Since we are taking an adibatic process, so from the first law of thermodynamics,
ΔU=W
⇒nCv(T2−T1)=−Pext(V2−V1)
Since it is a triatomic non linear system, hence
⇒nCv(T2−T1)=Pext(V2−V1) ⇒n3R(T2−300)=−2(nRT22−nR3001)
⇒3T2−900=−T2+600
⇒T2=375 K
We know, ΔH=nCpΔT=5×4×2(375−300)=3000 cal=3 kcal