Question

Equal volumes of two monoatomic gases, A and B at same temperature and pressure are mixed. The ratio of specific heats $\frac{C_p}{C_v}$ of the mixture will be:

• A. 0.83
• B. 1.5
• C. 3.3
• D. 1.67

Answer 1

The correct option is D 1.67

For a monoatomic gas,
$C_p=\frac{5R}{2}$ and $C_v=\frac{3R}{2}$

now, equal volume of gases at same T and P contain equal number of moles (Avogadro law) so let ${}^{\prime }{n}^{\prime }$ moles of gas A are there so ${}^{\prime }{n}^{\prime }$ moles will be of B.

So, for a mixture of A and B gas :
$C_{mix}$ = $\frac{n_1{C}_1+n_2{C}_1}{n_1+n_2}$
$C_{v_{mix}}$ $=\frac{\frac{n3R}{2}+\frac{n3R}{2}}{n+n}=\frac{3R}{2}$

$C_{p_{mix}}$ = $\frac{\frac{n5R}{2}+\frac{n5R}{2}}{n+n}=\frac{5R}{2}$
${\gamma }_{mix}=\frac{C_{p_{mix}}}{C_{v_{mix}}}$
$\frac{C_{p_{mix}}}{C_{v_{mix}}}=\frac{5}{3}$
$=1.67$