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Question

Select the incorrect relation. (Where symbols have their usual meanings)

A
Cp=γRγ1
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B
CpCv=R
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C
ΔU=PfVfPiVi1γ
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D
Cv=Rγ1
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Solution

The correct option is C ΔU=PfVfPiVi1γ
Solution:- (C) ΔU=PfVfPiVi1γ
As we know that,
ΔU=nCvΔT
Whereas,
n= No. of moles
Cv= Heat capacity at constant volume =Rγ1
ΔT= Change in temperature =TfTi
ΔU=nRγ1(TfTi)
ΔU=nRTfnRTiγ1.....(1)
Now from ideal gas equation,
PV=nRT
For the same no. of moles of a gas,
nRTf=PfVf
nRTi=PiVi
Substituting these values in eqn(1), we have
ΔU=PfVfPiViγ1
Hence the given option (C)ΔU=PfVfPiVi1γ is incorrect.

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