An ideal-gas mixture has one mole of gas A with γ₁=5/3 and n moles of gas B with γ₂=7/5, at the same temperature. Mixture γ=19/13. Find n.
Physics · Mixed Chapter
JEE Main Practice

Question

An ideal-gas mixture has one mole of gas A with γ₁=5/3 and n moles of gas B with γ₂=7/5, at the same temperature. Mixture γ=19/13. Find n.

G1 Physics · Accepted Answer

Step 1: For each gas, Cᵥ/R=1/(γ−1): A has Cᵥ₁/R=3/2, B has Cᵥ₂/R=5/2. Step 2: Total heat capacities are Cᵥ,total=R(3/2+5n/2), Cₚ,total=Cᵥ,total+(1+n)R. Step 3: γ_mix−1=(1+n)/(3/2+5n/2) = (19/13−1)=6/13. Step 4: 13(1+n)=3(3+5n) ⇒13+13n=9+15n ⇒n=2.