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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



Solution

As in fig 2, the system attains equilibrium, so,
PA=PB and TA=TB
PAVAnATAR=PBVBnBTBR
VAVB=nAnB
nA=5400R
nB=3300R
Due to sliding of piston vol. of A will be increased by x and that of B will be decreased by x.
VA=1+x
VB=3x
1+x3x=5400R3300R
4(1+x)=5(3-x)
4x+5x=11x=119
Hence volume of container A will be
VA=1+119=209=2.22

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