A mixture contains 16 g helium (molar mass 4 g/mol) and 16 g oxygen (molar mass 32 g/mol). Find γ = Cₚ/Cᵥ for the mixture (approximately).
Physics · Mixed Chapter
JEE Main Practice

Question

A mixture contains 16 g helium (molar mass 4 g/mol) and 16 g oxygen (molar mass 32 g/mol). Find γ = Cₚ/Cᵥ for the mixture (approximately).

G1 Physics · Accepted Answer

Step 1: nHe = 16/4 = 4 mol and nO₂ = 16/32 = 0.5 mol. Step 2: At ordinary temperature He is monatomic: Cᵥ = 3R/2, Cₚ = 5R/2. O₂ is diatomic: Cᵥ = 5R/2, Cₚ = 7R/2. Step 3: Total Cᵥ = 4(3R/2) + 0.5(5R/2) = 7.25R. Step 4: Total Cₚ = 4(5R/2) + 0.5(7R/2) = 11.75R. Thus γ = 11.75/7.25 ≈ 1.62.