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For an ideal gas the molar heat capacity...

For an ideal gas the molar heat capacity varies as `C=C_V+3aT^2`. Find the equation of the process in the variables (T,V) where a is a constant.

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The correct Answer is:
A, B, C
`dQ=dU+dW`
`CdT=C_VdT+pdV`
`(C_V+3aT^2)dT=C_VdT+pdV`
`:.` `3aT^2dT=pdV=((RT)/(V))dV`
`:.` `((3a)/(R))TdT=(dV)/(V)`
Integrating, we get
`((3aT^2)/(2R))=InV-InC`
`V=Ce^((3aT^2)/(2R))` or `Ve^(-(3aT^2)/(2R))`=const ant`
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