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Question

In a thermally isolated system, two boxes filled with an ideal gas are connected by a valve. When the valve is in closed position, states of the box 1 and 2, respectively, are (1 atm, V.T) and 0.5 atm, 4V. T). When the valve is opened, the final pressure of the system is approximately

A
0.5atm
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B
0.6atm
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C
0.75atm
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D
1.0atm
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Solution

The correct option is C 0.6atm
After opening of at equilibrium temperature and pressure of whole gas be T1,P1
n1=1×VRT
n2=0.5×V×4RT
n1+n2=n
VRT+V×42RT=5VP1RT1
P1T1=0.6T
No heat exchange and no work is done (since molecules do not push anything against which it moves)
ΔQ=0,ΔW=0
δU=0
n1CvT+n2CvT=(n1+n2)CvT1
T1=T
Hence , P1T1=0.6T
P1=0.6atm

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