One mole of ideal monoatomic gas `(gamma=5//3)` is mixed with one mole of diatomic gas `(gamma=7//5)`. What is `gamma` for the mixture? `gamma` Denotes the ratio of specific heat at constant pressure, to that at constant volume

Options

A. `3//2`
B. `2//5`
C. `2//7`
D. `4//7`

Answer

A

Explanation

`gamma` for mixture
`gamma_("mix")=((n_1 gamma_1)/(gamma_1 -1)+(n_2 gamma_2)/(gamma_2-1))/((n_1)/(gamma_1-1)+(n_2)/(gamma_2-1))=(n_1(C_V)_1+n_2(C_V)_2)/((C_V)_1+(C_V)_2)`
`((1xx5/3)/(5/3-1)+(1xx7/5)/(7/5-1))/((1)/((5/3-1))+(1)/((7/5-1))) = 3/2 =1.5`