Calculate the velocity of sound in a mixture of two gases obtained by mixing `m_(1)` and `m_(2)` of them if the velocity of sound in them be `C_(1)` and `C_(2)`. The atomicity of the two gases is the same.

Options

A. `c=sqrt((m_(1)c_(1)^(2)+m_(2)c_(2)^(2))/(m_(1)+m_(2)))`
B. `c=sqrt((m_(2)c_(1)^(2)+m_(1)c_(2)^(2))/(m_(1)+m_(2)))`
C. `c=sqrt((m_(2)c_(2)+m_(1)c_(2))/(m_(1)+m_(2)))`
D. `c=m_(2)sqrt((c_(2)^(2)+c_(1)^(2))/(m_(1)+m_(2)))`

Answer

A

Explanation

Total no. of moles in mixture is `n=n_(1)+n_(2)`
`(m_(1)+m_(2))/(M_(mix))=(m_(1))/(M_(1))+(m_(2))/(M_(2))`
Here velocity of sound `C=sqrt((gammaP)/(rho))=sqrt((gammaRT)/(M))`
`impliesM prop (1)/(c^(2))implies M=(K)/(c^(2))`