1 mole of a gas with `gamma=7//5` is mixed with 1 mole of a gas with `gamma=5//3`, then the value of `gamma` for the resulting mixture is

Options

A. `7//5`
B. `2//5`
C. `24//16`
D. `12//7`

Answer

C

Explanation

`(n_(1) + n_(2))/(gamma-1) = (n_(1))/(gamma_(1) - 1) + (n_(2))/(gamma_(2) - 1)`
`implies (1 + 1)/(gamma-1) = (1)/((5//3) - 1) + (1)/((7//5) - 1)`
`implies (2)/(gamma-1) = (3)/(2) + (5)/(2) = 4 implies gamma = (3)/(2) = (24)/(16)`