A closed tank has two compartments A and B, both filled with oxygen (assumed$$ to be ideal $$gas).The partition separating the two compartments is fixed and is a perfect heat insulator (Figure$$ $$1). If the old partition is replaced by a new partition which can slide and conduct heat but does NOT allow the gas to leak across (Figure$$ $$2), the volume (in$$ $$m3) of the compartment A after the system attains equilibrium is $$______$$.

Question

A closed tank has two compartments A and B, both filled with oxygen (assumed$$ to be ideal $$gas).The partition separating the two compartments is fixed and is a perfect heat insulator (Figure$$ $$1). If the old partition is replaced by a new partition which can slide and conduct heat but does NOT allow the gas to leak across (Figure$$ $$2), the volume (in$$ $$m3) of the compartment A after the system attains equilibrium  is $$______$$.

Infinity Learn · Accepted Answer

$$P1=5$$                $$P2=1v1=1$$                   $$v2=3T1=400$$             $$T2=300n1=5400R$$        $$n2=3300RLet$$ volume $$be(v+x)$$                      $$v=(3-x)$$                           $$15-5x=4+4xPATA=PBTB$$⇒nb×$$Rvb1=nb2$$×$$Rvb2$$⇒$$5400(4+x)=3300R(3$$−$$x)$$⇒$$5(3$$−$$x)=4+4x$$⇒$$x=119v=1+x=1+119=209=2.22$$

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