If one mole of a mono-atomic gas `(gamma=5//3)` is mixed with one mole of a diatomic gas `(gamma=7//5)`, the value of `gamma` for the mixture is :

Options

A. `1.40`
B. `1.50`
C. `1.53`
D. `3.07`

Answer

B

Explanation

`gamma_1 = 5//3` means gas is monatomic or `C_(V_(1)) = 3/2 R`
`gamma_2 = 7 //5` means gas is diatomic or `C_(V_(2)) = 5//2R`
`C_V` (of the mixture) `= (n_1 C_(V_(1))+ n_2 C_(V_(2)))/(n_1 + n_2) = ((1)(3/2 R)+(1)(5/2)R)/(1+1) = 2R`
`C_p` (of the mixture) `= C_V + R = 3R " "gamma_("mixture") = C_p/C_V = (3R)/(2R) = 1/5`