A gaseos mixture consists of equal number of moles of two ideal gases having adiabatic exponents `gamma_(1)` and `gamma_(2)` and molar speific heats at constant volume `C_(v_(1))` and `C_(v_(2))` respectively. Which of the following statements is/are correct?

Options

A. Adiabatic exponent for gaseous mixture is equal to `(gamma_(1)+gamma_(2))/(2)`
B. Molar specific heat at constant volume for gaseous mixture is equal to `(C_(v_(1))+C_(v_(2)))/(2)`
C. Molar specific heat at constant pressure for gaseous mixture is equal to `(C_(v_(1))+C_(v_(2))+R)/(2)`
D. Adiabatic exponent for gaseous mixture is `1 +(2R)/(C_(v_(1))+C_(v_(2)))`

Answer

B, D

Explanation

`C_(v) = (n_(1)C_(v_(1))+n_(2)C_(v_(2)))/(n_(1)+n_(2))`
and `C_(P_(eq)) =C_(V_(eq)) +R, gamma =(C_(P_(eq)))/(C_(V_(eq)))`