A closed vessel contains 0.1 mole of a monatomic ideal gas at 200 K. If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be close to ___________ .

Assuming  Q=0,  W=0We have      Δ U=0         ⇒   n1CV1Tf−T1+n2CV2Tf−T2=0⇒   n1CV1Tf−T1=-n2CV2Tf−T2=0⇒   n1Tf−T1=-n2Tf−T2∵For same gasCV1=CV2 ⇒   n1Tf-  n1T1=-n2Tf+n2T2⇒   n1Tf+n2Tf=  n1T1+n2T2⇒    Tf=n1T1+n2T2n1+n2        =0.1200+0.054000.1+0.05=20+200.15          =266.6666 K