightarrow \frac{13 R}{6} = \frac{n_{1} C_{v 1} + 2 n_{1} C_{v 2}}{n_{1} + 2 n_{1}} [∵ \frac{n_{1}}{n_{2}} = \frac{1}{2}] \Rightarrow \frac{13 R}{2} = C_{v 1} + 2 C_{v 2}$

Possible values are, $C_{v 1} = \frac{3 R}{2}, C_{v 2} = \frac{5 R}{2}$

∴ Gases are monatomic (like He) and diatomic (like N₂)

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