A gaseous mixture is prepared by mixing a monatomic gas and a rigid diatomic gas. If the mole fraction of the monatomic gas in the mixture is x , the ratio of the mean square speed of the gas molecules to the square of the speed of sound in the mixture is given by

Step-by-step solution

The molar heat capacity at constant volume for a monatomic gas is C_ v1 = 3 2 R and for a rigid diatomic gas is C_ v2 = 5 2 R . Let the total number of moles be 1 . Then the mixture contains x moles of the monatomic gas and (1-x) moles of the diatomic gas. The molar heat capacity at constant volume for the mixture is: C_ v,mix = x ( 3 2 R ) + (1-x) ( 5 2 R ) = 5 - 2x 2 R The molar heat capacity at constant pressure for the mixture is: C_ p,mix = C_ v,mix + R = 7 - 2x 2 R The adiabatic index of the mixture is: _ mix