The velocity of sound in hydrogen at STP is `1400ms^(-1)`. Find the velocity of sound in a mixture with 3 parts by volume of oxygen and 2 parts by volume of hydrogen at `819^(@)C`?

Explanation

`V_(H_(2))=sqrt((gammaP)/(rho_(H_(2))))=sqrt((gammaRT)/(M_(H_(2))))`
Let the number of moles of hydrogen in the mixture be 2n. The number of moles of oxygen will then be 3n. The mean molar mass of a mixture is given by
`M_(mix)=(n_(1)M_(1)+n_(2)M_(2))/(n_(1)+n_(2))=(2nMH_(H_(2))+3nM_(O_(2)))/(2n+3n)`
`thereforeM_(mix)=(2M_(H_(2))+3(16M_(H_(2))))/(5)" "(becauseM_(O_(2))=16M_(H_(2)))`
or `M_(mix)=(50M_(H_(2)))/(5)=10M_(H_(2))`
since both these gases are diatomic, `gamma` of the mixture remains unchanged. hence at STP, the speed of sound in this mixture is given by
`v_(mix)=sqrt((gammaRT)/(10M_(H_(2))))=126sqrt(10)m//s" "[becausegamma=(7)/(5),M_(H_(2))=2xx10^(-3)kg]`
When the temperature is raised to `819^(@)C` i.e., 1092 K it becomes 4 times its value at STP. At STP the velocity is `126sqrt(10)`. When the temperature becomes 4 times, the velocity doubles as STP and velocity is `126sqrt(10)`. when the temperature becomes 4 times, the velocity doubles as `vpropsqrt(T)`. hence the velocity of sound in the gas mixture is `252sqrt(10)ms^(-1)`.