Question

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

Answer 1

Correct Answer - C
(c) If `n_1` moles of adiabatic exponent `gamma_1` is mixed with `n_2` moles of adiabatic exponent `gamma_2` then the adiabatic component of the resulting mixture is given by
`(n_1+n_2)/(gamma-1)=(n_1)/(gamma_1-1)+(n_2)/(gamma_2-1)`
`(1+1)/(gamma-1)=1/(7/5-1)+1/(5/3-1) :. 2/(gamma-1)=5/2+3/2=4`
`:. 2=4gamma-4 rArr gamma=6/4=3/2`