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Question

A gas is expanded from volume V0 to 2V0 under three different processes. Process 1 is isobaric process, Process 2 is isothermal and process 3 is adiabatic. Let ΔU1,ΔU2 and ΔU3 be the changed in internal energy of the gas in these three processes. Then
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A
ΔU1>ΔU2>ΔU3
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B
ΔU1<ΔU2<ΔU3
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C
ΔU2<ΔU1<ΔU3
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D
ΔU2<ΔU3<ΔU1
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Solution

The correct option is C ΔU1>ΔU2>ΔU3
For process (1): Isobaric

ΔW=PΔV

PV=nRT

PΔV=nRΔT

ΔT=ΔWnR

ΔU=nR(r1)

ΔT=nRr1.ΔWnR

U1=ΔTr1

For process (2): Isothermal: ΔT=0

δU=0

For process (3): Adiabatic: ΔQ=0

ΔW=ΔU

U3=ΔW

nRr1ΔT=ΔW

ΔT=ΔW(r1)nR

So,

U1>U2>U3

Hence, the answer is ΔU1>ΔU2>ΔU3

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