If one mole of a mono atomic gas  γ=53 , is mixed with one mole of diatomic gas  γ=75,  what is the value of γ  for the mixture.

specific heat of mixture of gases at constant volume is  Cvmixture=n1CV1+n2Cv2n1+n2 Cvmixture=(1)32R+(1)52R2=2RAverage CPmixture= Cvmixture+R ⇒CPmixture=2R+R ⇒CPmixture=3R  ∴for mixture of gases  γ=CPmixture Cvmixture  ⇒γmix=3R2R ⇒γmix=32