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.

Question

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.

Infinity Learn · Accepted Answer

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 $$byP2V0=n1+n2RT$$⇒$$P=n1+n2RT2V0=3n1RT2V0$$⇒$$P=3R2V0n1T=3R2V0P0V0RT02313T0=6926P0$$

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.

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