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 ${\gamma }_{\text{m}}=\frac{\text{12}}{8}=\frac{\text{24}}{\text{16}}$