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Question

# An ideal gas has a molar heat capacity Cv at constant volume. It undergoes a process given by T=T0eαV, where T0 and α are constants. Find the molar heat capacity of the gas as a function of V.

A
CvVRα
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B
Cv+VR
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C
Cv+RαV
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D
CvV2Rα
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Solution

## The correct option is A Cv−VRαGiven, the process equation is - T=T0eαV Differentiating w.r.t T on both sides, dTdT=T0eαV×−αV2(dVdT) =−αV2T(dVdT) =αV2(PVnR)(dVdT) {∵PV=nRT} ⇒1=−αVR(PndVdT) ⇒Pn(dVdT)=(−VRα)……(i) Also, we know that dQ=dU+dW ⇒nCdT=nCvdT+PdV ⇒C=Cv+1n(PdVdT)……(ii) Putting (i) in (ii), C=Cv−VRα

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