A gas is a mixture of two parts by volume of hyprogen and part by volume of nitrogen at `STP`. If the velocity of sound in hydrogen at `0^(@) C` is `1300 m//s` . Find the velocity of sound in the gaseous mixure at `27^(@)C`.

Answer

A

Explanation

Equal volume of different gass contains equal number of modes at `STP`.
`:. n prop V`
`M = (n_(1)M_(1) + n_(2)M_(2))/(n_(1) + n_(2))`
= `((2)(2) + (1)(28))/(2 +1) = 10.67`
`nu = sqrt((gamma RT)/(M))`
`:. (nu_(2))/(nu_(1)) = sqrt((T_(2))/(T_(1)). (M_(1))/(M_(2)))`
or `nu_(2) = (sqrt((T_(2))/(T_(1)). (M_(1))/(M_(2)))) nu_(1)`
= `(sqrt(300/(273) xx (2)/(10.67)))(1300)`
`~~ 591 m//s`