If one mole of a monoatomic gas `(gamma=7//53)` is mixed with one mole of a diatomic gas `(gamma = 7//5)` the value of `gamma` for the mixture is .

Options

A. `1.4`
B. `1.5`
C. `1.53`
D. `3.07`

Explanation

For monoatomic gas `C_(v) = (3)/(2) Rt , C_(p) = (5)/(2) RT`
For diatomic gas, `C_(V) = (5)/(2)RT, C_(P) = (7)/(2)RT`
Thus for mixture of 1 mole each
`C_(V) = ((3)/(2)RT+(5)/(2)RT)/(2)` and `C_(P) = ((5)/(2)RT+(7)/(2)RT)/(2)`
Therefore `C_(P)//C_(V)= (3RT)/(2RT) =1.5` .