If one mole of a monoatomic 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 monoatomic or
`C_(v_(1)) = 3/2 R`
`gamma_(2) = 7/5` means gas is diatomic or
`C_(v_(2)) = 5/2 R`
`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 he mixture) `= C_(v) + R = 3R`
`:. gamma_("mixture") = (C_(p))/(C_(v)) = (3R)/(2R) = 1.5`