Helium and oxygen gases are contained in two identical vessels at temperatures  T0  and  respectively. Their respective pressures are P0 and  4P0. They are  connected  by a thin pipe and are allowed to diffuse without any loss of energy. The equilibrium  pressure of the gaseous mixture is  69P013N. Find N.

Let  n1 and n2  be the number of moles of Helium and oxygen gases respectively, and  v0  be volume of each vessel.  Then from equation of staten1=P0V0RT0  and  n2=4P0V0R2T0=2P0V0RT0⇒n2=2n1 If T is the final temperature, then the initial total internal energy (kinetic) of the two  gases must be equal to that of the final mixture.Ui=n13RT02+n25R2T02Uf=n13RT2+n25RT2Ui=Uf gives T=T03n1+10n23n1+5n2=T03n1+20n13n1+10n1=2313T0 The final pressure P will be given byP2V0=n1+n2RT⇒P=n1+n2RT2V0=3n1RT2V0⇒P=3R2V0n1T=3R2V0P0V0RT02313T0=6926P0