簡答或推導題 (5 分)
Find \( \left(\frac{\partial U}{\partial V}\right)_{T} \) for a gas with the state equation of \( (p+a)V = nRT \), where \( a \) is a constant with the unit of pressure. (Hint: \( dU = TdS - pdV, dA = -SdT - pdV \) )
Find \( \left(\frac{\partial U}{\partial V}\right)_{T} \) for a gas with the state equation of \( (p+a)V = nRT \), where \( a \) is a constant with the unit of pressure. (Hint: \( dU = TdS - pdV, dA = -SdT - pdV \) )