A massless piston divides a closed, thermally insulated cylinder into two equal parts. One part contains m=28 gram of nitrogen at temperature T0. At this temperature one- third of molecules are dissociated into atoms and the other part is evacuated. The piston is released and the gas fills the whole volume of the cylinder. Then the piston is slowly displaced back to its initial position. The increase in internal energy of the gas is: (Neglect further dissociation of molecules during motion of the piston)

Molar mass of N2= M=28 g mol-1  Number of moles of N2,n0=mM=2828=1 mol Since,  One-third molecules are dissociated into atoms.   N2 →2N ∴ No. of moles of diatomic N2=23mol and  No. of moles of monatomic nitrogen =2×13=23 mol CV mix=n1Cv1+n2Cv2n1+n2=2332R+2352R23+23=2R ∴CP mix=CV mix+R=2R+R=3R ∴γmix=CP mixCV mix=1.5 Now,  Piston is diaplaced back to its initial position, and during the adiabatic  compression, volume of the gas mixture is halved.  ∴T1V1γ-1=T2V2γ-1 ⇒T0V0γ-1=T2V02γ-1 ⇒T2=T02 Change in Internal energy= ΔU=n1+n2CVT2-T0=23+23×2RT02-T0=83RT0(2-1)