The van der Waals equation of state describes the behavior of real gases by incorporating parameters for molecular size and intermolecular forces. To demonstrate that (∂Cv/∂V) at constant temperature equals zero, one must analyze the heat capacity at constant volume, defined as Cv = (∂Q/∂T)v = (∂U/∂T)v. The internal energy U can be expressed using the van der Waals equation, which accounts for the interactions and volume occupied by gas molecules. By applying thermodynamic principles, it can be shown that changes in volume do not affect Cv at constant temperature for gases described by this equation. Understanding these relationships is crucial for accurately modeling gas behavior under various conditions.
