Three moles of oxygen are mixed with two moles of helium. What will be the ratio of specific heats at constant pressure and constant volume for the mixture?

2.5

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3.5

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1.5

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1

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Solution

The correct option is C $1.5$
For a monatomic gas like helium $γ_{H e} = \frac{5}{3}$
For a diatomic gas like oxygen $γ O_{2} = \frac{7}{5}$
$∴ γ_{m i x} = \frac{3 \times γ_{O_{2}} + 2 \times γ_{H e}}{(3 + 2)}$
$= \frac{3 \times \frac{7}{5} + 2 \times \frac{5}{3}}{5} = \frac{\frac{21}{5} + \frac{10}{3}}{5} = \frac{113}{15 \times 5} = 1.5$

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Three moles of oxygen are mixed with two moles of helium. What will be the ratio of specific heats at constant pressure and constant volume for the mixture?

The correct option is C 1.5For a monatomic gas like helium γHe=53For a diatomic gas like oxygen γO2=75∴γmix=3×γO2+2×γHe(3+2)=3×75+2×535=215+1035=11315×5=1.5