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12.Kinetic Theory of Gases
normal
$1\ mole$ of a gas with $\gamma$ = $7/5$ is mixed with $1\ mole$ of a gas with $\gamma$ = $5/3$, then the value of $\gamma$ for the resulting mixture is
A
$\frac{7}{5}$
B
$\frac{2}{5}$
C
$\frac{24}{16}$
D
$\frac{12}{7}$
Solution
$\frac{n_{1}+n_{2}}{\gamma_{m}-1}=\frac{n_{1}}{\gamma_{1}-1}+\frac{n_{2}}{\gamma_{2}-1}$
$\frac{1+1}{\gamma_{m}-1}=\frac{1}{\left(\frac{7}{5}-1\right)}+\frac{1}{\left(\frac{5}{3}-1\right)}$
$\frac{2}{\gamma_{m}-1}=\frac{5}{2}+\frac{3}{2}$
or $\frac{2}{\gamma_{m}-1}=\frac{8}{2}$
or $\quad 8 y_{m}-8=4$
or $\quad 8 y_{m}=12$
or $\quad \gamma_{m}=\frac{12}{8}=\frac{24}{16}$
Standard 11
Physics
