Q. If 2 moles of diatomic gas and 1 mole of monatomic gas are mixed, then the ratio of specific heats for the mixture is

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A

$\frac{7}{3}$

B

$\frac{5}{4}$

C

$\frac{19}{13}$

D

$\frac{15}{19}$

Solution:

$\mu_1=1, \gamma_1=5 / 3$ (for monatomic gas)
and $\mu_2=2, \gamma_2=7 / 5$ (for diatomic gas).
Form formula
$ \gamma_{\text {mixture }}=\frac{\frac{\mu_1 \gamma_1}{\gamma_1-1}+\frac{\mu_2 \gamma_2}{\gamma_2-1}}{\frac{\mu_1}{\gamma_1-1}+\frac{\mu_2}{\gamma_2-1}} $
$ =\frac{\frac{1 \times \frac{5}{3}}{\frac{5}{3}-1}+\frac{2 \times \frac{7}{5}}{\frac{7}{5}-1}}{\frac{1}{\frac{5}{3}-1}+\frac{2}{\frac{7}{5}-1}}=\frac{\frac{5}{3}+7}{\frac{3}{2}+5}=\frac{19}{13}$

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