Question

Find the speed of sound in a mixture of 1 mole of $He$ and 2 mole of $O_2$ at ${27}^{\circ }C.$

• A. $480m{s}^{-1}$
• B. $621m{s}^{-1}$
• C. $401m{s}^{-1}$
• D. $601m{s}^{-1}$

Answer 1

The correct option is C $401m{s}^{-1}$

$M_{Mix}=\frac{n_1{M}_1+n_2{M}_2}{n_1+n_2}$
$=\frac{1\times 4+2\times 32}{1+2}=\frac{68}{3}$
$C_{V\left(mixture\right)}=\frac{n_1{C}_{V1}+n_2{C}_{V2}}{n_1+n_2}=\frac{(1\times \frac{3}{2}+2\times \frac{5}{2})R}{1+2}$
$=\frac{13}{6}R$
$C_{P\left(mix\right)}=C_v+R=\frac{19}{6}R$ or $\frac{C_p}{C_v}=\frac{19}{13}R$
$v=\sqrt{\frac{19}{13}\times \frac{8.31\times 300}{\frac{68}{3}\times {10}^{-3}}}=400.9m{s}^{-1}$