Question

The velocity of sound in hydrogen at $0^o$c is $1200$ m/s. When some amount fo oxygen is mixed with hydrogen, the velocity decreases to $500$ m/s. Determine the ratio of $H_2$ and $O_2$ by volume in the mixture, given that the density of the oxygen is $6$ times that of hydrogen.

Answer 1

Since we know that

$V=\sqrt{\frac{\gamma P}{{\rho }_H}}$

$\therefore 1200=\sqrt{\frac{\gamma P}{{\rho }_H}}$..$\left(1\right)$

Let there be x volume of $H_2$ and y volume of $O_2$

Then $(x+y){\rho }_{mix}=x{\rho }_H+y{\rho }_0=x{\rho }_H+16y{\rho }_H$

$\Rightarrow {\rho }_{mix}=\frac{(x+16y)}{x+y}{\rho }_H;500=\sqrt{\frac{\gamma P(x+y)}{(x+16y){\rho }_H}}$ ..$\left(2\right)$

Dividing $\left(1\right)$ and $\left(2\right)$,

$\frac{12}{5}=\sqrt{\frac{x+16y}{x+y}}$

or $\frac{x}{y}=\frac{2.2}{1}$.