If one mole of a monatomic gas `(gamma=5/3)` is mixed with one mole of a diatomic gas `(gamma=7/5),` the value of gamma for mixture is

Options

A. 1.5
B. 1.54
C. 1.4
D. 1.45

Answer

A

Explanation

For monatomic gas `C_(V)=3//2`R and for diatomic gas `C_(V)=5//2`R. since one mole of each gas is mixed together, the `C_(V)'` of the mixture will be
`C_(V)'=(1)/(2)[(3)/(2)R+(5)/(2)R]=2R`
`C_(p)'=C_(V)'+R=2R+R=3R`
`gamma_(mix)=(C_(p)')/(C_(V)')=(3R)/(2R)=1.5`