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

A, B, C

Explanation

Number of moles of helium `n = 8/4=2`
Number of moles of Oxygen n' `=16/32=1/2`
For monoatomic helium gas f = 3
`C_v=f/2R=3/2R`
For diatomic oxygen gas f = 5
`C_v=f/2R=5/2R`
`C_v=(nCv+n'C'v)/(n+n')`
`=(2xx3/2R+1/2xx5/2R)/(2+1/2)`
`=(3R+5/4R)/(3/2)=(((12+5)/4)R)/(3//2)`
`=(17/4xx2/3)R`
`=17/6R`
`r=C_p/C_v=1+R/C_v`
`=1+(R)/((17//6)R)`
`=1+6/17=23/17`