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Q.
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?
Kinetic Theory
Solution:
For a monatomic gas like helium $\gamma_{He} = \frac{5}{3}$
For a diatomic gas like oxygen $\gamma_{O_2} = \frac{7}{5}$
$\therefore \quad\gamma_{mix} = \frac{3 \,\times\,\gamma _{O_2} + 2\,\times\, \gamma _{He}}{\left(3 \,+ \, 2\right)}$
$= \frac{3\,\times\, \frac{7}{5}+2\,\times\, \frac{5}{3}}{5} = \frac{\frac{21}{5} + \frac{10}{3}}{5} = \frac{113}{15\,\times\,5} = 1.5$