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3 moles of mono-atomic gas $(\gamma=5 / 3)$ is mixed with 1 mole of a diatomic gas $(\gamma=7 / 3) .$ The value of $\gamma$ for the mixture will be
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The correct answer is:
$\frac{11}{7}$
The number of degrees of ireedom for the mixture is
$\therefore$$\begin{aligned} f_{\text {mix }} &=\frac{n_{1} f_{1}+n_{2} f_{2}}{n_{1}+n_{2}} \\ &=\frac{3 \times 3+1 \times 5}{4}=\frac{7}{2} \\ \gamma &=1+\frac{2}{f} \end{aligned}$
$\Rightarrow \quad \gamma=1+\frac{4}{7}=\frac{11}{7}$
$\therefore$$\begin{aligned} f_{\text {mix }} &=\frac{n_{1} f_{1}+n_{2} f_{2}}{n_{1}+n_{2}} \\ &=\frac{3 \times 3+1 \times 5}{4}=\frac{7}{2} \\ \gamma &=1+\frac{2}{f} \end{aligned}$
$\Rightarrow \quad \gamma=1+\frac{4}{7}=\frac{11}{7}$
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