Step 1: Analyze each statement. Statement I: True.
Work depends on the path taken and not just the initial and final states, so it is a path function.
Statement II: True.
Enthalpy is proportional to the amount of substance, hence it is an extensive property.
Statement III: True.
Lattice enthalpy can be determined using the Born–Haber cycle by applying Hess's law.
Conclusion: All three statements are correct.