Q: Find the speed of sound in a mixture of 1 mol of helium and 2 mol of oxygen at 27°C.

Sol: $\large \gamma_{mix} = \frac{C_{P_{mix}}}{C_{V_{mix}}} $

$\large = \frac{19R/6}{13R/6} = \frac{19}{13}$

$\large M_{mix} = \frac{n_1 M_1 + n_2 M_2}{n_1 + n_2} $

$\large M_{mix} = \frac{1 \times 4 + 2 \times 32 }{1 + 2} $

$\large = \frac{68}{3} \times 10^{-3} kg/mol $

$\large v = \sqrt{\frac{\gamma_{mix}R T}{M_{mix}}}$

$\large v = \sqrt{\frac{19}{13}\times \frac{8.314 \times 300}{68 \times 10^{-3}/3}}$

≈ 401 m/s