Heat capacities of a gas mixture

You will find $C_v$, $C_p$ and $\gamma$ of any mixture of ideal gases.

The idea. One gas: $C_v = \tfrac{f}{2}R$ and $\gamma = 1 + \tfrac{2}{f}$. A mixture: $C_v$ is the average of the values of $C_v$, weighted by the moles. Then $C_p = C_v + R$ and $\gamma = C_p/C_v$.

Your tasks.

1. In cv_gas, return $C_v$ of one gas from its $f$, in J/(mol K).
2. In cv_mixture, the list parts holds pairs (moles, f). Return $C_v$ of the mixture.
3. In gamma_mixture, return $\gamma$ of the mixture.