Question

Calculate the value of `gamma` for a gaseous mixture consisting of `n_(1)` moles of oxygen and `n_(2)` moles of carbon of carbon dioxide. The values of `gamma` for oxygen and carbon dioxide are `gamma_(1) and gamma_(2)` respectively. Assume the gases to be ideal.
[Hint: `U_(m) = U_(1) + U_(2) and U = (nRT)/(gamma-1)`]

Answer 1

`U_(m) = U_(1) + U_(2)`
`U_(1) = (n_(1)RT)/(r_(1) - 1) U_(2) = (n_(2)RT)/(r_(2)) - 1`
`U_(m) = (n_(1) +n_(2)RT)/(r_(mix) - 1)`
`(n_(1) + n_(2)RT)/(r_(mix) - 1) = (n_(1)RT)/(r_(1) -1) + (n_(2)RT)/(r_(2) - 1)`
`(n_(1) + n_(2))/(r_(mix) - 1) = (n_(1)(r_(2) - 1))/(r_(1)-1) + (n_(2)(r_(1)-1)/(r_(2)-1)`
`(n_(1)+n_(2))(r_(1)-1)(r_(2)-1)/(n_(1)(r_(2)-1) + (n_(2)r_(2)-1) + r_(mix)`
`r_(mix) = (r_(1)r_(2)n_(1) +n_(2)) -n_(1)r_(1) +n_(2)r_(2))/(n_(1)r_(2)-1)+n_(2)r_(2)-1)`