Question

Two ideal gas have the same value of $C_P/C_V=\gamma$. What will be the value of this ratio for a mixture of the two such gases in the ratio 1 : 2?

Answer 1

Let the heat capacities be $C_P$ and $C_V$ for gas 1 and $n{C}_P$ and $n{C}_V$ for gas 2. Thus for the mixture, heat capacities will be

$C_V^{\prime }=\frac{C_V+2n{C}_V}{3}=\frac{1+2n}{3}{C}_V$

Also, $C_P^{\prime }=\frac{C_P+2n{C}_P}{3}=\frac{1+2n}{3}{C}_P$

Thus, for the mixture,

${\gamma }^{\prime }=\frac{{C^{\prime }}_P}{{C^{\prime }}_V}=\frac{C_P}{C_V}=\gamma$

Answer is $\gamma$