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). If the old partitiion is replaced by a new partition which can slide and conduct heat but dows NOT allow the gas to leak across (Figure2) , the volume ( in `m^(3))` of the compartment A after the system attains equilibrium is `"________________"`

A closed tank has two compartments A and B, both filled with oxygen (a

1.	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). If the old partitiion is replaced by a new partition which can slide and conduct heat but dows NOT allow the gas to leak across (Figure2) , the volume ( in `m^(3))` of the compartment A after the system attains equilibrium is `"________________"`
Answer» Correct Answer - 2.22 `P_(1) = 5` `P_(2)=1` `v_(1)=1` `v_(2)=3` ` T_(1) = 400` `T_(2)= 300` `n_(1)= (5)/(400R) ` `n_(2)=(3)/(300R)` Let volume be `(v+x) v= (3-x) 15-5x= 4+4x` `(P_(A))/(T_(A))=(P_(B))/(T_(B))` `implies (n_(b_(1))xxR)/(v_(b_(1)))=(n_(b_(2))xxR)/(v_(b_(2)))` `implies (5)/(400(4+x))=(3)/(300R(3-x))` `implies 5(3-x) = 4+4x` `implies x= (11)/(9)` `v= 1+x=1+(11)/(9) = ((20)/(9))=2.22`

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