Consider two ideal gases that share the same value of C_p / C_V = . If these two gases are mixed in a 1 : 2 ratio, what will be the value of this ratio for the resulting mixture?

Step-by-step solution

For an ideal gas, the molar heat capacities at constant volume and constant pressure are related to by C_V = R - 1 and C_P = R - 1 . Since both gases have the same value of , their molar heat capacities are equal, i.e., C_ V1 = C_ V2 = C_V and C_ P1 = C_ P2 = C_P . For a mixture of two gases with number of moles n₁ and n₂ , the equivalent heat capacities are given by: C_ V_ mix = n₁ C_ V1 + n₂ C_ V2 n₁ + n₂ = (n₁ + n₂) C_V n₁ + n₂ = C_V C_ P_ mix = n₁ C_ P1 + n₂ C_ P2 n₁ + n₂ = (n₁ + n₂) C_P n₁ + n₂ = C_P The ratio