Question

One mole of ideal monatomic gas $\bigg(\gamma = \dfrac{5}{3} \bigg)$ is mixed with one mole of diatomic gas $\bigg(\gamma = \dfrac{7}{5}\bigg)$. What is $\gamma$ for the mixture ?​

Answer 1

Answer:

$n_1=1$

$\gamma_1 = \frac{5}{3}$

$n_2=1$

$\gamma_2 = \frac{7}{5}$

$\frac{nR}{r - 1} = constant$

$\frac{n_2+n_1}{\gamma-1 } = \frac{n_1}{\gamma_1-1}+\frac{n_2}{\gamma_2-1 }$

$\frac{2}{\gamma-1 }=\frac{3}{5-3}+\frac{5}{7-5 }$

$= \frac{3}{2} + \frac{5}{2}$

$\frac{2}{\gamma-1 }=\frac{5 + 3}{2} = \frac{8}{2} = 4$

$\gamma-1= \frac{2}{4} = \frac{1}{2}$

$\gamma = 1 + \frac{1}{2} = \frac{3}{2}$

$\gamma = \frac{3}{2}$

hope it helps ✔︎✔️.