A gaseous mixture consists of 16g of helium and 16 g of oxygen. The ratio `(C_p)/(C_v)` of the mixture is

Options

A. `1.59`
B. `1.62`
C. `1.4`
D. `1.54`

Answer

B

Explanation

`C_(v) =(n_(1)C_(v_(1))+n_(2)C_(v_(2)))/(n_(1)+n_(2))`
For helium, `n_(1) = (16)/(4) = 4` and `gamma_(1) = (5)/(3)`
For oxygen `n_(2) = (16)/(32) = (1)/(6)` and `gamma_(2) = (7)/(5)`
`C_(v_(1)) = (R )/(gamma_(1)-1) = (R )/((5)/(3)-1) -(3)/(2)R`
`C_(v_(2)) = (R )/(gamma_(2)-1) = (R)/((7)/(5)-1)=(5)/(2)`
`:. C_(v) = (4xx(3)/(2)R+(1)/(2),(5)/(2)R)/(4+(1)/(2)) = (6R+(5)/(4)R)/((9)/(2))`
`= (29 R xx 2)/(9xx4) = (29R)/(18), C_(P) = C_(V) +R`
`rArr (C_(P))/(C_(V)) = (C_(V)+R)/(C_(V)) = 1+(R)/(C_(V))`
`rArr (C_(P))/(C_(V)) = (R)/((29)/(18)R) +1 rArr (C_(P))/(C_(V)) = (18)/(19) +1`
`= (18 +19)/(29) = 1.62`