One mole of gas having `gamma = 7//5` is mixed with 1 mole of a gas having `gamma = 4//3`. What will be `gamma` for the mixture ?

Options

A. `(15)/(11)`
B. `(5)/(13)`
C. `(5)/(11)`
D. `(15)/(13)`

Answer

A

Explanation

a. For `gamma = (7)/(5), C_(v) = (R )/(gamma -1) = (R )/((7)/(5) - 1) = (5 R)/(2)`
`C_(P) = (gamma R)/(gamma - 1) = ((7//5) R)/((7)/(5) - 1) = (7R)/(2)`
For `gamma = (4)/(3), C_(v) = 3 R, C_(P) = 4R`
`:. gamma_(mix) = ((7)/(2) + 4)/((5)/(2) + 3) = (15)/(11)`