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 `m^(3)`) of the compartment A after the system attains equilibrium is ____.

Answer

2.22

Explanation

`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`