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Question

For the case of an ideal gas, find the equation of the process in which the molar heat capacity varies as C=Cv+αT2, where α is constant. Take V0 to be the initial volume of the gas.

A
V=V0eαT22R
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B
V=V0e2αTR
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C
V=V0eαT2R
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D
V=V0eT2αR
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Solution

The correct option is A V=V0eαT22R
C=Cv+αT2(i)
Also, we know that
C=Cv+Pn(dVdT)(ii)
Comparing (i) and (ii)
αT2=Pn(dVdT)
αT/2=/nR/TV/n(dVdT) {PV=nRT}
αT=RV(dVdT)
Integrating on both sides,
dVV=αRT dT
lnV=(αR)T22+constant
For T=0,V=V0
ln(VV0)=(αR)T22
V=V0eαT22R

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