Question

Two ideal monoatomic and diatomic gases are mixed with one another to form an ideal gas mixture. The equation of the adiabatic process of the mixture is $PV^{\gamma }=$ constant, where $\gamma =\frac{11}{7}$ If $n_{1}$ and $n_{2}$ are the number of moles of the monoatomic and diatomic gases in the mixture respectively, find the ratio $\frac{n_{1}}{n_{2}}$

Answer 1

$\gamma _{m i x}=\frac{n_{1} C p_{1} + n_{2} C p_{2}}{n_{1} C v_{1} + n_{2} C v_{2}}$
$\frac{11}{7}=\frac{n_{1} \left(\frac{5}{2} R\right) + n_{2} \left(\frac{7}{2} R\right)}{n_{1} \left(\frac{3}{2} R\right) + n_{2} \left(\frac{5}{2} R\right)}$
$\frac{n_{1}}{n_{2}}=3$