Question

The speed of sound in a mixture of 1 mole of helium and 2 moles of oxygen at ${27}^{0}C$ is

• A. 400 $m{s}^{-1}$
• B. 800 $m{s}^{-1}$
• C. 1200 $m{s}^{-1}$
• D. 600 $m{s}^{-1}$

Answer 1

The correct option is A 400 $m{s}^{-1}$

$v=\sqrt{\frac{rRT}{M}}M=\frac{n_1{M}_1+n_2{M}_2}{n_1+n_2}=(1\times 4+2\times 32)/(1+2)=68/3\times {10}^{-3}kg/mol$

For mixture;

$C_v=\frac{n_{1}C{v}_1+n_{2}C{v}_2}{n_1+n_2}$

$C_v$ for helium $=3R/2$

$C_v$ for oxygen $=5R/2$

$C-v(1\times 3R/2+2\times 5R/2)/(1+2)=13R/6C_p=C_v+R=R+13R/6=19R/6$

Now,

$Y_{mix}=C_p/C_v=19/13V_{mix}=0.068/3kg/mol$

Now, speed of sound in mixture $=\sqrt{\frac{\frac{19}{13}\times \frac{25}{3}\times 300}{\frac{68}{3}\times {10}^{-3}}}=400.9m/s$