Which of the following statement is false?

Explanation: Functions are of two types:

1. State function: The functions or properties which don't depend upon the path taken but only the initial and final state are called state functions. Some examples are Pressure, Temperature, etc.
2. Path function: The functions or properties which depend on the path taken and change with the change in course are called path functions. Some examples are Work, Heat, etc.

Considering each statement individually,

• Option D is correct because work does appear on the boundaries. This is because work only appears as changed in the state at the boundary of the system.
• Option C is correct because this is the definition of state function.
• Option B is correct since temperature only depends on the initial and the final state.
• Option A, however, is incorrect since work varies with change in path taken and is hence a path function.

Final Answer: Hence, the correct option is A: Work is a state function.