Adabatic work is a state function

The statement "Adabatic work is a state function" is not correct.

Work, in general, is not a state function, but a path function. This means that it depends on the path taken to reach the final state from the initial state.

In the case of adiabatic work, it is the work done in a system where no heat is exchanged with the surroundings. The work done in an adiabatic process depends on the specific process and cannot be determined solely by the initial and final states of the system. Therefore, adiabatic work is not a state function.