Two moles of an ideal gas with $\frac{C_{p}}{C_{V}}=\frac{5}{3}$ are mixed with 3
moles of another ideal gas with $\frac{C_{p}}{C_{V}}=\frac{4}{3}$. The value of $\frac{C_{p}}{C_{V}}$ for the mixture is:
Correct Option: , 4
(4) Using, $\gamma_{\text {mixture }}=\frac{n_{1} C_{p_{1}}+n_{2} C_{p_{2}}}{n_{1} C_{v_{1}}+n_{2} C_{v_{2}}}$
$\Rightarrow \frac{n_{1}}{\gamma_{1}-1}+\frac{n_{2}}{\gamma_{2}-1}=\frac{n_{1}+n_{2}}{\gamma_{m}-1}$
$\Rightarrow \frac{3}{\frac{4}{3}-1}+\frac{2}{\frac{5}{3}-1}=\frac{5}{\gamma_{m}-1}$
$\Rightarrow \frac{9}{1}+\frac{2 \times 3}{2}=\frac{5}{\gamma_{m}-1}$
$\Rightarrow \gamma_{m}-1=\frac{5}{12}$
$\Rightarrow \gamma_{m}=\frac{17}{12}=1.42$
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