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Question

Which one among the following is the correct option for right relationship between CP and CV for one mole of ideal gas?

A
CV=RCP
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B
CP+CV=R
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C
CPCV=R
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D
CP=RCV
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Solution

The correct option is C CPCV=R
At constant volume, qV=CVΔT=ΔU
At constant pressure, qP=CPΔT=ΔH
For a mole of an ideal gas,
ΔH=ΔU+Δ(PV)
=ΔU+Δ(RT)
=ΔU+RΔT

On putting the values of ΔH and ΔU, we have CPΔT=CVΔT+RΔT
CP=CV+R
CPCV=R

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