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

After we changed the partition to movable and conducting, pressure and temperature on both sides will be equal.
Hence `(n_(A))/(V_(A)) = (n_(B))/(V_(B))`.... (A)
Let after sliding volume of chamber A = V
Then volume of chamber `B= 4-V`
From initial conditions we can estimate `n_(A) and n_(B)`
`n_(A) = (p_(A)V_(A))/(RT_(A)) n_(B) = (p_(B) V_(B))/(RT_(B))`
`(n_(A))/(n_(B)) = (p_(A))/(p_(B)) xx (V_(A))/(V_(B)) xx (T_(B))/(T_(A)) = ((5))/((1)) xx ((1))/((3)) xx ((300))/((400)) = (5)/(4)`
`(n_(A))/(n_(B)) = (5)/(4)`
Using equation : `(V_(A))/(V_(B)) = (n_(A))/(n_(B))`
`(V)/(4-V) = (5)/(4) rArr V = (20)/(9) = 2.22 m^(3)`