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Question

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 .

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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=3−x

1+x3−x=5400R3300R

4(1+x)=5(3-x)

4x+5x=11⇒x=119

Hence volume of container A will be

VA=1+119=209=2.22

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=3−x

1+x3−x=5400R3300R

4(1+x)=5(3-x)

4x+5x=11⇒x=119

Hence volume of container A will be

VA=1+119=209=2.22

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