If 7 gm N₂ is mixed with 20 gm Ar, then Cₚ/Cᵥ of the mixture will be

Correct option is C. 17/11
For N₂, f = 5
For Ar, f = 3
For N₂, Cᵥ = 5/2R, Cₚ = 7/2R, moles = 7/28 = 1/4
Ar, Cᵥ = 3/2R, Cₚ = 5/2R, moles = 20/40 = 1/2
Cₚₘᵢₓ = (n₁Cₚ₁ + n₂Cₚ₂)/(n₁ + n₂) = (1/4 × 7/2R + 1/2 × 5/2R)/(1/4 + 1/2) = (7R/8 + 5R/4)/(3/4) = (17R/8)/(3/4) = 17R/6
Cᵥₘᵢₓ = (n₁Cᵥ₁ + n₂Cᵥ₂)/(n₁ + n₂) = (1/4 × 5/2R + 1/2 × 3/2R)/(1/4 + 1/2) = (5R/8 + 3R/4)/(3/4) = (11R/8)/(3/4) = 11R/6
γₘᵢₓ = Cₚₘᵢₓ/Cᵥₘᵢₓ = (17R/6)/(11R/6) = 17/11.