Question

$1$ mole of a gas with $\gamma =\frac{7}{5}$ is mixed with $1$ mole of a gas $\gamma =\frac{5}{3}$ , then the value of $\gamma $ for the resulting mixture is

• A. $\frac{7}{5}$
• B. $\frac{2}{5}$
• C. $\frac{24}{16}$
• D. $\frac{12}{7}$

Answer 1

Answer: (C)

For mixture of gases
$\frac{n_{1} + n_{2}}{\gamma _{\text{m}} - 1} = \frac{n_{1}}{\gamma _{1} - 1} + \frac{n_{2}}{\gamma _{2} - 1}$
$\frac{1 + 1}{\left(\gamma \right)_{\text{m}} - 1} = \frac{1}{\left(\frac{7}{5} - 1\right)} + \frac{1}{\left(\frac{5}{3} - 1\right)}$
$\frac{2}{\gamma _{\text{m}} - 1} = \frac{5}{2} + \frac{3}{2}$
or $\frac{2}{\gamma _{\text{m}} - 1} = \frac{8}{2}$
or $8 \gamma _{\text{m}} - 8 = 4$
or $8 \gamma _{\text{m}} = \text{12}$
or $\gamma _{\text{m}} = \frac{\text{12}}{8} = \frac{\text{24}}{\text{16}}$