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The velocity of sound in hydrogen at `0^@C` is `1200(m)/(s)`. When some amount of oxygen is mixed with hydrogen, the velocity decreases to `500(m)/(s)`. Determine the ratio of `H_2` to `O_2` by volume in this mixture, given that the density of oxygen in 16 times that of hydrogen. |
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Answer» Given that `1200=sqrt((gammaP)/(rho_H))` ..(i) ltbr. Let there be x volume of `H_2` and y volume of `O_2` then, `(x+y)rho_(mix)=xrho_h+yrho_0=xrho_H+16yrho_H` `impliesrho_(mix)=((x+16y))/(x+y)rho_H` `500=sqrt((gammaP(x+y))/((x+16y)rho_H))` ..(ii) Dividing Eq. (ii) by Eq. (i) `(12)/(5)=sqrt((x+16y)/(x+y))` or `(x)/(y)=(2.2)/(1)` |
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