Thermodynamics

Statement I: Work is a path function.
True.
Work depends on the path taken between initial and final states, not just on the states themselves. Hence, work is a path function.
Statement II: Enthalpy is an extensive property.
True.
Enthalpy (H) depends on the amount of substance. If the system size doubles, enthalpy doubles. So it is an extensive property.
Statement III: Lattice enthalpy of ionic compounds can be obtained from BornHaber cycle.
True.
The Born-Haber cycle uses Hess's law to calculate lattice enthalpy indirectly from measurable thermodynamic quantities.
Correct statements: II and III are correct, and actually, I is also correct.
Wait, let's double-check statement I :
Work is NOT a state function (true), but it is a path function - the statement says "Work is a path function" - That is correct.
Therefore all three I, II, and III are correct.
Final Answer: Option D - I, II and III