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Question:

A closed tank has two compartments A and B, both filled with oxygen (assumed to be an 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:

P1=5P2=1
V1=1
V2=3
Vt=V1+V2=1+3=4
T1=400K
T2=300K
n1=5400R
n2=3300R
Let volume V1(new)=x
V2(new)=(4−x)
PATA=PBTB
→n1×RV1(new)=n2×RV2(new)
→5400(x)=3300(4−x)
→5(4−x)=4x
V1(new)=209=2.22.