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Question

# An ideal gas has a molar heat capacity at constant volume CV. Find the molar heat capacity of this gas as a function of its volume V, if it undergoes a process T=ToeαV2, where To and α are constants.

A
CV+RαV
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B
CV+αRmV
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C
CV+RαV2
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D
CV+R2αV2
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Solution

## The correct option is D CV+R2αV2Given, T=ToeαV2 Differentiating on both sides with respect to 'T', d(T)dT=ToeαV2×2αVdVdT ⇒1=T(2αVdVdT) .......(1) By using first law of thermodynamics, we can say that, ΔQ=ΔU+ΔW or nCdT=nCVdT+PdV or C=CV+PndVdT .....(2) Using ideal gas equation in (1), we get, 1=(PVnR)2αVdVdT ⇒1=2αV2R(PndVdT) ⇒(PndVdT)=R2αV2 .......(3) Substituting (3) in (2), C=CV+R2αV2 Thus, option (d) is the correct answer.

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