One mole of an ideal monoatomic gas with γ=5/3 is mixed with one mole of an ideal diatomic gas with γ=7/5. Find γ=Cₚ/Cᵥ for the mixture.
Physics · Thermodynamics
JEE Advanced

Question

One mole of an ideal monoatomic gas with γ=5/3 is mixed with one mole of an ideal diatomic gas with γ=7/5. Find γ=Cₚ/Cᵥ for the mixture.

G1 Physics · Accepted Answer

For one mole of the monoatomic gas, Cᵥ=3R/2 and Cₚ=5R/2. For one mole of the rigid diatomic gas, Cᵥ=5R/2 and Cₚ=7R/2. For the mixture, Cᵥ,total=4R and Cₚ,total=6R, so γ=6R/4R=3/2=1.5.