Three moles of oxygen are mixed with 2, moles of helium. What will be ratio of specific heats at con

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12.Kinetic Theory of Gases

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Three moles of oxygen are mixed with $2\, moles$ of helium. What will be the ratio of specific heats at constant pressure and constant volume for the mixture ?

A

$2.5$

B

$3.5$

C

$1.5$

D

$1$

Solution

For a monatomic gas like helium $\gamma_{H e}=\frac{5}{3}$

For a diatomic gas like oxygen $\gamma O_{2}=\frac{7}{5}$

$\therefore \gamma_{\operatorname{mix}}=\frac{3 \times \gamma_{O_{2}}+2 \times \gamma_{H e}}{(3+2)}$

$=\frac{3 \times \frac{7}{5}+2 \times \frac{5}{3}}{5}=\frac{\frac{21}{5}+\frac{10}{3}}{5}=\frac{113}{15 \times 5}=1.5$

Standard 11

Physics

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