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 ____.

Explanation

Number of moles of `O_(2)` in each compartment can be calculated as,
`n_(A) = (PV)/(RT) = (5 xx 1)/(R xx 400) = (5)/(400 R)`
`n_(B) = (PV)/(RT) = (1 xx 3)/(R xx 300) = (1)/(100 R)`
In new condition of thermal equilibrium:
`T_(A) = T_(B)`
`V_(A) = (1 + x) , V_(B) = (3 - x)`
`P_(A) = P_(B)`
`T_(A) = T_(B)`
`(P_(A) V_(A))/(n_(A)R) = (P_(B) V_(B))/(n_(B)R)`
`((1 + x))/((5)/(400R)xx R) = ((3 - x))/((1)/(100R) xx R)`
`4 (1 + x) = 5 (3 - x)`
`9x = 11`
`x = (11)/(9)`
Volume of compartment `(A) = 1 + x`
`= 1 + (11)/(9) = (20)/(9) = 2.22 m^(3)`