Question

In a container two gases $He$ and $O_2$ are mixed with $1$ mole of each gas. The average value of $\frac{C_p}{C_v}$ for the mixture will be

• A. $1.5$
• B. $2.5$
• C. $3.5$
• D. $4.5$

Answer 1

The correct option is A $1.5$

For $He$, $C_V=\frac{R}{\gamma -1}=\frac{3R}{2}$,
$C_P=C_V+R=\frac{5R}{2}$

For $O_2,C_V=\frac{R}{\frac{7}{5}-1}=\frac{5R}{2}$

$C_P=\frac{7R}{2}$

When gases are mixed effective heat capacity ratio is
${\gamma }_{eff}=\frac{n_1{C}_{p1}+n_2{C}_{p2}}{n_1{C}_{v1}+n_2{C}_{v2}}$

As $n_1=n_2=1$

${\gamma }_{eff}=\frac{C_{p1}+C_{p2}}{C_{v1}+C_{v2}}$

${\gamma }_{eff}=\frac{\frac{7R}{2}+\frac{5R}{2}}{\frac{5R}{2}+\frac{3R}{2}}=\frac{12R}{8R}=1.5$