# Ratio of specific heats of mixture of gases

Suppose I have $1$ mole of a monoatomic gas and $1$ mole of a diatomic gas. If I mix them, the ratio of their specific heats at constant pressure to that constant volume becomes:$$\gamma = \frac{3}{2}$$

I came up with this result be averaging $C_p$ and $C_v$ of both the gases over $1+1=2$ moles. My question is why this works? Why averaging out gives the right solution? How will I go about calculating the $\gamma$ of mixture of gases if there are more than $1$ mole in each gaseous system?