Question

One mole of ideal monoatomic gas $(\gamma =\frac{5}{3})$ is mixed with one mole of diatomic gas $(\gamma =\frac{7}{5})$. What is $\gamma$ for the mixture? $\gamma$ denotes the ratio of specific heat at constant pressure, to that at constant volume.

• A. $\frac{3}{2}$
• B. $\frac{23}{15}$
• C. $\frac{35}{23}$
• D. $\frac{4}{3}$

Answer 1

The correct option is A

$\frac{3}{2}$

For a monoatomic gas, $C_v=3\frac{R}{2}$ and for a diatomic gas, $C_v=\frac{5R}{2}$. Since one mole of each gas is mixed together, the $C_v$ of the mixture will
$C_v=\frac{1}{2}[\frac{3R}{2}+\frac{5R}{2}]=2R$
Now $C_p-C_v=R.$ Therefore, for the mixture, $C_p=R+C_v=R+2R=3R.$ Hence, the ratio of the specific heats of the mixture is
$\gamma =\frac{C_p}{C_v}=\frac{3R}{2R}=\frac{3}{2}$,