If three moles of monoatomic gas (γ = (5)/(3)) is mixed with two...

Given:

$\begin{cases}{f}_{1} = 3, & {f}_{2} = 5 \\ {n}_{1} = 3, & {n}_{2} = 2\end{cases}$

Now, for mixture

${f}_{\text{mixture}} = \dfrac{{n}_{1}{f}_{1} + {n}_{2}{f}_{2}}{{n}_{1} + {n}_{2}} = \dfrac{9 + 10}{5} = \dfrac{19}{5}$

Therefore, ${\gamma}_{\text{mixture}} = 1 + \dfrac{2}{{f}_{\text{mixture}}} = 1 + \dfrac{2 \times 5}{19} = \dfrac{29}{19} = 1 . 52$