When 1 mole of monoatomic gas is mixed with 2 moles of diatomic gas, then find `C_(P), C_(v), f and gamma` for the mixture of gases.

Options

A. `(7)/(3)`
B. `(5)/(4)`
C. `(19)/(13)`
D. `(15)/(19)`

Answer

C

Explanation

c. `mu_(1) = 1, gamma_(1) = 5//3` (for monatomic gas) and `mu_(2) = 2, gamma_(2) = 7//5` (for diatomic gas).
From formula
`gamma_("mixture")= ((mu_(1) gamma_(1))/(gamma_(1) - 1) + (mu_(2) gamma_(2))/(gamma_(2) -1))/((mu_(1))/(gamma_(1) - 1) +(mu_(2))/(gamma_(2) -1))`
`= ((1 xx (5)/(3))/((5)/(3)-1) + (2 xx (7)/(5))/((7)/(5)-1))/((1)/((5)/(3) - 1) + (2)/((7)/(5) - 1)) = ((5)/(2) + 7)/((3)/(2) + 5) = (19)/(13)`