The ratio `gamma=(C_(P))/(C_(V))` for a gas mixture consisting of 8 g of helium and 16 g of oxygen is

Options

A. `(23)/(15)`
B. `(15)/(23)`
C. `(27)/(17)`
D. `(17)/(27)`

Answer

C

Explanation

Helisum is monoatomic gas and oxygen is diatomic gas
`{:(C_p " of oxygen" =7/2 R),(C_V " of oxygen" = 5/2 R):}:|{:(C_P " of helium" = 5/2 R),(C_V " of helium" = 3/2 R):}:| {:(n_1 "of oxygen "=2),(n_2 " of helium"=0.5):}`
`gamma_(mix)=(n_(1)C_(P_(1))+n_(1)C_(r_(1)))/(n_(1)V_(1)+n_(2)C_(V_(2)))=(2xx(5)/(2)R+(1)/(2)xx(7)/(2)R)/(2xx(3)/(2)R+(1)/(2)xx(5)/(2)R)=(27)/(17)`