A gaseous mixture is prepared by mixing n moles of a monatomic gas and 2n moles of a rigid diatomic gas. The ratio of specific heats at constant pressure to that at constant volume for this mixture is:

Step-by-step solution

For a monatomic gas, the number of degrees of freedom is f₁ = 3 . For a rigid diatomic gas, the number of degrees of freedom is f₂ = 5 . The effective number of degrees of freedom for a mixture of n₁ moles of gas 1 and n₂ moles of gas 2 is given by: f_ mix = n₁ f₁ + n₂ f₂ n₁ + n₂ Substituting the given values ( n₁ = n and n₂ = 2n ): f_ mix = n(3) + 2n(5) n + 2n = 3n + 10n 3n = 13 3 The ratio of specific heats for the mixture _ mix is: _ mix = 1 + 2 f_ mix = 1 + 2 ( 13 3 ) = 1 + 6 13 = 19 13 Answer: 19 13