One mole of ideal monoatomic gas (γ=53) is mixed with one mole of diatomic gas (γ=75). What is γ for the mixture? γ denotes the ratio of specific heat at constant pressure, to that at constant volume.
32
For a monoatomic gas, Cv=3R2 and for a diatomic gas, Cv=5R2. Since one mole of each gas is mixed together, the Cv of the mixture will
Cv=12[3R2+5R2]=2R
Now Cp−Cv=R. Therefore, for the mixture, Cp=R+Cv=R+2R=3R. Hence, the ratio of the specific heats of the mixture is
γ=CpCv=3R2R=32,