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

Answer

D

Explanation

For mixture of gases, `C_v = (n_1C_(v_1)+n_(2)C_(v_2))/(n_(1)+n_(2))`
where `C = f/2 R , f` is degree of freedom
and `C_p = (n_1C_(P_1)+n_(2)C_(P_2))/(n_(1)+n_(2))`
where `C_(p) = (1+f/2)R`
For helium, `n_(1) = 4, f=3`
For oxygen , `n_(2) = 1/2 , f = 5`
`:. (C_p)/(C_v) = (4xx(5R)/(2)+1/2xx(7R)/(2))/(4xx(3R)/2 + 1/2 xx (5R)/2) = (47)/(29)`
`=1.62`.