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)/(11)`
D. `(17)/(27)`

Answer

C

Explanation

Helium is a mono atomic gas and oxygen is diatomic gas.
`C_(P)= of O_(2)= (7)/(2) R, C_(P) "of helium"= (5)/(2)R ,n_(1) "of oxygen"=2`
`C_(V) of O_(2)= (5)/(2)R , C_(V) "of helium"= (3)/(2)R, n_(2) "of oxygen"=0.5`
`gamma_("mix")= (n_(1)C_(P_(1))+ n_(2)C_(P_(2)))/(n_(1)C_(V_(1))+ n_(2)C_(V_(2)))= (2 xx (5)/(2)R+ (1)/(2) xx (7)/(2) R)/(2 xx(3)/(2)R+ (1)/(2) xx (5)(2)R)= (27)/(17)`