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

Explanation

`C_(V)=(n_(1)c_(1)+n_(2)c_(2))/(n_(1)+n_(2))=(c_(1)+c_(2))/(2)" as "n_(1)=n_(2)`
`C_(P)=C_(V)+R`
`therefore gamma=(C_(P))/(C_(V))=1+(R)/(C_(V))`
where `C_(V)=((3R//2)+(5R//2))/(2)=2R`
`therefore gamma=1+(R)/(2R)=1+(1)/(2)=1.5`